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Set Theroy , Relations and Mappings GATE - 1 | 75 Questions | 75 mins | Free Test |
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Complex Numbers GATE - 1 | 75 Questions | 75 mins | Free Test |
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Determinants and Matrices GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Determinants and Matrices GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Quadratic Equations GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Permutations and Combinations GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Mathematical Induction and Its Application GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Binomial Theorem and Its application GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Sequences and Series GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Trigonometry GATE - 1 | 75 Questions | 75 mins | Free Test |
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Coordinate Geometry - I GATE - 1 | 75 Questions | 75 mins | Free Test |
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Coordinate Geometry - II GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Vector Algebra GATE - 1 | 75 Questions | 75 mins | Free Test |
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Three Dimensional Geometry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Statistics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Probability GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Differential Calculus GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Integral Calculus GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Differential Equations GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Functions GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Differentiability and Differentiation GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Application of Derivatives GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Indefinite Integration GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Define Integrals and Its Application GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Cartesian Coordinate System GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Circle GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Conic Sections GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Trigonometric Functions, Identities and Equation GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Inverse Trigonometric Functions GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Properties of Triangles, Height and Distances GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Mathematical Reasoning GATE - 1 | 75 Questions | 75 mins | Free Test |
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Units and measurement GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Units and measurement GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Description of Motion in One Dimension GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Description of Motion in Two and three Dimension GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Description of Motion in Two and three Dimension GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Newton's Laws of Motion GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Work, Energy and Power GATE - 1 | 75 Questions | 75 mins | Free Test |
Work, Energy and Power GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Rotational Motion and Moment of Inertia GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Rotational Motion and Moment of Inertia GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Gravitation GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Gravitation GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Properties of Matter GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Properties of Matter GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Properties of Matter GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Oscillations GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Oscillations GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Waves GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Waves GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Heat and Thermodynamics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Heat and Thermodynamics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Transference of Heat GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Transference of Heat GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Electrostatistics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Electrostatistics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Current Electricity GATE - 1 | 75 Questions | 75 mins | Free Test |
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Thermal and Chemical Effects of Currents GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Thermal and Chemical Effects of Currents GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Magnetostatics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Magnetostatics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Electromagnetic induction And Alternating Currents GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Electromagnetic induction And Alternating Currents GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Ray optics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Ray optics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Wave Optics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Wave Optics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Electromagnetic Waves GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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electrons and Protons GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
electrons and Protons GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Atoms , Molecules And Nuclei GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Atoms , Molecules And Nuclei GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Solids and Semiconductor devices GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Solids and Semiconductor devices GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Principles of Communication GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Magnetic Effects of Currents GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
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Properties of Solids GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Mechanical Properties of Fluids GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Thermal Properties of Matter GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Kinetic Theory of Gases GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Simple Harmonic Motion GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Capacitance GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Magnetism and Matter GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Dual Nature of Matter and Radiation GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Nuclear Physics and Radioactivity GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Electronic Devices GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Electronic Devices GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Experimental Physics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Wave Motion GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Atomic Structure and Periodic properties of Elements GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Atomic Structure and Periodic properties of Elements GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Atomic Structure and Periodic properties of Elements GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Atomic Structure and Periodic properties of Elements GATE - 4 | 75 Questions | 75 mins | Unlock & Practice Now |
Atomic Structure and Periodic properties of Elements GATE - 5 | 75 Questions | 75 mins | Unlock & Practice Now |
Atomic Structure and Periodic properties of Elements GATE - 6 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Bonding GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Bonding GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Bonding GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Bonding GATE - 4 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Bonding GATE - 5 | 75 Questions | 75 mins | Unlock & Practice Now |
States of Matter GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
States of Matter GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Energetics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Energetics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Equilibirium GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Equilibirium GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Ionic Equiliberia in Aqueous Solution - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Ionic Equiliberia in Aqueous Solution - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Electrochemistry GATE - 1 | 75 Questions | 75 mins | Free Test |
Electrochemistry GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Oxidation-Reduction GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Oxidation-Reduction GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Solutions GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Solutions GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Rates of Chemical Reactions and Chemical Kinetics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Rates of Chemical Reactions and Chemical Kinetics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Adsorption and Colloids GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Adsorption and Colloids GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Nuclear Chemistry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Nuclear Chemistry GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Purification And Characteristics of Organic Compounds - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Purification And Characteristics of Organic Compounds - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
S.I. Units , Significant Figures , Equivalent Mass , Atomic Mass , Mole Concept And Chemical Calculations GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
S.I. Units , Significant Figures , Equivalent Mass , Atomic Mass , Mole Concept And Chemical Calculations GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Elements, Their Occurrence and Extraction - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Elements, Their Occurrence and Extraction - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry Of Non-Metals - I (Hydrogen, Oxygen and Nitrogen) GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry Of Non-Metals - I (Hydrogen, Oxygen and Nitrogen) GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry Of Non-Metals - I (Hydrogen, Oxygen and Nitrogen) GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry Of Non-Metals - II (Boron,Silicon,Phosphorous,Sulphur,Halogens and noble gases) GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry Of Non-Metals - II (Boron,Silicon,Phosphorous,Sulphur,Halogens and noble gases) GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry Of Non-Metals - II (Boron,Silicon,Phosphorous,Sulphur,Halogens and noble gases) GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of Lighter Metals GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of Lighter Metals GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of Heavier Metals GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of Heavier Metals GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of s and p-Block elements GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of s and p-Block elements GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry of s and p-Block elements GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Transition metals including lanthanides and actinides GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Transition metals including lanthanides and actinides GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Coordination compounds and organometallics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Coordination compounds and organometallics GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Introduction to organic chemistry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Introduction to organic chemistry GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Types of Bond Fission, Nature of reagents and preparation GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Types of Bond Fission, Nature of reagents and preparation GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Petroleum GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Organic Chemistry Based on Functional Group - I GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Organic Chemistry Based on Functional Group - I GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Organic Chemistry Based on Functional Group - I GATE - 3 | 75 Questions | 75 mins | Unlock & Practice Now |
Organic Chemistry Based on Functional Group - II GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Organic Chemistry Based on Functional Group - II GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Organic Chemistry Based on Functional Group - III GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Some Important points and important questions on organic chemistry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Some Important points and important questions on organic chemistry GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Synthetic and natural polymers GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Synthetic and natural polymers GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Bio-Molecules : Structure and functions and chemistry of some biological Process GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Bio-Molecules : Structure and functions and chemistry of some biological Process GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry in action GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Environmental chemistry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Environmental chemistry GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Matter and Laws of Chemical Combination GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Equations and Stoichiometry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
State of Matter : Gaseous and Liquid States GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
State of Matter : Gaseous and Liquid States GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
State of Matter : Solid State GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemical Thermodynamics GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Redox Reaction GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Classification of Elements and Periodicity in Properties GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Classification of Elements and Periodicity in Properties GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
General Principles and Process of Isolation of Elements GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
General Principles and Process of Isolation of Elements GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
d- and f- block Elements GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
d- and f- block Elements GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry in Everyday Life GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
Chemistry in Everyday Life GATE - 2 | 75 Questions | 75 mins | Unlock & Practice Now |
Principles related to Practical Chemistry GATE - 1 | 75 Questions | 75 mins | Unlock & Practice Now |
GATE (Graduate Aptitude Test in Engineering) is an national level entrance exam for admission to PG courses in the field of engineering and technology. Candidates can get admissions into M.Tech./Ph.D.
Read MoreWhich online tests series question bank including steps and solutions with self evaluation.
One Answer for the above all questions. Online Tests India - GATE - Civil Engineering Practice Test PackGATE 2018 exam dates will be declared when the notification will be released in July, 2017. Candidates may check tentative dates below.
Events |
Dates (Tentative) |
Commencement of Online Application Form |
First week of September 2017 |
Last Date of Application Form Submission |
First week of October 2017 |
Corrections in Application Form |
Second week of October 2017 |
Last Date to request for change in |
First week of January 2018 |
Admit Card Availability |
First & Second Saturday & Sunday of |
GATE 2018 Exam Date |
First & Second Saturday & Sunday of |
Answer Key Released On |
Within a few days after examination |
Result Declaration |
Last week of March 2018 |
Downloading of Score Card Begins |
Last week of March 2018 to Last week of |
Counselling Commence |
Second week of April 2018 |
GATE 2018 exam dates will be declared when the notification will be released in July, 2017. Candidates may check tentative dates below.
Read MoreEligibility Criteria for GATE 2018
Qualification Required |
Description about the Qualifying Degree |
Status of the Degree |
Year |
B.E./B.Tech./B.Pharm. |
4-years B.Tech (after 10+2) in any |
Pursuing final |
2018 |
B.Arch. |
5-years bachelor’s degree in |
Pursuing final |
2018 |
B.Sc.(Research)/ B.S. |
4-years Bachelor’s degree in |
Pursuing final |
2018 |
M.Sc./M.A./MCA |
Master’s degree in Science/Mathematics |
Currently in the final |
2018 |
Int.M.E/M.Tech |
4-years Post-BSc Integrated |
Presently in |
2019 |
Int. M.E./ M.Tech or |
5-years Integrated Master’s |
Currently in the 4^{th}/5^{th} |
2019 |
Int. M.Sc/ Int. B.S.-M.S. |
Integrated M.Sc. or Five year |
Pursuing final |
2018 |
Professional |
B.E/B.Tech/B.Arch equivalent |
Completed section |
NA |
Note: International candidates should have completed Bachelor’s degree in Engineering/Technology or Post-graduate (M.Sc.) degree in any relevant science subject.AT the time of filling the application form, students have to upload their proof of qualification eligibility. Students who have passed the qualifying degree in 2017 or before are required to submit the degree certificate/provisional certificate while the other candidates have to upload certificate from Principal/head of the institution.
Eligibility Criteria for GATE 2018 Qualification Required Descr
Read MoreGATE Exam Pattern
Course: GATE is conducted for M.Tech./Ph.D. programme in IITs , IISc and various other institutions.
Number of Papers: GATE 2018 is held for total 23 papers. Candidates are allowed to appear in only one of the 23 papers.
Mode of Examination: The examination mode will be online only (CBT).
Exam Duration: The examination duration will be 3 hours.
Number of Questions: Total 65 questions of maximum 100 marks will be asked in GATE 2018.
Type of Questions: Multiple Choice Questions (MCQ) & Numerical Answer Type Questions (NAT) will appear in GATE examination. For MCQ, 4 choices will be provided while there will be no options provided for NAT. Students are required to enter the real number in Numerical Answer Type Questions with the help of virtual keypad.
Section Common in All GATE Papers: General Aptitude (GA) section is common in all papers. It will contain total 150 questions of maximum 15 marks (5 questions of 1 mark and 5 questions of 2 marks).
New Section: In the paper of XE, new section (H) namely Atmospheric and Oceanic Sciences has been included from the year 2017.
Marking Scheme: MCQ and NAT questions will carry 1 or 2 marks in all papers.
Negative Marking: There will be a negative marking of 1/3 marks for the questions carrying 1 mark. Likewise, for questions carrying 2 marks, 2/3 marks will be deducted. No negative marking for Numerical Answer Type questions.
Exam Pattern For All Papers Except GG, XE, XL:
Exam Pattern For Paper GG:
Exam Pattern For Paper XE:
Exam Pattern For Paper XL:
GATE Exam Pattern Course: GATE is conducted for M.Tech./Ph.D. programme in IITs , IISc and various other institutions. Number of Papers: GATE 2018 is held for total 23 papers. Candidates are allowed to appear in onl
Read MoreGraduate Aptitude Test in Engineering ( GATE ) Entrance Examination General Aptitude ( GA ) syllabus
Verbal Ability: English Grammar, Sentence Completion, Verbal Analogies, Word Groups, Instructions, Critical Reasoning and Verbal Deduction.
Numerical Ability: Numerical Computation, Numerical Estimation, Numerical Reasoning and Data Interpretation.
Graduate Aptitude Test in Engineering ( GATE ) Entrance Examination General Aptitude ( GA ) syllabus Verbal Ability: English Grammar, Sentence Completion, Verbal Analogies, Word Groups, Instructions, Critical Reasoning and Verbal Deductio
Read MoreSection 1: Engineering Mathematics
Linear Algebra:
Vector algebra, Matrix algebra, systems of linear equations, rank of a matrix, eigenvalues and eigen vectors.
Calculus:
Functions of single variable, limit, continuity and differentiability, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals. Theorems of Stokes, Gauss and Green.
Differential Equations:
First order linear and nonlinear differential equations, higher order linear ODEs with constant coefficients. Partial differential equations and separation of variables methods.
Special Topics:
Fourier Series, Laplace Transforms, Numerical methods for linear and nonlinear algebraic equations, Numerical integration and differentiation.
Section 2: Flight Mechanics
Atmosphere:
Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts.
Airplane performance:
Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; take off and landing; steady climb & descent,-absolute and service ceiling; cruise, cruise climb, endurance or loiter; load factor, turning flight, V-n diagram; Winds: head, tail & cross winds.
Static stability:
Angle of attack, sideslip; roll, pitch & yaw controls; longitudinal stick fixed & free stability, horizontal tail position and size; directional stability, vertical tail position and size; dihedral stability. Wing dihedral, sweep & position; hinge moments, stick forces.
Dynamic stability:
Euler angles; Equations of motion; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lat-directional dynamics; longitudinal modes; lateral-directional modes.
Section 3: Space Dynamics
Central force motion, determination of trajectory and orbital period in simple cases.
Orbit transfer, in-plane and out-of-plane.
Section 4: Aerodynamics
Basic Fluid Mechanics:
Conservation laws: Mass, momentum (Integral and differential form); Potential flow theory: sources, sinks, doublets, line vortex and their superposition; Viscosity, Reynold's number.
Airfoils and wings:
Airfoil nomenclature; Aerodynamic coefficients: lift, drag and moment; Kutta-Joukoswki theorem; Thin airfoil theory, Kutta condition, starting vortex; Finite wing theory: Induced drag, Prandtl lifting line theory; Critical and drag divergence Mach number.
Compressible Flows:
Basic concepts of compressibility, Conservation equations; One dimensional compressible flows, Fanno flow, Rayleigh flow; Isentropic flows, normal and oblique shocks, Prandtl-Meyer flow; Flow through nozzles and diffusers.
Special Topics:
Elementary ideas of viscous flows including boundary layers; Wind Tunnel Testing: Measurement and visualization techniques.
Section 5: Structures
Strength of Materials:
States of stress and strain. Stress and strain transformation. Mohr's Circle. Principal stresses. Three-dimensional Hooke's law. Plane stress and strain; Failure theories: Maximum stress, Tresca and von Mises; Strain energy. Castigliano's principles. Analysis of statically determinate and indeterminate trusses and beams. Elastic flexural buckling of columns.
Flight Vehicle Structures:
Characteristics of aircraft structures and materials. Torsion, bending and flexural shear of thin-walled sections. Loads on aircraft.
Structural Dynamics:
Free and forced vibrations of undamped and damped SDOF systems. Free vibrations of undamped 2-DOF systems.
Special Topics:
Vibration of beams. Theory of elasticity: Equilibrium and compatibility equations, Airy’s stress function.
Section 6: Propulsion
Basics:
Thermodynamics, boundary layers and heat transfer and combustion thermo-chemistry.
Thermodynamics of aircraft engines:
Thrust, efficiency and engine performance of turbojet, turboprop, turbo shaft, turbofan and ramjet engines, thrust augmentation of turbojets and turbofan engines. Aero thermodynamics of non-rotating propulsion components such as intakes, combustor and nozzle.
Axial compressors:
Angular momentum, work and compression, characteristic performance of a single axial compressor stage, efficiency of the compressor and degree of reaction.
Axial turbines:
Axial turbine stage efficiency
Centrifugal compressor:
Centrifugal compressor stage dynamics, inducer, impeller and diffuser.
Rocket propulsion:
Thrust equation and specific impulse, vehicle acceleration, drag, gravity losses, multi-staging of rockets. Classification of chemical rockets, performance of solid and liquid propellant rockets.
Section 1: Engineering Mathematics Linear Algebra: Vector algebra, Matrix algebra, systems of linear equations, rank of a matrix, eigenvalues and eigen vectors. Calculus: Functions of single variable, limit, contin
Read MoreSection 1: Engineering Mathematics
Linear Algebra:
Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.
Calculus:
Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus:
Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green's theorems.
Differential Equations:
Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs - Laplace, heat and wave equations.
Probability and Statistics:
Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.
Numerical Methods:
Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson's rule; single and multi-step methods for differential equations.
Section 2: Farm Machinery
Machine Design:
Design and selection of machine elements – gears, pulleys, chains and sprockets and belts; overload safety devices used in farm machinery; measurement of force, torque, speed, displacement and acceleration on machine elements.
Farm Machinery:
Soil tillage; forces acting on a tillage tool; hitch systems and hitching of tillage implements; functional requirements, principles of working, construction and operation of manual, animal and power operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting, threshing and transport; testing of agricultural machinery and equipment; calculation of performance parameters - field capacity, efficiency, application rate and losses; cost analysis of implements and tractors.
Section 3: Farm Power
Sources of Power:
Sources of power on the farm - human, animal, mechanical, electrical, wind, solar and biomass; bio-fuels.
Farm Power:
Thermodynamic principles of I.C. engines; I.C. engine cycles; engine components; fuels and combustion; lubricants and their properties; I.C. engine systems – fuel, cooling, lubrication, ignition, electrical, intake and exhaust; selection, operation, maintenance and repair of I.C. engines; power efficiencies and measurement; calculation of power, torque, fuel consumption, heat load and power losses.
Tractors and Power tillers:
Type, selection, maintenance and repair of tractors and powertillers; tractor clutches and brakes; power transmission systems – gear trains, differential, final drives and power take-off; mechanics of tractor chassis; traction theory; three point hitches- free link and restrained link operations; mechanical steering and hydraulic control systems used in tractors; tractor tests and performance.
Human engineering and safety in design of tractor and agricultural implements.
Section 4: Soil and Water Conservation Engineering
Fluid Mechanics:
Ideal and real fluids, properties of fluids; hydrostatic pressure and its measurement; hydrostatic forces on plane and curved surface; continuity equation; Bernoulli’s theorem; laminar and turbulent flow in pipes, Darcy- Weisbach and Hazen-Williams equations, Moody’s diagram; flow through orifices and notches; flow in open channels.
Soil Mechanics:
Engineering properties of soils; fundamental definitions and relationships; index properties of soils; permeability and seepage analysis; shear strength, Mohr’s circle of stress, active and passive earth pressures; stability of slopes.
Hydrology:
Hydrological cycle and components; meteorological parameters, their measurement and analysis of precipitation data; runoff estimation; hydrograph analysis, unit hydrograph theory and application; stream flow measurement; flood routing, hydrological reservoir and channel routing.
Surveying and Leveling:
Measurement of distance and area; instruments for surveying and leveling; chain surveying, methods of traversing; measurement of angles and bearings, plane table surveying; types of leveling; theodolite traversing; contouring; computation of areas and volume.
Soil and Water Erosion:
Mechanics of soil erosion, soil erosion types, wind and water erosion, factors affecting erosion; soil loss estimation; biological and engineering measures to control erosion; terraces and bunds; vegetative waterways; gully control structures, drop, drop inlet and chute spillways; earthen dams.
Watershed Management:
Watershed characterization; land use capability classification;rainwater harvesting structures,check dams and farm ponds.
Section 5: Irrigation and Drainage Engineering
Soil-Water-Plant Relationship:
Water requirement of crops; consumptive use and evapo-transpiration; measurement of infiltration, soil moisture and irrigation water infiltration.
Irrigation Water Conveyance and Application Methods:
Design of irrigation channels and underground pipelines; irrigation scheduling; surface, sprinkler and micro irrigation methods, design and evaluation of irrigation methods; irrigation efficiencies.
Agricultural Drainage:
Drainage coefficient; planning, design and layout of surface and sub-surface drainage systems; leaching requirement and salinity control; irrigation and drainage water quality and reuse.
Groundwater Hydrology:
Groundwater occurrence; Darcy’s Law, steady flow in confined and unconfined aquifers, evaluation of aquifer properties; groundwater recharge.
Wells and Pumps:
Types of wells, steady flow through wells; classification of pumps; pump characteristics; pump selection and installation.
Section 6: Agricultural Processing Engineering
Drying:
Psychrometry – properties of air-vapors mixture; concentration and drying of liquid foods - evaporators, tray, drum and spray dryers; hydrothermal treatment; drying and milling of cereals, pulses and oilseeds.
Size Reduction and Conveying:
Mechanics and energy requirement in size reduction of granular solids; particle size analysis for comminuted solids; size separation by screening; fluidization of granular solids-pneumatic, bucket, screw and belt conveying; cleaning and grading; effectiveness of grain cleaners; centrifugal separation of solids, liquids and gases.
Processing and By-product Utilization:
Processing of seeds, spices, fruits and vegetables; By-product utilization from processing industries.
Storage Systems:
Controlled and modified atmosphere storage; perishable food storage, godowns, bins and grain silos.
Section 7: Dairy and Food Engineering
Heat and Mass Transfer:
Steady state heat transfer in conduction, convection and radiation; transient heat transfer in simple geometry; working principles of heat exchangers; diffusive and convective mass transfer; simultaneous heat and mass transfer in agricultural processing operations; material and energy balances in food processing systems; water activity, sorption and desorption isotherms.
Preservation of Food:
Kinetics of microbial death – pasteurization and sterilization of milk and otherliquid foods; preservation of food by cooling and freezing; refrigeration and cold storage basics and applications.
Section 1: Engineering Mathematics Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors. Calculus: Limit, continuity and differentiability; Partial Derivatives; Max
Read MoreSection 1: Architecture and Design
Visual composition in 2D and 3D; Principles of Art and Architecture; Organization of space; Architectural Graphics; Computer Graphics– concepts of CAD, BIM, 3D modeling and Architectural rendition; Programming languages and automation. Anthropometrics; Planning and design considerations for different building types; Site planning; Circulation- horizontal and vertical; Barrier free design; Space Standards; Building Codes; National Building Code.
Elements, construction, architectural styles and examples of different periods of Indian and Western History of Architecture; Oriental, Vernacular and Traditional architecture; Architectural developments since Industrial Revolution; Influence of modern art on architecture; Art nouveau, Eclecticism, International styles, Post Modernism, Deconstruction in architecture; Recent trends in Contemporary Architecture; Works of renowned national and international architects.
Section 2: Building Materials, Construction and Management
Behavioral characteristics and applications of different building materials viz. mud, timber, bamboo, brick, concrete, steel, glass, FRP, AAC, different polymers, composites.
Building construction techniques, methods and details; Building systems and prefabrication of building elements; Principles of Modular Coordination; Estimation, specification, valuation, professional practice; Construction planning and equipments; Project management techniques e.g. PERT, CPM etc.
Section 3: Building and Structures
Principles of strength of materials; Design of structural elements in wood, steel and RCC; Elastic and Limit State design; Structural systems in RCC and Steel; Form and Structure; Principles of Pre-stressing; High Rise and Long Span structures, gravity and lateral load resisting systems; Principles and design of disaster resistant structures.
Section 4: Environmental Planning and Design
Ecosystem- natural and man-made ecosystem; Ecological principles; Concepts of Environmental Impact Analysis; Environmental considerations in planning and design; Thermal comfort, ventilation and air movement; Principles of lighting and illumination; Climate responsive design; Solar architecture; Principles of architectural acoustics; Green Building- Concepts and Rating; ECBC; Building Performance Simulation and Evaluation; Environmental pollution- types, causes, controls and abatement strategies.
Section 5: Urban Design
Concepts and theories of urban design; Public Perception; Townscape; Public Realm; Urban design interventions for sustainable development and transportation; Historical and modern examples of urban design; Public spaces, character, spatial qualities and Sense of Place; Elements of urban built environment – urban form, spaces, structure, pattern, fabric, texture, grain etc; Principles, tools and techniques of urban design; Urban renewal and conservation; Site planning; Landscape design; Development controls – FAR, densities and building byelaws.
Section 6: Urban Planning and Housing
Planning process; Types of plans - Master Plan, City Development Plan, Structure Plan, Zonal Plan, Action Area Plan, Town Planning Scheme, Regional Plan; Salient concepts, theories and principles of urban planning; Sustainable urban development; Emerging concepts of cities - Eco-City, Smart City, Transit Oriented Development (TOD), SEZ, SRZ etc.
Housing; Concepts, principles and examples of neighbourhood; Housing typologies; Slums; Affordable Housing; Housing for special areas and needs; Residential densities; Standards for housing and community facilities; National Housing Policies, Programs and Schemes.
Section 7: Planning Techniques and Management
Tools and techniques of Surveys – Physical, Topographical, Landuse and Socioeconomic Surveys; Methods of non-spatial and spatial data analysis; Graphic presentation of spatial data; Application of G.I.S and Remote Sensing techniques in urban and regional planning; Decision support system and Land Information System.
Urban Economics; Law of demand and supply of land and its use in planning; Social, Economical and environmental cost benefit analysis; Techniques of financial appraisal; Management of Infrastructure Projects; Development guidelines such as URDPFI; Planning Legislation and implementation – Land Acquisition Act, PPP etc.; Local self-governance.
Section 8: Services, Infrastructure and Transportation
Building Services: Water supply; Sewerage and drainage systems; Sanitary fittings and fixtures; Plumbing systems; Principles of internal and external drainage system; Principles of electrification of buildings; Intelligent Buildings; Elevators and Escalators - standards and uses; Air-Conditioning systems; Firefighting Systems; Building Safety and Security systems.
Urban Infrastructure – Transportation, Water Supply, Sewerage, Drainage, Solid Waste Management, Electricity and Communications.
Process and Principles of Transportation Planning and Traffic Engineering; Road capacity; Traffic survey methods; Traffic flow characteristics; Traffic analyses and design considerations; Travel demand forecasting; Land-use – transportation - urban form inter-relationships; Design of roads, intersections, grade separators and parking areas; Hierarchy of roads and level of service; Traffic and transport management and control in urban areas,; Mass transportation planning; Paratransits and other modes of transportation, Pedestrian and slow moving traffic planning; Intelligent Transportation Systems.
Principles of water supply and sanitation systems; water treatment; Water supply and distribution system; Water harvesting systems; Principles, Planning and Design of storm water drainage system; Sewage disposal methods; Methods of solid waste management - collection, transportation and disposal; Recycling and Reuse of solid waste; Power Supply and Communication Systems, network, design and guidelines.
Section 1: Architecture and Design Visual composition in 2D and 3D; Principles of Art and Architecture; Organization of space; Architectural Graphics; Computer Graphics– concepts of CAD, BIM, 3D modeling and Architectural rendition; Programming languages and automat
Read MoreSection 1: Engineering Mathematics
Linear Algebra:
Matrices and determinants, Systems of linear equations, Eigen values and Eigen vectors.
Calculus:
Limit, continuity and differentiability, Partial derivatives, Maxima and minima, Sequences and series, Test for convergence, Fourier Series.
Differential Equations:
Linear and nonlinear first order ODEs, higher order ODEs with constant coefficients, Cauchy’s and Euler’s equations, Laplace transforms, PDE- Laplace, heat and wave equations.
Probability and Statistics:
Mean, median, mode and standard deviation, Random variables, Poisson, normal and binomial distributions, Correlation and regression analysis.
Numerical Methods:
Solution of linear and nonlinear algebraic equations, Integration of trapezoidal and Simpson’s rule, Single and multistep methods for differential equations.
Section 2: General Biotechnology
Biochemistry: Biomolecules - structure and functions; Biological membranes, structure, action potential and transport processes; Enzymes- classification, kinetics and mechanism of action; Basic concepts and designs of metabolism (carbohydrates, lipids, amino acids and nucleic acids) photosynthesis, respiration and electron transport chain; Bioenergetics
Microbiology: Viruses - structure and classification; Microbial classification and diversity(bacterial, algal and fungal); Methods in microbiology; Microbial growth and nutrition; Aerobic and anaerobic respiration; Nitrogen fixation; Microbial diseases and host-pathogen interaction
Cell Biology: Prokaryotic and eukaryotic cell structure; Cell cycle and cell growth control; Cell-Cell communication, Cell signaling and signal transduction
Molecular Biology and Genetics: Molecular structure of genes and chromosomes; Mutations and mutagenesis; Nucleic acid replication, transcription, translation and their regulatory mechanisms in prokaryotes and eukaryotes; Mendelian inheritance; Gene interaction; Complementation; Linkage, recombination and chromosome mapping; Extra chromosomal inheritance; Microbial genetics (plasmids, transformation, transduction, conjugation); Horizontal gene transfer and Transposable elements; RNA interference; DNA damage and repair; Chromosomal variation; Molecular basis of genetic diseases
Analytical Techniques: Principles of microscopy-light, electron, fluorescent and confocal; Centrifugation- high speed and ultra; Principles of spectroscopy-UV, visible, CD, IR, FTIR, Raman, MS, NMR; Principles of chromatography- ion exchange, gel filtration, hydrophobic interaction, affinity, GC,HPLC, FPLC; Electrophoresis; Microarray
Immunology: History of Immunology; Innate, humoral and cell mediated immunity; Antigen; Antibody structure and function; Molecular basis of antibody diversity; Synthesis of antibody and secretion; Antigen-antibody reaction; Complement; Primary and secondary lymphoid organ; B and T cells and macrophages; Major histocompatibility complex (MHC); Antigen processing and presentation; Polyclonal and monoclonal antibody; Regulation of immune response; Immune tolerance; Hypersensitivity; Autoimmunity; Graft versus host reaction.
Bioinformatics: Major bioinformatic resources and search tools; Sequence and structure databases; Sequence analysis (biomolecular sequence file formats, scoring matrices, sequence alignment, phylogeny); Data mining and analytical tools for genomic and proteomic studies; Molecular dynamics and simulations (basic concepts including force fields, protein-protein, protein-nucleic acid, protein-ligand interaction)
Section 3: Recombinant DNA Technology
Restriction and modification enzymes; Vectors; plasmid, bacteriophage and other viral vectors, cosmids, Ti plasmid, yeast artificial chromosome; mammalian and plant expression vectors; cDNA and genomic DNA library; Gene isolation, cloning and expression ; Transposons and gene targeting; DNA labeling; DNA sequencing; Polymerase chain reactions; DNA fingerprinting; Southern and northern blotting; In-situ hybridization; RAPD, RFLP; Site-directed mutagenesis; Gene transfer technologies; Gene therapy
Section 4: Plant and Animal Biotechnology
Totipotency; Regeneration of plants; Plant growth regulators and elicitors; Tissue culture and Cell suspension culture system: methodology, kinetics of growth and, nutrient optimization; Production of secondary metabolites by plant suspension cultures; Hairy root culture; transgenic plants; Plant products of industrial importance
Animal cell culture; media composition and growth conditions; Animal cell and tissue preservation; Anchorage and non-anchorage dependent cell culture; Kinetics of cell growth; Micro & macro-carrier culture; Hybridoma technology; Stem cell technology; Animal cloning; Transgenic animals
Section 5: Bioprocess Engineering and Process Biotechnology
Chemical engineering principles applied to biological system, Principle of reactor design, ideal and non-ideal multiphase bioreactors, mass and heat transfer; Rheology of fermentation fluids, Aeration and agitation; Media formulation and optimization; Kinetics of microbial growth, substrate utilization and product formation; Sterilization of air and media; Batch, fed-batch and continuous processes; Various types of microbial and enzyme reactors; Instrumentation control and optimization; Unit operations in solid-liquid separation and liquid-liquid extraction; Process scale-up, economics and feasibility analysis
Engineering principle of bioprocessing- Upstream production and downstream; Bioprocess design and development from lab to industrial scale; Microbial, animal and plant cell culture platforms; Production of biomass and primary/secondary metabolites; Biofuels, Bioplastics, industrial enzymes, antibiotics; Large scale production and purification of recombinant proteins; Industrial application of chromatographic and membrane based bioseparation methods; Immobilization of biocatalysts (enzymes and cells) for bioconversion processes; Bioremediation-Aerobic and anaerobic processes for stabilization of solid / liquid wastes
Section 1: Engineering Mathematics Linear Algebra: Matrices and determinants, Systems of linear equations, Eigen values and Eigen vectors. Calculus: Limit, continuity and differentiability, Partial derivatives, Max
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.
Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher order linear equations with constant coefficients; Euler-Cauchy equations; Laplace transform and its application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of onedimensional diffusion equation; first and second order one-dimensional wave equation and two-dimensional Laplace equation.
Probability and Statistics: Definitions of probability and sampling theorems; Conditional probability; Discrete Random variables: Poisson and Binomial distributions; Continuous random variables: normal and exponential distributions; Descriptive statistics - Mean, median, mode and standard deviation; Hypothesis testing.
Numerical Methods: Accuracy and precision; error analysis. Numerical solutions of linear and non-linear algebraic equations; Least square approximation, Newton’s and Lagrange polynomials, numerical differentiation, Integration by trapezoidal and Simpson’s rule, single and multi-step methods for first order differential equations.
Section 2: Structural Engineering
Engineering Mechanics: System of forces, free-body diagrams, equilibrium equations; Internal forces in structures; Friction and its applications; Kinematics of point mass and rigid body; Centre of mass; Euler’s equations of motion; Impulse-momentum; Energy methods; Principles of virtual work.
Solid Mechanics: Bending moment and shear force in statically determinate beams; Simple stress and strain relationships; Theories of failures; Simple bending theory, flexural and shear stresses, shear centre; Uniform torsion, buckling of column, combined and direct bending stresses.
Structural Analysis: Statically determinate and indeterminate structures by force/ energy methods; Method of superposition; Analysis of trusses, arches, beams, cables and frames; Displacement methods: Slope deflection and moment distribution methods; Influence lines; Stiffness and flexibility methods of structural analysis.
Construction Materials and Management: Construction Materials: Structural steel - composition, material properties and behaviour; Concrete - constituents, mix design, short-term and long-term properties; Bricks and mortar; Timber; Bitumen. Construction Management: Types of construction projects; Tendering and construction contracts; Rate analysis and standard specifications; Cost estimation; Project planning and network analysis - PERT and CPM.
Concrete Structures: Working stress, Limit state and Ultimate load design concepts; Design of beams, slabs, columns; Bond and development length; Prestressed concrete; Analysis of beam sections at transfer and service loads.
Steel Structures: Working stress and Limit state design concepts; Design of tension and compression members, beams and beam- columns, column bases; Connections - simple and eccentric, beam-column connections, plate girders and trusses; Plastic analysis of beams and frames.
Section 3: Geotechnical Engineering
Soil Mechanics: Origin of soils, soil structure and fabric; Three-phase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability - one dimensional flow, Darcy’s law; Seepage through soils - two-dimensional flow, flow nets, uplift pressure, piping; Principle of effective stress, capillarity, seepage force and quicksand condition; Compaction in laboratory and field conditions; One dimensional consolidation, time rate of consolidation; Mohr’s circle, stress paths, effective and total shear strength parameters, characteristics of clays and sand.
Foundation Engineering: Sub-surface investigations - scope, drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theories - Rankine and Coulomb; Stability of slopes - finite and infinite slopes, method of slices and Bishop’s method; Stress distribution in soils - Boussinesq’s and Westergaard’s theories, pressure bulbs; Shallow foundations - Terzaghi’s and Meyerhoff’s bearing capacity theories, effect of water table; Combined footing and raft foundation; Contact pressure; Settlement analysis in sands and clays; Deep foundations - types of piles, dynamic and static formulae, load capacity of piles in sands and clays, pile load test, negative skin friction.
Section 4: Water Resources Engineering
Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum, energy and corresponding equations; Potential flow, applications of momentum and energy equations; Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth.
Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Kinematics of flow, velocity triangles; Basics of hydraulic machines, specific speed of pumps and turbines; Channel Hydraulics - Energy-depth relationships, specific energy, critical flow, slope profile, hydraulic jump, uniform flow and gradually varied flow
Hydrology: Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed, infiltration, unit hydrographs, hydrograph analysis, flood estimation and routing, reservoir capacity, reservoir and channel routing, surface run-off models, ground water hydrology - steady state well hydraulics and aquifers; Application of Darcy’s law.
Irrigation: Duty, delta, estimation of evapo-transpiration; Crop water requirements; Design of lined and unlined canals, head works, gravity dams and spillways; Design of weirs on permeable foundation; Types of irrigation systems, irrigation methods; Water logging and drainage; Canal regulatory works, cross-drainage structures, outlets and escapes.
Section 5: Environmental Engineering
Water and Waste Water: Quality standards, basic unit processes and operations for water treatment. Drinking water standards, water requirements, basic unit operations and unit processes for surface water treatment, distribution of water. Sewage and sewerage treatment, quantity and characteristics of wastewater. Primary, secondary and tertiary treatment of wastewater, effluent discharge standards. Domestic wastewater treatment, quantity of characteristics of domestic wastewater, primary and secondary treatment. Unit operations and unit processes of domestic wastewater, sludge disposal.
Air Pollution: Types of pollutants, their sources and impacts, air pollution meteorology, air pollution control, air quality standards and limits.
Municipal Solid Wastes: Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal).
Noise Pollution: Impacts of noise, permissible limits of noise pollution, measurement of noise and control of noise pollution.
Section 6: Transportation Engineering
Transportation Infrastructure: Highway alignment and engineering surveys; Geometric design of highways - cross-sectional elements, sight distances, horizontal and vertical alignments; Geometric design of railway track; Airport runway length, taxiway and exit taxiway design.
Highway Pavements: Highway materials - desirable properties and quality control tests; Design of bituminous paving mixes; Design factors for flexible and rigid pavements; Design of flexible pavement using IRC: 37-2012; Design of rigid pavements using IRC: 58-2011; Distresses in concrete pavements.
Traffic Engineering: Traffic studies on flow, speed, travel time - delay and O-D study, PCU, peak hour factor, parking study, accident study and analysis, statistical analysis of traffic data; Microscopic and macroscopic parameters of traffic flow, fundamental relationships; Control devices, signal design by Webster’s method; Types of intersections and channelization; Highway capacity and level of service of rural highways and urban roads.
Section 7: Geomatics Engineering
Principles of surveying; Errors and their adjustment; Maps - scale, coordinate system; Distance and angle measurement - Levelling and trigonometric levelling; Traversing and triangulation survey; Total station; Horizontal and vertical curves.
Photogrammetry - scale, flying height; Remote sensing - basics, platform and sensors, visual image interpretation; Basics of Geographical information system (GIS) and Geographical Positioning system (GPS).
Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector dentities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.
Differential Equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.
Complex Variables: Analytic functions, Cauchy's integral theorem, Taylor and Laurent series, Residue theorem.
Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions. Linear regression analysis.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule. Single and multi-step methods for numerical solution of differential equations.
Section 2: Process Calculations and Thermodynamics
Steady and unsteady state mass and energy balances including multiphase, multicomponent, reacting and non-reacting systems. Use of tie components; recycle, bypass and purge calculations; Gibb’s phase rule and degree of freedom analysis.
First and Second laws of thermodynamics. Applications of first law to close and open systems. Second law and Entropy. Thermodynamic properties of pure substances: Equation of State and residual properties, properties of mixtures: partial molar properties, fugacity, excess properties and activity coefficients; phase equilibria: predicting VLE of systems; chemical reaction equilibrium.
Section 3: Fluid Mechanics and Mechanical Operations
Fluid statics, Newtonian and non-Newtonian fluids, shell-balances including differential form of Bernoulli equation and energy balance, Macroscopic friction factors, dimensional analysis and similitude, flow through pipeline systems, flow meters, pumps and compressors, elementary boundary layer theory, flow past immersed bodies including packed and fluidized beds, Turbulent flow: fluctuating velocity, universal velocity profile and pressure drop.
Particle size and shape, particle size distribution, size reduction and classification of solid particles; free and hindered settling; centrifuge and cyclones; thickening and classification, filtration, agitation and mixing; conveying of solids.
Section 4: Heat Transfer
Steady and unsteady heat conduction, convection and radiation, thermal boundary layer and heat transfer coefficients, boiling, condensation and evaporation; types of heat exchangers and evaporators and their process calculations. Design of double pipe, shell and tube heat exchangers, and single and multiple effect evaporators.
Section 5: Mass Transfer
Fick’s laws, molecular diffusion in fluids, mass transfer coefficients, film, penetration and surface renewal theories; momentum, heat and mass transfer analogies; stage-wise and continuous contacting and stage efficiencies; HTU & NTU concepts; design and operation of equipment for distillation, absorption, leaching, liquid-liquid extraction, drying, humidification, dehumidification and adsorption.
Section 6: Chemical Reaction Engineering
Theories of reaction rates; kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors; residence time distribution, single parameter model; non-isothermal reactors; kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis.
Section 7: Instrumentation and Process Control
Measurement of process variables; sensors, transducers and their dynamics, process modeling and linearization, transfer functions and dynamic responses of various systems, systems with inverse response, process reaction curve, controller modes (P, PI, and PID); control valves; analysis of closed loop systems including stability, frequency response, controller tuning, cascade and feed forward control.
Section 8: Plant Design and Economics
Principles of process economics and cost estimation including depreciation and total annualized cost, cost indices, rate of return, payback period, discounted cash flow, optimization in process design and sizing of chemical engineering equipments such as compressors, heat exchangers, multistage contactors.
Section 9: Chemical Technology
Inorganic chemical industries (sulfuric acid, phosphoric acid, chlor-alkali industry), fertilizers (Ammonia, Urea, SSP and TSP); natural products industries (Pulp and Paper, Sugar, Oil, and Fats); petroleum refining and petrochemicals; polymerization industries (polyethylene, polypropylene, PVC and polyester synthetic fibers).
Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value
Read MoreSection 1: Engineering Mathematics
Discrete Mathematics: Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, generating functions.
Linear Algebra: Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition.
Calculus: Limits, continuity and differentiability. Maxima and minima. Mean value theorem. Integration.
Probability: Random variables. Uniform, normal, exponential, poisson and binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.
Section 2: Digital Logic
Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point).
Section 3: Computer Organization and Architecture
Machine instructions and addressing modes. ALU, data‐path and control unit. Instruction pipelining. Memory hierarchy: cache, main memory and secondary storage; I/O interface (interrupt and DMA mode).
Section 4: Programming and Data Structures
Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.
Section 5: Algorithms
Searching, sorting, hashing. Asymptotic worst case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide‐and‐conquer. Graph search, minimum spanning trees, shortest paths.
Section 6: Theory of Computation
Regular expressions and finite automata. Context-free grammars and push-down automata. Regular and contex-free languages, pumping lemma. Turing machines and undecidability.
Section 7: Compiler Design
Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation.
Section 8: Operating System
Processes, threads, inter‐process communication, concurrency and synchronization. Deadlock. CPU scheduling. Memory management and virtual memory. File systems.
Section 9: Databases
ER‐model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints, normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control.
Section 10: Computer Networks
Concept of layering. LAN technologies (Ethernet). Flow and error control techniques, switching. IPv4/IPv6, routers and routing algorithms (distance vector, link state). TCP/UDP and sockets, congestion control. Application layer protocols (DNS, SMTP, POP, FTP, HTTP). Basics of Wi-Fi. Network security: authentication, basics of public key and private key cryptography, digital signatures and certificates, firewalls.
Section 1: Engineering Mathematics Discrete Mathematics: Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, ge
Read MoreSection 1: Physical Chemistry
Structure: Postulates of quantum mechanics. Time dependent and time independent Schrödinger equations. Born interpretation. Particle in a box. Harmonic oscillator. Rigid rotor. Hydrogen atom: atomic orbitals. Multi-electron atoms: orbital approximation. Variation and first order perturbation techniques. Chemical bonding: Valence bond theory and LCAO-MO theory. Hybrid orbitals. Applications of LCAO-MOT to H_{2}^{+}, H_{2} and other homonuclear diatomic molecules, heteronuclear diatomic molecules like HF, CO, NO, and to simple delocalized π– electron systems. Hückel approximation and its application to annular π– electron systems. Symmetry elements and operations. Point groups and character tables. Origin of selection rules for rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Einstein coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance: nuclear g factor, chemical shift, nuclear coupling.
Equilibrium: Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy. Partial molar quantities. Thermodynamics of mixing. Chemical potential. Fugacity, activity and activity coefficients. Chemical equilibria. Dependence of equilibrium constant on temperature and pressure. Non-ideal solutions. Ionic mobility and conductivity. Debye-Hückel limiting law. Debye-Hückel-Onsager equation. Standard electrode potentials and electrochemical cells. Potentiometric and conductometric titrations. Phase rule. Clausius Clapeyron equation. Phase diagram of one component systems: CO_{2}, H_{2}O, S; two component systems: liquid-vapour, liquid-liquid and solid-liquid systems. Fractional distillation. Azeotropes and eutectics. Statistical thermodynamics: microcanonical and canonical ensembles, Boltzmann distribution, partition functions and thermodynamic properties.
Kinetics: Transition state theory: Eyring equation, thermodynamic aspects. Potential energy surfaces and classical trajectories. Elementary, parallel, opposing and consecutive reactions. Steady state approximation. Mechanisms of complex reactions. Unimolecular reactions. Kinetics of polymerization and enzyme catalysis. Fast reaction kinetics: relaxation and flow methods. Kinetics of photochemical and photophysical processes.
Surfaces and Interfaces: Physisorption and chemisorption. Langmuir, Freundlich and BET isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity. Self-assembly. Physical chemistry of colloids, micelles and macromolecules.
Section 2: Inorganic Chemistry
Main Group Elements: Hydrides, halides, oxides, oxoacids, nitrides, sulfides – shapes and reactivity. Structure and bonding of boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes. Allotropes of carbon. Chemistry of noble gases, pseudohalogens, and interhalogen compounds. Acid-base concepts.
Transition Elements: Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel diagrams, charge-transfer spectra. Magnetic properties of transition metal complexes. Reaction mechanisms: kinetic and thermodynamic stability, substitution and redox reactions.
Lanthanides and Actinides: Recovery. Periodic properties, spectra and magnetic properties.
Organometallics: 18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metalcarbene complexes and metallocenes. Fluxionality in organometallic complexes. Types of organometallic reactions. Homogeneous catalysis - Hydrogenation, hydroformylation, acetic acid synthesis, metathesis and olefin oxidation. Heterogeneous catalysis - Fischer Tropsch reaction, Ziegler-Natta polymerization.
Radioactivity: Decay processes, half-life of radioactive elements, fission and fusion processes.
Bioinorganic Chemistry: Ion (Na^{+} and K^{+}) transport, oxygen binding, transport and utilization, electron transfer reactions, nitrogen fixation, metalloenzymes containing magnesium, molybdenum, iron, cobalt, copper and zinc.
Solids: Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structures of AX, AX_{2}, ABX_{3} type compounds, spinels, band theory, metals and semiconductors.
Instrumental Methods of Analysis: UV-visible spectrophotometry, NMR and ESR spectroscopy, mass spectrometry. Chromatography including GC and HPLC. Electroanalytical methods- polarography, cyclic voltammetry, ion-selective electrodes. Thermoanalytical methods.
Section 3: Organic Chemistry
Stereochemistry: Chirality of organic molecules with or without chiral centres and determination of their absolute configurations. Relative stereochemistry in compounds having more than one stereogenic centre. Homotopic, enantiotopic and diastereotopic atoms, groups and faces. Stereoselective and stereospecific synthesis. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism. Configurational and conformational effects, and neighbouring group participation on reactivity and selectivity/specificity.
Reaction Mechanisms: Basic mechanistic concepts – kinetic versus thermodynamic control, Hammond’s postulate and Curtin-Hammett principle. Methods of determining reaction mechanisms through identification of products, intermediates and isotopic labeling. Nucleophilic and electrophilic substitution reactions (both aromatic and aliphatic). Addition reactions to carbon-carbon and carbon-heteroatom (N,O) multiple bonds. Elimination reactions. Reactive intermediates – carbocations, carbanions, carbenes, nitrenes, arynes and free radicals. Molecular rearrangements involving electron deficient atoms.
Organic Synthesis: Synthesis, reactions, mechanisms and selectivity involving the following classes of compounds – alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids, esters, nitriles, halides, nitro compounds, amines and amides. Uses of Mg, Li, Cu, B, Zn and Si based reagents in organic synthesis. Carbon-carbon bond formation through coupling reactions - Heck, Suzuki, Stille and Sonogoshira. Concepts of multistep synthesis - retrosynthetic analysis, strategic disconnections, synthons and synthetic equivalents. Umpolung reactivity – formyl and acyl anion equivalents. Selectivity in organic synthesis – chemo-, regio- and stereoselectivity. Protection and deprotection of functional groups. Concepts of asymmetric synthesis – resolution (including enzymatic), desymmetrization and use of chiral auxilliaries. Carbon-carbon bond forming reactions through enolates (including boron enolates), enamines and silyl enol ethers. Michael addition reaction. Stereoselective addition to C=O groups (Cram and Felkin-Anh models).
Pericyclic Reactions and Photochemistry: Electrocyclic, cycloaddition and sigmatropic reactions. Orbital correlations - FMO and PMO treatments. Photochemistry of alkenes, arenes and carbonyl compounds. Photooxidation and photoreduction. Di-π-methane rearrangement, Barton reaction.
Heterocyclic Compounds: Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole, quinoline and isoquinoline.
Biomolecules: Structure, properties and reactions of mono- and di-saccharides, physicochemical properties of amino acids, chemical synthesis of peptides, structural features of proteins, nucleic acids, steroids, terpenoids, carotenoids, and alkaloids.
Spectroscopy: Applications of UV-visible, IR, NMR and Mass spectrometry in the structural determination of organic molecules.
Section 1: Physical Chemistry Structure: Postulates of quantum mechanics. Time dependent and time independent Schrödinger equations. Born interpretation. Particle in a box. Harmonic oscillator. Rigid rotor. Hydrogen atom: atomic orbitals. Multi-
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness.
Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.
Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.
Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stoke's theorems.
Complex Analysis: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and Laurent's series, residue theorem.
Numerical Methods: Solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria.
Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions - binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis.
Section 2: Networks, Signals and Systems
Network solution methods: nodal and mesh analysis; Network theorems: superposition, Thevenin and Norton’s, maximum power transfer; Wye‐Delta transformation; Steady state sinusoidal analysis using phasors; Time domain analysis of simple linear circuits; Solution of network equations using Laplace transform; Frequency domain analysis of RLC circuits; Linear 2‐port network parameters: driving point and transfer functions; State equations for networks.
Continuous-time signals: Fourier series and Fourier transform representations, sampling theorem and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time signals; LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques.
Section 3: Electronic Devices
Energy bands in intrinsic and extrinsic silicon; Carrier transport: diffusion current, drift current, mobility and resistivity; Generation and recombination of carriers; Poisson and continuity equations; P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photo diode and solar cell; Integrated circuit fabrication process: oxidation, diffusion, ion implantation, photolithography and twin-tub CMOS process.
Section 4: Analog Circuits
Small signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits: clipping, clamping and rectifiers; Single-stage BJT and MOSFET amplifiers: biasing, bias stability, mid-frequency small signal analysis and frequency response; BJT and MOSFET amplifiers: multi-stage, differential, feedback, power and operational; Simple op-amp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, single-transistor and opamp configurations; Function generators, wave-shaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.
Section 5: Digital Circuits
Number systems; Combinatorial circuits: Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders and PLAs; Sequential circuits: latches and flip‐flops, counters, shift‐registers and finite state machines; Data converters: sample and hold circuits, ADCs and DACs; Semiconductor memories: ROM, SRAM, DRAM; 8-bit microprocessor (8085): architecture, programming, memory and I/O interfacing.
Section 6: Control Systems
Basic control system components; Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and lag-lead compensation; State variable model and solution of state equation of LTI systems.
Section 7: Communications
Random processes: autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems; Analog communications: amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers, circuits for analog communications; Information theory: entropy, mutual information and channel capacity theorem; Digital communications: PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.
Section 8: Electromagnetics
Electrostatics; Maxwell’s equations: differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector; Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth; Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart; Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations; Antennas: antenna types, radiation pattern, gain and directivity, return loss, antenna arrays; Basics of radar; Light propagation in optical fibers.
Section 1: Engineering Mathematics Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness. Calculus:
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.
Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step methods for differential equations.
Transform Theory: Fourier Transform, Laplace Transform, z‐Transform. Electrical Engineering
Section 2: Electric Circuits
Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, Ideal current and voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem, Two‐port networks, Three phase circuits, Power and power factor in ac circuits.
Section 3: Electromagnetic Fields
Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits,Self and Mutual inductance of simple configurations.
Section 4: Signals and Systems
Representation of continuous and discrete‐time signals, Shifting and scaling operations, Linear Time Invariant and Causal systems, Fourier series representation of continuous periodic signals, Sampling theorem, Applications of Fourier Transform, Laplace Transform and z-Transform.
Section 5: Electrical Machines
Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency; Three phase transformers: connections, parallel operation; Auto‐transformer, Electromechanical energy conversion principles, DC machines: separately excited, series and shunt, motoring and generating mode of operation and their characteristics, starting and speed control of dc motors; Three phase induction motors: principle of operation, types, performance, torque-speed characteristics, no-load and blocked rotor tests, equivalent circuit, starting and speed control; Operating principle of single phase induction motors; Synchronous machines: cylindrical and salient pole machines, performance, regulation and parallel operation of generators, starting of synchronous motor, characteristics; Types of losses and efficiency calculations of electric machines.
Section 6: Power Systems
Power generation concepts, ac and dc transmission concepts, Models and performance of transmission lines and cables, Series and shunt compensation, Electric field distribution and insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, GaussSeidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power factor correction, Symmetrical components, Symmetrical and unsymmetrical fault analysis, Principles of over‐current, differential and distance protection; Circuit breakers, System stability concepts, Equal area criterion.
Section 7: Control Systems
Mathematical modeling and representation of systems, Feedback principle, transfer function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of linear time invariant systems, Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci, Stability analysis, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State space model, State transition matrix.
Section 8: Electrical and Electronic Measurements
Bridges and Potentiometers, Measurement of voltage, current, power, energy and power factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement; Oscilloscopes, Error analysis.
Section 9: Analog and Digital Electronics
Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers; Amplifiers: Biasing, Equivalent circuit and Frequency response; Oscillators and Feedback amplifiers; Operational amplifiers: Characteristics and applications; Simple active filters, VCOs and Timers, Combinational and Sequential logic circuits, Multiplexer, Demultiplexer, Schmitt trigger, Sample and hold circuits, A/D and D/A converters, 8085 Microprocessor: Architecture, Programming and Interfacing.
Section 10: Power Electronics
Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET, IGBT; DC to DC conversion: Buck, Boost and Buck-Boost converters; Single and three phase configuration of uncontrolled rectifiers, Line commutated thyristor based converters, Bidirectional ac to dc voltage source converters, Issues of line current harmonics, Power factor, Distortion factor of ac to dc converters, Single phase and three phase inverters, Sinusoidal pulse width modulation.
Section 1: Engineering Mathematics Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper
Read MoreSection 1: Ecology
Population ecology; metapopulation dynamics; growth rates; density independent growth; density dependent growth; niche concept;
Species interactions: Plant-animal interactions; mutualism, commensalism, competition and predation; trophic interactions; functional ecology; ecophysiology; behavioural ecology;
Community ecology: Community assembly, organization and evolution; biodiversity: species richness, evenness and diversity indices; endemism; species-area relationships;
Ecosystem structure, function and services; nutrient cycles; biomes; habitat ecology; primary and secondary productivity; invasive species; global and climate change; applied ecology.
Section 2: Evolution
Origin, evolution and diversification of life; natural selection; levels of selection.
Types of selection (stabilizing, directional etc.); sexual selection; genetic drift; gene flow; adaptation; convergence; species concepts;
Life history strategies; adaptive radiation; biogeography and evolutionary ecology;
Origin of genetic variation; Mendelian genetics; polygenic traits, linkage and recombination; epistasis, gene-environment interaction; heritability; population genetics;
Molecular evolution; molecular clocks; systems of classification: cladistics and phenetics; molecular systematics; gene expression and evolution.
Section 3: Mathematics and Quantitative Ecology
Mathematics and statistics in ecology; Simple functions (linear, quadratic, exponential, logarithmic, etc); concept of derivatives and slope of a function; permutations and combinations; basic probability (probability of random events; sequences of events, etc); frequency distributions and their descriptive statistics (mean, variance, coefficient of variation, correlation, etc).
Statistical hypothesis testing: Concept of p-value; Type I and Type II error, test statistics like t-test and Chi-square test; basics of linear regression and ANOVA.
Section 4: Behavioural Ecology
Classical ethology; neuroethology; evolutionary ethology; chemical, acoustic and visual signaling
Mating systems; sexual dimorphism; mate choice; parenting behaviour Competition; aggression; foraging behaviour; predator–prey interactions; Sociobiology: kin selection, altruism, costs and benefits of group-living.
Section 1: Ecology Population ecology; metapopulation dynamics; growth rates; density independent growth; density dependent growth; niche concept; Species interactions: Plant-animal interactions; mutualism, commensalism, competition and predation; trophic interact
Read MoreCommon Section
Earth and Planetary system, size, shape, internal structure and composition of the earth; atmosphere and greenhouse effect; isostasy; elements of seismology; physical properties of the interior of the earth; continents and continental processes; physical oceanography; geomagnetism and paleomagnetism, continental drift, plate tectonics.
Weathering; soil formation; action of river, wind, glacier and ocean; earthquakes, volcanism and orogeny. Basic structural geology, mineralogy and petrology. Geological time scale and geochronology; stratigraphic principles; major stratigraphic divisions of India. Engineering properties of rocks and soils. Ground water geology. Geological and geographical distribution of ore, coal and petroleum resources of India.
Introduction to remote sensing. Engineering properties of rocks and soils. Ground water geology.
Principles and applications of gravity, magnetic, electrical, electromagnetic, seismic and radiometric methods of prospecting for oil, mineral and ground water; introductory well logging.
Part A: Geology
Geomorphic processes and agents; development and evolution of landforms; slope and drainage; processes in deep oceanic and near-shore regions; quantitative and applied geomorphology.
Mechanism of rock deformation; primary and secondary structures; geometry and genesis of folds, faults, joints and unconformities; cleavage, schistosity and lineation; methods of projection; tectonites and their significance; shear zones; superposed folding; basement-cover relationship.
Crystallography - symmetry, forms and twinning; crystal chemistry; optical mineralogy, classification of minerals, diagnostic physical and optical properties of rock - forming minerals.
Cosmic abundance of elements; meteorites; geochemical evolution of the earth; geochemical cycles; distribution of major, minor and trace elements in crust and mantle; elements of geochemical thermodynamics; isotope geochemistry; geochemistry of waters including solution equilibria and water-rock interaction.
Igneous rocks – classification, forms and textures; magmatic differentiation; binary and ternary phase diagrams; major and trace elements as monitors of partial melting and magma evolutionary processes. Sedimentary rocks – texture and structure; sedimentary processes and environments, sedimentary facies, provencance and basin analysis. Metamorphic rocks – structures and textures. Physico-chemical conditions of metamorphism and concept of metamorphic facies, grade and baric types; metamorphism of pelitic, mafic and impure carbonate rocks; role of fluids in metamorphism; metamorphic P-T-t paths and their tectonic significance. Association of igneous, sedimentary and metamorphic rocks with tectonic setting. Igneous and metamorphic provinces and important sedimentary basins of India.
Morphology, classification and geological significance of important invertebrates, vertebrates, plant fossils and microfossils.
Principles of Stratigraphy and concepts of correlation – lithostratigraphy, biostratigraphy and chronostratigraphy. Indian stratigraphy – Precambrian and Phanerozoic. Overview of Himalayan Geology.
Ore-mineralogy and optical properties of ore minerals; ore forming processes vis-à- vis ore-rock association (magmatic, hydrothermal, sedimentary, supergene and metamorphogenic ores); fluid inclusions as an ore genetic tool. Coal and petroleum geology; marine mineral resources. Prospecting and exploration of economic mineral deposits - sampling, ore reserve estimation, geostatistics, mining methods. Ore dressing and mineral economics. Origin and distribution of mineral, fossil and nuclear fuel deposits in India.
Engineering properties of rocks and soils; rocks as construction materials; role of geology in the construction of engineering structures including dams, tunnels and excavation sites; natural hazards. Ground water geology – exploration, well hydraulics and water quality. Basic principles of remote sensing – energy sources and radiation principles, atmospheric absorption, interaction of energy with earth’s surface, aerial-photo interpretation, multispectral remote sensing in visible, infrared, thermal IR and microwave regions, digital processing of satellite images. GIS – basic concepts, raster and vector mode operations.
Part B: Geophysics
The earth as a planet; different motions of the earth; gravity field of the earth, Clairaut's theorem, size and shape of earth; geochronology; seismology and interior of the earth; variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth; earthquakes-causes and measurements, magnitude and intensity, focal mechanisms, earthquake quantification, source characteristics, seismotectonics and seismic hazards; digital seismographs, geomagnetic field, paleomagnetism; oceanic and continental lithosphere; plate tectonics; heat flow; upper and lower atmospheric phenomena.
Scalar and vector potential fields; Laplace, Maxwell and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green's theorem; Image theory; integral equations in potential theory; Eikonal equation and Ray theory. Basic concepts of forward and inverse problems of geophysics, Ill-posedness of inverse problems.
'G' and 'g' units of measurement, absolute and relative gravity measurements; Land, airborne, shipborne and bore-hole gravity surveys; various corrections in gravity data reduction - free air, Bouguer and isostatic anomalies; density estimates of rocks; regional and residual gravity separation; principle of equivalent stratum; upward and downward continuation; wavelength filtering; preparation and analysis of gravity maps; gravity anomalies and their interpretation - anomalies due to geometrical and irregular shaped bodies, depth rules, calculation of mass.
Earth's magnetic field - elements, origin and units of measurement, magnetic susceptibility of rocks and measurements, magnetometers, Land, airborne and marine magnetic surveys, corrections, preparation of magnetic maps, upward and downward continuation, magnetic anomalies-geometrical shaped bodies, depth estimates, Image processing concepts in processing of magnetic anomaly maps; Interpretation of processed magnetic anomaly data.
Conduction of electricity through rocks, electrical conductivities of metals, non-metals, rock forming minerals and different rocks, concepts of D.C. resistivity measurement, various electrode configurations for resistivity sounding and profiling, application of filter theory, Type-curves over multi-layered structures, Dar-Zarrouck parameters, reduction of layers, coefficient of anisotropy, interpretation of resistivity field data, equivalence and suppression, self potential and its origin, field measurement, Induced polarization, time and frequency domain IP measurements; interpretation and applications of IP, ground-water exploration, environmental and engineering applications.
Basic concept of EM induction, Origin of electromagnetic field, elliptic polarization, methods of measurement for different source-receiver configuration, components in EM measurements. Skin-depth, interpretation and applications; earth's natural electromagnetic field, tellurics, magneto-tellurics; geomagnetic depth sounding principles, electromagnetic profiling, methods of measurement, processing of data and interpretation. Geological applications including groundwater, mining and hydrocarbon exploration.
Seismic methods of prospecting; Elastic properties of earth materials; Reflection, refraction and CDP surveys; land and marine seismic sources, generation and propagation of elastic waves, velocity - depth models, geophones, hydrophones, recording instruments (DFS), digital formats, field layouts, seismic noises and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D and 3D seismic data acquisition, processing and interpretation; CDP stacking charts, binning, filtering, dip-moveout, static and dynamic corrections, Digital seismic data processing, seismic deconvolution and migration methods, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP, AVO. Reservoir geophysics.
Geophysical signal processing, sampling theorem, aliasing, Nyquist frequency, Fourier series, periodic waveform, Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, auto correlation, cross correlation, convolution, deconvolution, principles of digital filters, windows, poles and zeros.
Principles and techniques of geophysical well-logging. SP, resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic, cement bond logging, micro-logs. Quantitative evaluation of formations from well logs; well hydraulics and application of geophysical methods for groundwater study; application of bore hole geophysics in ground water, mineral and oil exploration.
Radioactive methods of prospecting and assaying of minerals (radioactive and non radioactive) deposits, half-life, decay constant, radioactive equilibrium, G M counter, scintillation detector, semiconductor devices, application of radiometric for exploration and radioactive waste disposal.
Geophysical inverse problems; non-uniqueness and stability of solutions; quasi-linear and non-linear methods including Tikhonov's regularization method, Backus-Gilbert method, simulated annealing, genetic algorithms and artificial neural network.
Common Section Earth and Planetary system, size, shape, internal structure and composition of the earth; atmosphere and greenhouse effect; isostasy; elements of seismology; physical properties of the interior of the earth; continents and continental processes; physical oc
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, Eigen values and Eigen vectors.
Calculus: Mean value theorems, theorems of integral calculus, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equation (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s equations, initial and boundary value problems, solution of partial differential equations: variable separable method.
Analysis of complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’s series, residue theorem, solution of integrals.
Probability and Statistics: Sampling theorems, conditional probability, mean, median, mode and standard deviation, random variables, discrete and continuous distributions: normal, Poisson and binomial distributions.
Numerical Methods: Matrix inversion, solutions of non-linear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis.
Section 2: Electrical Circuits:
Voltage and current sources: independent, dependent, ideal and practical; v-i relationships of resistor, inductor, mutual inductor and capacitor; transient analysis of RLC circuits with dc excitation.
Kirchoff’s laws, mesh and nodal analysis, superposition, Thevenin, Norton, maximum power transfer and reciprocity theorems.
Peak-, average- and rms values of ac quantities; apparent-, active- and reactive powers; phasor analysis, impedance and admittance; series and parallel resonance, locus diagrams, realization of basic filters with R, L and C elements.
One-port and two-port networks, driving point impedance and admittance, open-, and short circuit parameters.
Section 3: Signals and Systems
Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer function, frequency response of first and second order linear time invariant systems, impulse response of systems; convolution, correlation. Discrete time system: impulse response, frequency response, pulse transfer function; DFT and FFT; basics of IIR and FIR filters.
Section 4: Control Systems
Feedback principles, signal flow graphs, transient response, steady-state-errors, Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci, design of lead, lag and lead-lag compensators, state-space representation of systems; time-delay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo and stepper motors, servo valves; on-off, P, P-I, P-I-D, cascade, feedforward, and ratio controllers.
Section 5: Analog Electronics
Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of operational amplifiers; applications of opamps: difference amplifier, adder, subtractor, integrator, differentiator, instrumentation amplifier, precision rectifier, active filters and other circuits. Oscillators, signal generators, voltage controlled oscillators and phase locked loop.
Section 6: Digital Electronics
Combinational logic circuits, minimization of Boolean functions. IC families: TTL and CMOS. Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flipflops, shift registers, timers and counters; sample-and-hold circuit, multiplexer, analog-todigital (successive approximation, integrating, flash and sigma-delta) and digital-toanalog converters (weighted R, R-2R ladder and current steering logic). Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/settling time); basics of number systems, 8-bit microprocessor and microcontroller: applications, memory and input-output interfacing; basics of data acquisition systems.
Section 7: Measurements
SI units, systematic and random errors in measurement, expression of uncertainty - accuracy and precision index, propagation of errors. PMMC, MI and dynamometer type instruments; dc potentiometer; bridges for measurement of R, L and C, Q-meter. Measurement of voltage, current and power in single and three phase circuits; ac and dc current probes; true rms meters, voltage and current scaling, instrument transformers, timer/counter, time, phase and frequency measurements, digital voltmeter, digital multimeter; oscilloscope, shielding and grounding.
Section 8: Sensors and Industrial Instrumentation
Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal conditioning circuits; transducers for industrial instrumentation: displacement (linear and angular), velocity, acceleration, force, torque, vibration, shock, pressure (including low pressure), flow (differential pressure, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters) temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer and semiconductor); liquid level, pH, conductivity and viscosity measurement.
Section 9: Communication and Optical Instrumentation
Amplitude- and frequency modulation and demodulation; Shannon's sampling theorem, pulse code modulation; frequency and time division multiplexing, amplitude-, phase, frequency-, pulse shift keying for digital modulation; optical sources and detectors: LED, laser, photo-diode, light dependent resistor and their characteristics; interferometer: applications in metrology; basics of fiber optic sensing.
Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, systems of linear equations, Eigen values and Eigen vectors. Calculus: Mean value theorems, theorems of integral calculus, partial derivatives, maxima an
Read MoreSection 1: Linear Algebra
Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan-canonical form, Hermitian, SkewHermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators, definite forms.
Section 2: Complex Analysis
Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Zeros and singularities; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.
Section 3: Real Analysis
Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, compactness, completeness, Weierstrass approximation theorem; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.
Section 4: Ordinary Differential Equations
First order ordinary differential equations, existence and uniqueness theorems for initial value problems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties.
Section 5: Algebra
Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems, automorphisms; cyclic groups and permutation groups, Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria; Fields, finite fields, field extensions.
Section 6: Functional Analysis
Normed linear spaces, Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.
Section 7: Numerical Analysis
Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); numerical solution of ordinary differential equations: initial value problems: Euler’s method, Runge-Kutta methods of order 2.
Section 8: Partial Differential Equations
Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave in two dimensional Cartesian coordinates, Interior and exterior Dirichlet problems in polar coordinates; Separation of variables method for solving wave and diffusion equations in one space variable; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
Section 9: Topology
Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Section 10: Probability and Statistics
Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties (Discrete uniform, Binomial, Poisson, Geometric, Negative binomial, Normal, Exponential, Gamma, Continuous uniform, Bivariate normal, Multinomial), expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators; Interval estimation; Testing of hypotheses, standard parametric tests based on normal, , , distributions; Simple linear regression.
Section 11: Linear programming
Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems; Hungarian method for solving assignment problems.
Section 1: Linear Algebra Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan-canonical form, Hermi
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.
Differential equations: First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace's equations.
Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series.
Probability and Statistics: Definitions of probability, sampling theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.
Section 2: Applied Mechanics and Design
Engineering Mechanics: Free-body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations, collisions.
Mechanics of Materials: Stress and strain, elastic constants, Poisson's ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength.
Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope.
Vibrations: Free and forced vibration of single degree of freedom systems, effect of damping; vibration isolation; resonance; critical speeds of shafts.
Machine Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.
Section 3: Fluid Mechanics and Thermal Sciences
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy, forces on submerged bodies, stability of floating bodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends and fittings.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept and electrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system, Heisler's charts; thermal boundary layer, dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, StefanBoltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis.
Thermodynamics: Thermodynamic systems and processes; properties of pure substances, behaviour of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in various processes; second law of thermodynamics; thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations.
Applications: Power Engineering: Air and gas compressors; vapour and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles. Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines.
Section 4: Materials, Manufacturing and Industrial Engineering
Engineering Materials: Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials.
Casting, Forming and Joining Processes: Different types of castings, design of patterns, moulds and cores; solidification and cooling; riser and gating design. Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy. Principles of welding, brazing, soldering and adhesive bonding.
Machining and Machine Tool Operations: Mechanics of machining; basic machine tools; single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, design of jigs and fixtures.
Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements; comparators; gauge design; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools.
Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning.
Inventory Control: Deterministic models; safety stock inventory control systems.
Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.
Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors. Calculus: Functions of single variable, limit, continuity and differentiability, mean value th
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrices and Determinants; Systems of linear equations; Eigen values and Eigen vectors.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.
Differential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations.
Probability and Statistics: Measures of central tendency; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.
Numerical Methods: Solutions of linear algebraic equations; Integration of trapezoidal and Simpson’s rule; Single and multi-step methods for differential equations.
Section 2: Mine Development and Surveying
Mine Development: Methods of access to deposits; Underground drivages; Drilling methods and machines; Explosives, blasting devices and practices.
Mine Surveying: Levels and leveling, theodolite, tacheometry, triangulation; Contouring; Errors and adjustments; Correlation; Underground surveying; Curves; Photogrammetry; Field astronomy; EDM and Total Station; Introductory GPS.
Section 3: Geomechanics and Ground Control
Engineering Mechanics: Equivalent force systems; Equations of equilibrium; Two dimensional frames and trusses; Free body diagrams; Friction forces; Particle kinematics and dynamics; Beam analysis.
Geomechanics: Geo-technical properties of rocks; Rock mass classification; Instrumentation and stress measurement techniques; Theories of rock failure; Ground vibrations; Stress distribution around mine openings; Subsidence; Rock bursts and coal bumps; Slope stability.
Ground Control: Design of pillars; Roof supporting systems; Mine filling.
Section 4: Mining Methods and Machinery
Mining Methods: Surface mining: layout, development, loading, transportation and mechanization, continuous surface mining systems; Underground coal mining: bord and pillar systems, room and pillar mining, longwall mining, thick seam mining methods; highwall mining; Underground metal mining: open, supported and caved stoping methods, stope mechanization, ore handling systems.
Mining Machinery: Generation and transmission of mechanical, hydraulic and pneumatic power; Materials handling: haulages, conveyors, face and development machinery, hoisting systems, pumps, crushers.
Section 5: Surface Environment, Mine Ventilation, and Underground Hazards
Surface Environment: Air, water and soil pollution : Standards of quality, causes and dispersion of contamination, and control; Noise; Land reclamation.
Mine Ventilation: Underground atmosphere; Heat load sources and thermal environment, air cooling; Mechanics of air flow, distribution, natural and mechanical ventilation; Mine fans and their usage; Auxiliary ventilation; Ventilation planning; Ventilation networks.
Subsurface Hazards: Mine Gases. Underground hazards from fires, explosions, dust and inundation; Rescue apparatus and practices; Safety in mines; Accident data analysis; Mine lighting; Mine legislation; Occupational safety.
Section 6: Mine Economics, Mine Planning, Systems Engineering
Mine Economics: Mineral resource classification; Discounted cash flow analysis; Mine valuation; Mine investment analysis; Mineral taxation.
Mine Planning: Sampling methods, practices and interpretation; Reserve estimation techniques: Basics of geostatistics and quality control; Optimization of facility location; Work-study.
Systems Engineering: Concepts of reliability; Reliability of simple systems; Maintainability and availability; Linear programming, transportation and assignment problems; Network analysis; Inventory models; Queueing theory; Basics of simulation.
Section 1: Engineering Mathematics Linear Algebra: Matrices and Determinants; Systems of linear equations; Eigen values and Eigen vectors. Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima an
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.
Calculus: Limit, continuity and differentiability; Partial derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line, Surface and volume integrals; Stokes, Gauss and Green’s theorems.
Differential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs – Laplace, one dimensional heat and wave equations.
Probability and Statistics: Definitions of probability and sampling theorems, conditional probability, Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.
Numerical Methods: Solutions of linear and non-linear (Bisection, Secant, Newton Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.
Section 2: Thermodynamics and Rate Processes
Laws of thermodynamics, activity, equilibrium constant, applications to metallurgical systems, solutions, phase equilibria, Ellingham and phase stability diagrams, thermodynamics of surfaces, interfaces and defects, adsorption and segregation; basic kinetic laws, order of reactions, rate constants and rate limiting steps; principles of electro chemistry- single electrode potential, electrochemical cells and polarizations, aqueous corrosion and protection of metals, galvanic corrosion, crevice corrosion, pitting corrosion, intergranular corrosion, selective leaching, oxidation and high temperature corrosion – characterization and control; heat transfer – conduction, convection and heat transfer coefficient relations, radiation, mass transfer – diffusion and Fick’s laws, mass transfer coefficients; momentum transfer – concepts of viscosity, shell balances, Bernoulli’s equation, friction factors.
Section 3: Extractive Metallurgy
Minerals of economic importance, comminution techniques, size classification, flotation, gravity and other methods of mineral processing; agglomeration, pyro-, hydro-, and electro-metallurgical processes; material and energy balances; principles and processes for the extraction of non-ferrous metals – aluminium, copper, zinc, lead, magnesium, nickel, titanium and other rare metals; iron and steel making – principles, role structure and properties of slags, metallurgical coke, blast furnace, direct reduction processes, primary and secondary steel making, ladle metallurgy operations including deoxidation, desulphurization, sulphide shape control, inert gas rinsing and vacuum reactors; secondary refining processes including AOD, VAD, VOD, VAR and ESR; ingot and continuous casting; stainless steel making, furnaces and refractories.
Section 4: Physical Metallurgy
Crystal structure and bonding characteristics of metals, alloys, ceramics and polymers, structure of surfaces and interfaces, nano-crystalline and amorphous structures; solid solutions; solidification; phase transformation and binary phase diagrams; principles of heat treatment of steels, cast iron and aluminium alloys; surface treatments; recovery, recrystallization and grain growth; structure and properties of industrially important ferrous and non-ferrous alloys; elements of X-ray and electron diffraction; principles of optical, scanning and transmission electron microscopy; industrial ceramics, polymers and composites; introduction to electronic basis of thermal, optical, electrical and magnetic properties of materials; introduction to electronic and opto-electronic materials.
Section 5: Mechanical Metallurgy
Elasticity, yield criteria and plasticity; defects in crystals; elements of dislocation theory – types of dislocations, slip and twinning, source and multiplication of dislocations, stress fields around dislocations, partial dislocations, dislocation interactions and reactions; strengthening mechanisms; tensile, fatigue and creep behaviour; superplasticity; fracture – Griffith theory, basic concepts of linear elastic and elastoplastic fracture mechanics, ductile to brittle transition, fracture toughness; failure analysis; mechanical testing – tension, compression, torsion, hardness, impact, creep, fatigue, fracture toughness and formability.
Section 6: Manufacturing Processes
Metal casting – patterns and moulds including mould design involving feeding, gating and risering, melting, casting practices in sand casting, permanent mould casting, investment casting and shell moulding, casting defects and repair; Hot, warm and cold working of metals; Metal forming – fundamentals of metal forming processes of rolling, forging, extrusion, wire drawing and sheet metal forming, defects in forming; Metal joining – soldering, brazing and welding, common welding processes of shielded metal arc welding, gas metal arc welding, gas tungsten arc welding and submerged arc welding; Welding metallurgy, problems associated with welding of steels and aluminium alloys, defects in welded joints; Powder metallurgy – production of powders, compaction and sintering; NDT using dyepenetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle methods.
Section 1: Engineering Mathematics Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors. Calculus: Limit, continuity and differentiability; Partial derivatives; Maxima an
Read MoreEngineering Mathematics
1. Linear Algebra:
Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.
2. Calculus:
Functions of single variable, Limit, continuity and differentiability, Taylor series, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
3. Differential equations:
First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial andboundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.
4. Complex variables:
Complex number, polar form of complex number, triangle inequality.
5. Probability and Statistics:
Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions, Linear regression analysis.
6. Numerical Methods:
Numerical solutions of linear and non-linear algebraic equations. Integration by trapezoidal and Simpson’s rule. Single and multi-step methods for numerical solution of differential equations.
Petroleum Engineering
7. Petroleum Exploration:
Classification and description of some common rocks with special reference to clastic and nonclastic reservoir rocks. Origin, migration and accumulation ofPetroleum. Petroleum exploration methods.
8. Oil and Gas Well Drilling Technology:
Well planning. Drilling method. Drilling rigs Rig operating systems. Drilling fluids function and properties. Drilling fluid maintenanceequipment. Oil & gas well cementing operations. Drill bit types and their applications. Drillstring & Casing string function, operations, selection & design. Drilling problems, their control& remedies. Directional drilling tools. Directional survey. Application of horizontal, multilateral,extended reach, slim wells.
9. Reservoir Engineering:
Petrophysical properties of reservoir rocks. Coring and core analysis. Reservoir fluid properties. Phase behavior of hydrocarbon system. Flow of fluidsthrough porous media. Water and gas coning. Reservoir pressure measurements. Reservoirdrives, drive mechanics and recovery factors. Reserve estimation & techniques.
10. Petroleum Production Operations:
Well equipments. Well completion techniques. Well production problems and mitigation. Well servicing & Workover operations. Workover &completion fluids. Formation damage. Well stimulation techniques. Artificial lift techniques.Field processing of oil & gas. Storage and transportation of petroleum and petroleumproducts. Metering and measurements oil & gas. Production system analysis & optimization.Production testing. Multiphase flow in tubing and flow-lines. Nodal system analysis. Pressure vessels, storage tanks, shell and tube heat exchangers, pumps and compressors, LNG value chain.
11. Offshore Drilling and Production Practices:
Offshore oil and gas operations & ocean environment. Offshore fixed platforms, Offshore mobile units, Station keeping methods likemooring & dynamic positioning system. Offshore drilling from fixed platform, jack-up, shipsand semi submersibles. Use of conductors and risers. Offshore well completion. Deep waterapplications of subsea technology. Offshore production: Oil processing platforms, waterinjection platforms, storage, SPM and SBM transportation and utilities. Deep water drilling rig.Deep water production system. Emerging deep water technologies.
12. Petroleum Formation Evaluation:
Evaluation of petrophysical of sub-surface formations: Principles applications, advantages and disadvantages of SP, resistivity, radioactive, acoustic logs and types of tools used. Evaluation of CBL/VDL, USIT, SFT, RFT. Production loggingtools, principles, limitations and applications. Special type of logging tools. Casing inspectiontools (principles, applications and limitations), Formations micro scanner (FMS), NMR loggingprinciples. Standard log interpretation methods. Cross-plotting methods.
13. Oil and Gas Well Testing:
Diffusivity equation, derivation & solutions. Radius of investigation. Principle of superposition. Horner’s approximation. Drill Stem Testing. PressureTransient Tests: Drawdown and build up-test analysis. Wellbore effects. Multilayer reservoirs.Injection well testing. Multiple well testing. Interference testing, Pulse testing, well-testanalysis by use of type curves. Gas well testing.
14. Health Safety and Environment in Petroleum Industry:
Health hazards in Petroleum Industry: Toxicity, Physiological, Asphyxiation, respiratory and skin effect of petroleum hydrocarbons, sour gases. Safety System: Manual & automatic shutdown system, blow downsystems. Gas detection system. Fire detection and suppression systems. Personal protectionsystem & measures. HSE Policies. Disaster & crisis management in Petroleum Industry.Environment: Environment concepts, impact on eco-system, air, water and soil. The impact ofdrilling & production operations on environment, Environmental transport of petroleum wastes.Offshore environmental studies. Offshore oil spill and oil spill control. Waste treatment methods.
15. Enhanced Oil Recovery Techniques:
Basic principles and mechanism of EOR, Screening of EOR process. Concept of pattern flooding, recovery efficiency, permeability heterogeneity.Macroscopic and microscopic displacement efficiency. EOR methods: Chemical flooding, Miscible flooding, Thermal recoveries (steam stimulation, hot water & steam flooding, in-situ combustion), Microbial EOR.
16. Latest trends in Petroleum Engineering:
Coal bed methane, shale gas, oil shale, gas hydrate, and heavy oil.
Engineering Mathematics 1. Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigenvectors. 2. Calculus: Functions of single variable, Limit, continuity and differentiability, Taylor seri
Read MoreSection 1: Mathematical Physics
Linear vector space: basis, orthogonality and completeness; matrices; vector calculus; linear differential equations; elements of complex analysis: CauchyRiemann conditions, Cauchy’s theorems, singularities, residue theorem and applications; Laplace transforms, Fourier analysis; elementary ideas about tensors: covariant and contravariant tensor, Levi-Civita and Christoffel symbols.
Section 2: Classical Mechanics
D’Alembert’s principle, cyclic coordinates, variational principle, Lagrange’s equation of motion, central force and scattering problems, rigid body motion; small oscillations, Hamilton’s formalisms; Poisson bracket; special theory of relativity: Lorentz transformations, relativistic kinematics, mass‐energy equivalence.
Section 3: Electromagnetic Theory
Solutions of electrostatic and magnetostatic problems including boundary value problems; dielectrics and conductors; Maxwell’s equations; scalar and vector potentials; Coulomb and Lorentz gauges; Electromagnetic waves and their reflection, refraction, interference, diffraction and polarization; Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation from a moving charge.
Section 4: Quantum Mechanics
Postulates of quantum mechanics; uncertainty principle; Schrodinger equation; one-, two- and three-dimensional potential problems; particle in a box, transmission through one dimensional potential barriers, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and spin; addition of angular momenta; time independent perturbation theory; elementary scattering theory.
Section 5: Thermodynamics and Statistical Physics
Laws of thermodynamics; macrostates and microstates; phase space; ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body radiation and Planck’s distribution law; Bose‐Einstein condensation; first and second order phase transitions, phase equilibria, critical point.
Section 6: Atomic and Molecular Physics
Spectra of one‐ and many‐electron atoms; LS and jj coupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; rotational and vibrational spectra of diatomic molecules; electronic transition in diatomic molecules, Franck‐Condon principle; Raman effect; NMR, ESR, X-ray spectra; lasers: Einstein coefficients, population inversion, two and three level systems.
Section 7: Solid State Physics & Electronics
Elements of crystallography; diffraction methods for structure determination; bonding in solids; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids: nearly free electron and tight binding models; metals, semiconductors and insulators; conductivity, mobility and effective mass; optical, dielectric and magnetic properties of solids; elements of superconductivity: Type-I and Type II superconductors, Meissner effect, London equation.
Semiconductor devices: diodes, Bipolar Junction Transistors, Field Effect Transistors; operational amplifiers: negative feedback circuits, active filters and oscillators; regulated power supplies; basic digital logic circuits, sequential circuits, flip‐flops, counters, registers, A/D and D/A conversion.
Section 8: Nuclear and Particle Physics
Nuclear radii and charge distributions, nuclear binding energy, Electric and magnetic moments; nuclear models, liquid drop model: semi‐empirical mass formula, Fermi gas model of nucleus, nuclear shell model; nuclear force and two nucleon problem; alpha decay, beta‐decay, electromagnetic transitions in nuclei; Rutherford scattering, nuclear reactions, conservation laws; fission and fusion; particle accelerators and detectors; elementary particles, photons, baryons, mesons and leptons; quark model.
Section 1: Mathematical Physics Linear vector space: basis, orthogonality and completeness; matrices; vector calculus; linear differential equations; elements of complex analysis: CauchyRiemann conditions, Cauchy’s theorems, singularities, residue theorem and applic
Read MoreSection 1: Engineering Mathematics
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.
Complex variables: Analytic functions, Cauchy’s integral theorem, Taylor series.
Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods for differential equations.
Section 2: General Engineering
Engineering Materials: Structure and properties correlation;engineering materials (metals, ceramics, polymers and composites) – properties and applications; stress strain behavior of metals and alloys;iron-carbon phase diagram, heat treatment of metals and alloys, its influence on mechanical properties.
Applied Mechanics: Engineering mechanics – equivalent force systems, free body concepts, equations of equilibrium; trusses; strength of materials – stress, strain and their relationship; failure theories, Mohr’s circle (stress), deflection of beams, bending and shear stress, Euler’s theory of columns.
Theory of Machines and Design: Analysis of planar mechanisms, cams and followers; governors and fly wheels; design of bolted, riveted and welded joints; interference/shrink fit joints; design of shafts, keys, spur gears, belt drives, brakes and clutches; pressure vessels.
Thermal and Fluids Engineering: Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, equations of continuity and momentum, capillary action, contact angle and wetting; thermodynamics – zeroth, first and second law of thermodynamics, thermodynamic system and processes, calculation of work and heat for systems and control volumes; air standard cycles; heat transfer – basic applications of conduction, convection and radiation.
Section 3: Manufacturing Processes I
Casting: types of casting processes and applications; patterns – types and materials; allowances; moulds and cores – materials, making, and testing; casting techniques of cast iron, steels and nonferrous metals and alloys; analysis of solidification and micro structure development; design of gating and riser; origin of defects.
Metal Forming: Stress-strain relations in elastic and plastic deformation; concept of flow stress; hot and cold working – forging, rolling, extrusion and wire drawing; sheet metal working processes – blanking, bending and deep drawing; ideal work and slab analysis; origin of metal working defects.
Joining of materials: Principles of fusion welding processes(manual metal arc, MIG, TIG, plasma arc, submerged arc welding processes)–different heat sources (flame, arc, resistive, laser, electron beam), and heat transfer and associated losses, flux application, feeding of filler rod; Principles of solid state welding processes (friction, explosive welding, ultrasonic welding processes); Principles of adhesive, brazing and soldering processes; Origins of welding defects.
Powder processing: Production of metal/ceramic powders, compaction and sintering of metals and ceramic powders.
Polymers and Composites: Plastic processing – injection, compression and blow molding, extrusion, calendaring and thermoforming; molding of composites.
Section 4: Manufacturing Processes II
Machine Tools and Machining: Basic machine tools like centre lathe, milling machine, and drilling machine – construction and kinematics; machining processes - turning, taper turning, thread cutting, drilling, boring, milling, gear cutting, thread production, grinding; geometry of single point cutting tools, chip formation, cutting forces, specific cutting energy and power requirements, Merchant’s analysis; basis of selection of machining parameters; tool materials, tool wear and tool life, economics of machining, thermal aspects of machining, cutting fluids, machinability; Jigs and fixtures – principles, applications, and design.
Non-traditional Manufacturing: Principles, applications, effect of process parameters on MRR and product quality of non-traditional machining processes – USM, AJM, WJM, AWJM, EDM and Wire cut EDM, LBM, EBM, PAM, CHM, ECM.
Computer Integrated Manufacturing: Basic concepts of CAD – geometric modeling, CAM – CNC and robotics – configurations, drives and controls, Group Technology and its applications – CAPP, cellular manufacturing and FMS.
Section 5: Quality and Reliability
Metrology and Inspection: Limits, fits, and tolerances, gauge design, interchangeability, selective assembly; linear, angular, and form measurements(straightness, squareness, flatness, roundness, and cylindricity) by mechanical and optical methods; inspection of screw threads and gears; surface finish measurement by contact and non-contact methods;tolerance analysis in manufacturing and assembly.
Quality management: Quality – concept and costs; quality assurance; statistical quality control, acceptance sampling, zero defects, six sigma; total quality management; ISO 9000.
Reliability and Maintenance: Reliability, availability and maintainability; distribution of failure and repair times; determination of MTBF and MTTR, reliability models; determination of system reliability; preventive maintenance and replacement.
Section 6: Industrial Engineering
Product Design and Development: Principles of good product design, tolerance design; quality and cost considerations; product life cycle; standardization, simplification, diversification, value engineering and analysis, concurrent engineering;comparison of production alternatives.
Work System Design: Taylor’s scientific management, Gilbreths’s contributions; productivity – concepts and measurements; method study, micro-motion study, principles of motion economy; work measurement –time study, work sampling, standard data, PMTS; ergonomics; job evaluation, merit rating, incentive schemes, and wage administration.
Facility Design: Facility location factors and evaluation of alternate locations; types of plant layout and their evaluation; computer aided layout design techniques; assembly line balancing; materials handling systems.
Section 7: Operations research and Operations management
Operation Research: Linear programming – problem formulation, simplex method, duality and sensitivity analysis; transportation and assignment models; network flow models, constrained optimization and Lagrange multipliers; Markovian queuing models; dynamic programming; simulation – manufacturing applications.
Engineering Economy and Costing: Elementary cost accounting and methods of depreciation; break-even analysis, techniques for evaluation of capital investments, financial statements, time-cost trade-off, resource leveling.
Production control: Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; aggregate production planning; master production scheduling; MRP and MRP-II; routing, scheduling and priority dispatching; Push and pull production systems, concept of JIT manufacturing system; Logistics, distribution, and supply chain management; Inventory – functions, costs, classifications, deterministic inventory models, quantity discount; perpetual and periodic inventory control systems.
Project management – PERT and CPM.
Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value
Read MoreEngineering Mathematics
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.
Differential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –Laplace, heat and wave equations.
Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.
Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.
Textile Engineering and Fibre Science
Section 1: Textile Fibers
Classification of textile fibers; Essential requirements of fiber forming polymers; Gross and fine structure of natural fibers like cotton, wool, silk, Introduction to important bast fibres; properties and uses of natural and man- made fibres including carbon, aramid and ultra high molecular weight polyethylene (UHMWPE) fibers; physical and chemical methods of fiber and blend identification and blend analysis.
Molecular architecture, amorphous and crystalline phases, glass transition, plasticization, crystallization, melting, factors affecting Tg and Tm; Production process of viscose and other regenerated cellulosic fibres such as polynosic, lyocell. Polymerization of nylon-6, nylon-66, poly (ethylene terephthalate), polyacrylonitrile and polypropylene; Melt Spinning processes for PET, polyamide and polypropylene; Wet and dry spinning processes for viscose and acrylic fibres; post spinning operations such as drawing, heat setting, tow- to-top conversion and different texturing methods.
Methods of investigating fibre structure e.g., Density, X-ray diffraction, birefringence, optical and electron microscopy, I.R. spectroscopy, thermal methods (DSC, DMA/TMA, TGA); structure and morphology of man-made fibres, mechanical properties of fibres, moisture sorption in fibres; fibre structure and property correlation.
Section 2: Yarn manufacture, Yarn structure and Properties
Principles of opening, cleaning and mixing/blending of fibrous materials, working principle of modern opening and cleaning equipment; the technology of carding, carding of cotton and synthetic fibres; Drafting operation, roller and apron drafting principle, causes of mass irregularity introduced by drafting; roller arrangements in drafting systems; principles of cotton combing, combing cycle, mechanism and function, combing efficiency, lap preparation; recent developments in comber; Roving production, mechanism of bobbin building, roving twist; Principle of ring spinning, forces acting on yarn and traveler, ring & traveler designs, mechanism of cop formation, causes of end breakages; Working principle of ring doubler and two for one twister, single and folded yarn twist, properties of double yarns, production of core spun yarn; Principles of compact, rotor, air jet, air vortex, core, wrap, twist less and friction spinning.
Yarn contraction, yarn diameter, specific volume & packing coefficient; Twist factor, twist strength relationship in spun yarns; Fibre configuration and orientation in yarn; Cause of fibre migration and its estimation; Irregularity index; Structure property relationship of compact ring, rotor, air-jet and friction spun yarns.
Section 3: Fabric manufacture, Structure and Properties
Principles of winding processes and machines, random, precision and step precision winding, package faults and their remedies; Yarn clearers and tensioners; Different systems of yarn splicing; Features of modern cone winding machines; Different types of warping creels; features of modern beam and sectional warping machines; Different sizing systems, sizing of spun and filament yarns, sizing machines; Principles of pirn winding processes and machines.
Primary and secondary motions of loom, cam design & kinematics of sley, effect of their settings and timings on fabric formation, fabric appearance and weaving performance; Dobby and jacquard shedding; Mechanics of weft insertion with shuttle, warp and weft stop motions, warp protection, weft replenishment; Principles of weft insertion systems of shuttle-less weaving machines; Principles of multiphase and circular looms.
Principles of weft and warp knitting, basic weft and warp knitted structures; Classification, production, properties and application of nonwoven fabrics, principle of web formation & bonding.
Basic woven fabric constructions and their derivatives; crepe, cord, terry, gauze, leno and double cloth constructions. Peirce’s equations for fabric geometry; elastica model of plain woven fabrics; thickness, cover and maximum set of woven fabrics.
Section 4: Textile Testing
Sampling techniques, sample size and sampling errors; Measurement of fibre length, fineness, crimp; measurement of cotton fiber maturity and trash content; High volume fibre testing; Measurement of yarn count, twist and hairiness; Tensile testing of fibers, yarns and fabrics; Evenness testing of slivers, rovings and yarns; Classimat fault analysis; Testing equipment for measurement of fabric properties like thickness, compressibility, air permeability, wetting & wicking, drape, crease recovery, tear strength, bursting strength and abrasion resistance; Instruments and systems for objective evaluation of fabric hand. Statistical analysis of experimental results, frequency distributions, correlation, significance tests, analysis of variance and control charts.
Section 5: Chemical processing
Impurities in natural fibre; Chemistry and practice of preparatory processes for cotton, wool and silk; Mercerization of cotton; Preparatory processes for manmade fibres and their blends.
Classification of dyes; Dyeing of cotton, wool, silk, polyester, nylon and acrylic with appropriate dye classes; Dyeing of polyester/cotton and polyester/wool blends; Dyeing machines; Dyeing of cotton knitted fabrics and machines used; Dye fibre interaction; Introduction to thermodynamics and kinetics of dyeing; Methods for determination of wash, light and rubbing fastness.
Styles of printing; Printing thickeners including synthetic thickeners; Printing auxiliaries; Printing of cotton with reactive dyes, wool, silk, nylon with acid and metal complex dyes, Printing of polyester with disperse dyes; Pigment printing; Resist and discharge printing of cotton, silk and polyester; Transfer printing of polyester; Inkjet printing.
Mechanical finishing of cotton. Stiff, soft, wrinkle resistant, water repellent, flame retardant and enzyme (bio-polishing) finishing of cotton; Milling, decatizing and shrink resistant finishing of wool; Antistatic and soil release finishing; Heat setting of synthetic fabrics; Minimum application techniques; Pollution control and treatment of effluents.
Engineering Mathematics Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors. Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; S
Read MoreGATE 2018 Application Form
The brief details of GATE Registration is given below:
GATE 2018 Applications Correction
GATE 2018 Application Form The brief details of GATE Registration is given below: All the candidates have to apply online only. GATE registration 2018 will be started from the
Read MoreGATE 2018 Admit Card
GATE 2018 Admit Card The GATE 2018 Admit Card will be available on the official site from 1st week of January 2018. The candidates have to log in to the GOAPS by using their enrollment ID and email address. This is one of the mos
Read MoreGATE 2018 Results:
GATE 2018 Results Date will be confirmed by the official’s hopeful candidates who have appeared or going to appear for the examination need to wait for few date after writing the examination to check their results, As per the IIT Exam Schedule released by the official on official website www.gate.iitr.ernet.In, the GATE 2018 Result or GATE Result 2018 is going to be announced on 27 March 2018. The aspirants can check their most awaited GATE Result 2018 from the links provided or directly through the official website. Till then you can check Answer Keys with or without question paper. You can also Check GATE 2018 Answer Keys till results are out. After the declaration of result, you can check your Gate 2018 Results Name Wise, School Wise, Roll.No Wise, Subject Wise, Branch Wise, State Wise or District Wise nothing but Zone Wise or Region Wise.
How to Check GATE 2018 Results:
GATE 2018 Results: GATE 2018 Results Date will be confirmed by the official’s hopeful candidates who have appeared or going to appear for the examination need to wait for few date after writing the examination to check their results, As per the IIT Exam Schedule rel
Read MoreGATE 2018 Score Card
GATE 2018 Score Card Score card reflects the candidate’s performance in entrance test. The qualified candidates are provided with a GATE score card. The Score Card will be having the validity of three years from the date of announcement of
Read MoreGATE Exam Centres
You have to choose three cities as your first, second and third choices. There is no restriction on the second and third chosen city to be in the same GATE zone as the first chosen city.
Zone |
GATE 2017 |
GATE 2017 Exam Cities |
1 |
IISc Bangalore |
Ananthapur, Bagalkot, Bengaluru, Bellary, Belgaum, Bidar, |
2 |
IIT Bombay |
Ahmedabad, Ahmednagar, Amravati, Anand, Aurangabad,Bhavnagar, |
3 |
IIT Delhi |
Ajmer, Alwar, Bahadurgarh, Bikaner, New Delhi, Faridabad, |
4 |
IIT Guwahati |
Agartala, Asansol, Dhanbad, Durgapur, Gangtok, Guwahati,Imphal, |
5 |
IIT Kanpur |
Agra, Aligarh, Allahabad, Bareilly, Bhopal, Gwalior, Jabalpur,Kanpur, |
6 |
IIT Kharagpur |
Balasore, Berhampur (Odisha), Bhilai, Bhimavaram, Bhubaneswar, |
7 |
IIT Madras |
Alappuzha, Aluva, Angamaly, Attingal, Bapatla, Chennai,Chengannur, |
8 |
IIT Roorkee |
Ambala, Amritsar, Bathinda, Bhimtal, Dehradun, Ghaziabad,Haldwani, |
9 |
Centres abroad |
Addis Ababa (Ethiopia), Colombo (Sri Lanka), Dhaka |
GATE Exam Centres You have to choose three cities as your first, second and third choices. There is no restriction on the second and third chosen city to be in the same GATE zone as the first chosen city.
Read MoreGATE 2018 Counselling
The GATE 2018 Result will be declared in the month of March 2018 at the official website of www.gate.iitr.ernet.in. So, the candidates those who have qualified in the GATE Exam 2018 are eagerly looking for the GATE 2018 Counselling Process. Students who taken the GATE Exam 2018 on various exam dates need to check the GATE counselling Dates Here. Depending on your GATE Score, you will provide the Admission into IISC and various IITs along with other NITs & top colleges in India. By this GATE 2018 CCMT(Centralized Counselling for M.Tech. / M.Arch./ M.Plan. Admissions) Counselling Process, you will get an Admission into various PG Courses which are offered by the NITs & Other popular colleges in India. Read this article and get the Complete details of GATE 2018 counselling Process like Documents required for GATE CCMT Counselling, GATE Counselling Exam Dates, Steps to go for MTech counselling 2018 through GATE.
Important Steps for Gate Counselling
Above you will provide the GATE CCMT 2018 Counselling Process to make the Process easy. The CCMT(Centralized Counselling for M.Tech. / M.Arch./ M.Plan. Admissions) conducts online admission process which is organized to provide admission into NITs and Other Institutions. The GATE 2018 Counselling process consists of three rounds as follows. Before going to attend the GATE 2018 Counselling Schedule, please go through the steps listed below.
Step I:
During the First Step, all the candidates are required to registered themselves at the official CCMT Website. After the Registration Process, you have to pay the registration fee as per their Category. After successful completion of fee payment, you are going to fill the choice of specializations in order. During the Choice Filling Process, you are requested to lock the filled choices.
Step II:
In next step, the officials allocated the seats to the Students based on their GATE Score and choice of Programmes. Once the candidate received the Seat allotment, you are requested to deposit the seat acceptance letter to the respective center and pay the Course Fee along with all the documents.
Step III: Finally, download the Seat allotment order from the official website and submit to the respective colleges for final submission.
Required Documents for GATE 2018 Counselling Process
GATE 2018 Counselling The GATE 2018 Result will be declared in the month of March 2018 at the official website of www.gate.iitr.ernet.in. So, the candidates those who have qualified in the GATE Exam 2018 are eagerly looking for the GATE 2018 Counselling Process. Students
Read MoreList of Documents/ Data required (Indian Candidates)
As GATE 2017 is going international as well excluding Pakistan the below list of documents will be required for international candidates.
Documents/ Data required (International Candidates)
List of Documents/ Data required (Indian Candidates) Personal information (name, date of birth, your personal mobile number, parent’s name, parent’s mobile number, etc) Address for Communication (including PIN code)
Read MoreGATE Preparation 2018
GATE 2018 Strategy should be well thought of as this will determine your GATE 2018 Score. So, here is a step wise list to tell you How to crack GATE 2018.
GATE Preparation 2018 GATE 2018 Strategy should be well thought of as this will determine your GATE 2018 Score. So, here is a step wise list to tell you How to crack GATE 2018. Determine your stream : This exam has some rela
Read MoreA: Engineering Mathematics (Compulsory)
Section 1: Linear Algebra
Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices; Cayley-Hamilton Theorem.
Section 2: Calculus
Functions of single variable: Limit, continuity and differentiability; Mean value theorems; Indeterminate forms and L'Hospital's rule; Maxima and minima; Taylor's theorem; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.
Functions of two variables: Limit, continuity and partial derivatives; Directional derivative; Total derivative; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications.
Sequence and series: Convergence of sequence and series; Tests for convergence; Power series; Taylor's series; Fourier Series; Half range sine and cosine series.
Section 3: Vector Calculus
Gradient, divergence and curl; Line and surface integrals; Green's theorem, Stokes theorem and Gauss divergence theorem (without proofs).
Section 4: Complex variables
Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy's integral theorem and integral formula (without proof); Taylor's series and Laurent series; Residue theorem (without proof) and its applications.
Section 5: Ordinary Differential Equations
First order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.
Section 6: Partial Differential Equations
Classification of second order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one dimensional heat and wave equations.
Section 7: Probability and Statistics
Axioms of probability; Conditional probability; Bayes' Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.
Section 8: Numerical Methods
Solution of systems of linear equations using LU decomposition, Gauss elimination and Gauss-Seidel methods; Lagrange and Newton's interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson's rule and Gaussian quadrature rule; Numerical solutions of first order differential equations by Euler's method and 4th order Runge-Kutta method.
B: Fluid Mechanics
Section 1: Flow and Fluid Properties
Viscosity, relationship between stress and strain-rate for Newtonian fluids, incompressible and compressible flows, differences between laminar and turbulent flows. Hydrostatics: Buoyancy, manometry, forces on submerged bodies.
Section 2: Kinematics
Eulerian and Lagrangian description of fluids motion, concept of local and convective accelerations, steady and unsteady flows.
Section 3: Integral analysis
Control volume analysis for mass, momentum and energy.
Section 4: Differential Analysis
Differential equations of mass and momentum for incompressible flows: inviscid - Euler equation and viscous flows - Navier-Stokes equations, concept of fluid rotation, vorticity, stream function, Exact solutions of Navier-Stokes equation for Couette Flow and Poiseuille flow.
Section 5: Inviscid flows
Bernoulli’s equation - assumptions and applications, potential function, Elementary plane flows - uniform flow, source, sink and doublet and their superposition for potential flow past simple geometries.
Section 6: Dimensional analysis
Concept of geometric, kinematic and dynamic similarity, some common non-dimensional parameters and their physical significance: Reynolds number, Froude number and Mach number.
Section 7: Internal flows
Fully developed pipe flow, empirical relations for laminar and turbulent flows: friction factor and Darcy-Weisbach relation.
Section 8: Prandtl boundary layer equations
Concept and assumptions, qualitative idea of boundary layer and separation, streamlined and bluff bodies, drag and lift forces. Flow measurements: Basic ideas of flow measurement using venturimeter, pitot-static tube and orifice plate.
C: Materials Science
Section 1: Processing of Materials:
Powder synthesis, sintering, chemical methods, crystal growth techniques, zone refining, preparation of nanoparticles and thin films
Section 2: Characterisation Techniques:
X-ray diffraction, spectroscopic techniques like UV-vis, IR, Raman. Optical and Electron microscopy
Section 3: Structure and Imperfections:
Crystal symmetry, point groups, space groups, indices of planes, close packing in solids, bonding in materials, coordination and radius ratio concepts, point defects, dislocations, grain boundaries, surface energy and equilibrium shapes of crystals
Section 4: Thermodynamics and Kinetics:
Phase rule, phase diagrams, solid solutions, invariant reactions, lever rule, basic heat treatment of metals, solidification and phase transformations, Fick’s laws of diffusion, mechanisms of diffusion, temperature dependence of diffusivity
Section 5: Properties of Materials:
Mechanical Properties: Stress-strain response of metallic, ceramic and polymer materials, yield strength, tensile strength and modulus of elasticity, toughness, plastic deformation, fatigue, creep and fracture
Electronic Properties: Free electron theory, Fermi energy, density of states, elements of band theory, semiconductors, Hall effect, dielectric behaviour, piezo, ferro, pyroelectric materials
Magnetic Properties: Origin of magnetism in metallic and ceramic materials, paramagnetism, diamagnetism, ferro and ferrimagnetism
Thermal Properties: Specific heat, thermal conductivity and thermal expansion, thermoelectricity
Optical Properties: Refractive index, absorption and transmission of electromagnetic radiation in solids, electrooptic and magnetoopticmaterials, spontaneous and stimulated emission, gas and solid state lasers
Section 6: Material types
Concept of amorphous, single crystals and polycrystalline materials, crystallinity and its effect on physical properties, metal, ceramic, polymers, classification of polymers, polymerization, structure and properties, additives for polymer products, processing and applications, effect of environment on materials, composites
Section 7: Environmental Degradation
Corrosion, oxidation and prevention
Section 8: Elements of Quantum Mechanics and Mathematics
Basics of quantum mechanics, quantum mechanical treatment of electrical, optical and thermal properties of materials, analytical solid geometry, differentiation and integration, differential equations, vectors and tensors, matrices, Fourier series, complex analysis, probability and statistics
D: Solid Mechanics
Equivalent force systems; free-body diagrams; equilibrium equations; analysis of determinate trusses and frames; friction; simple relative motion of particles; force as function of position, time and speed; force acting on a body in motion; laws of motion; law of conservation of energy; law of conservation of momentum.
Stresses and strains; principal stresses and strains; Mohr’s circle; generalized Hooke’s Law; thermal strain; theories of failure.
Axial, shear and bending moment diagrams; axial, shear and bending stresses; deflection (for symmetric bending); torsion in circular shafts; thin cylinders; energy methods (Castigliano’s Theorems); Euler buckling.
Free vibration of single degree of freedom systems.
E: Thermodynamics
Section 1: Basic Concepts
Continuum and macroscopic approach; thermodynamic systems (closed and open); thermodynamic properties and equilibrium; state of a system, state postulate for simple compressible substances, state diagrams, paths and processes on state diagrams; concepts of heat and work, different modes of work; zeroth law of thermodynamics; concept of temperature.
Section 2: First Law of Thermodynamics
Concept of energy and various forms of energy; internal energy, enthalpy; specific heats; first law applied to elementary processes, closed systems and control volumes, steady and unsteady flow analysis.
Section 3: Second Law of Thermodynamics
Limitations of the first law of thermodynamics, concepts of heat engines and heat pumps/refrigerators, Kelvin-Planck and Clausius statements and their equivalence; reversible and irreversible processes; Carnot cycle and Carnot principles/theorems; thermodynamic temperature scale; Clausius inequality and concept of entropy; microscopic interpretation of entropy, the principle of increase of entropy, T-s diagrams; second law analysis of control volume; availability and irreversibility; third law of thermodynamics.
Section 4: Properties of Pure Substances
Thermodynamic properties of pure substances in solid, liquid and vapor phases; P-vT behaviour of simple compressible substances, phase rule, thermodynamic property tables and charts, ideal and real gases, ideal gas equation of state and van der Waals equation of state; law of corresponding states, compressibility factor and generalized compressibility chart.
Section 5: Thermodynamic Relations
T-ds relations, Helmholtz and Gibbs functions, Gibbs relations, Maxwell relations, Joule-Thomson coefficient, coefficient of volume expansion, adiabatic and isothermal compressibilities, Clapeyron and Clapeyron-Clausius equations.
Section 6: Thermodynamic Cycles
Carnot vapor cycle, ideal Rankine cycle, Rankine reheat cycle, air-standard Otto cycle, air-standard Diesel cycle, air-standard Brayton cycle, vapor-compression refrigeration cycle.
Section 7: Ideal Gas Mixtures
Dalton’s and Amagat’s laws, properties of ideal gas mixtures, air-water vapor mixtures and simple thermodynamic processes involving them; specific and relative humidities, dew point and wet bulb temperature, adiabatic saturation temperature, psychrometric chart.
F: Polymer Science and Engineering
Section 1: Chemistry of high polymers
Monomers, functionality, degree of polymerizations, classification of polymers, glass transition, melting transition, criteria for rubberiness, polymerization methods: addition and condensation; their kinetics, metallocene polymers and other newer techniques of polymerization, copolymerization, monomer reactivity ratios and its significance, kinetics, different copolymers, random, alternating, azeotropic copolymerization, block and graft copolymers, techniques for copolymerizationbulk, solution, suspension, emulsion.
Section 2: Polymer Characterization
Solubility and swelling, concept of average molecular weight, determination of number average, weight average, viscosity average and Z-average molecular weights, polymer crystallinity, analysis of polymers using IR, XRD, thermal (DSC, DMTA, TGA), microscopic (optical and electronic) techniques.
Section 3: Synthesis and properties
Commodity and general purpose thermoplastics: PE, PP, PS, PVC, Polyesters, Acrylic, PU polymers. Engineering Plastics: Nylon, PC, PBT, PSU, PPO, ABS, Fluoropolymers Thermosetting polymers: PF, MF, UF, Epoxy, Unsaturated polyester, Alkyds. Natural and synthetic rubbers: Recovery of NR hydrocarbon from latex, SBR, Nitrile, CR, CSM, EPDM, IIR, BR, Silicone, TPE.
Section 4: Polymer blends and composites
Difference between blends and composites, their significance, choice of polymers for blending, blend miscibility-miscible and immiscible blends, thermodynamics, phase morphology, polymer alloys, polymer eutectics, plastic-plastic, rubber-plastic and rubber-rubber blends, FRP, particulate, long and short fibre reinforced composites.
Section 5: Polymer Technology
Polymer compounding-need and significance, different compounding ingredients for rubber and plastics, cross-linking and vulcanization, vulcanization kinetics.
Section 6: Polymer rheology
Flow of Newtonian and non-Newtonian fluids, different flow equations, dependence of shear modulus on temperature, molecular/segmental deformations at different zones and transitions. Measurements of rheological parameters by capillary rotating, parallel plate, cone-plate rheometer. Viscoelasticity-creep and stress relaxations, mechanical models, control of rheological characteristics through compounding, rubber curing in parallel plate viscometer, ODR and MDR.
Section 7: Polymer processing
Compression molding, transfer molding, injection molding, blow molding, reaction injection molding, extrusion, pultrusion, calendaring, rotational molding, thermoforming, rubber processing in two-roll mill, internal mixer.
Section 8: Polymer testing
Mechanical-static and dynamic tensile, flexural, compressive, abrasion, endurance, fatigue, hardness, tear, resilience, impact, toughness. Conductivity-thermal and electrical, dielectric constant, dissipation factor, power factor, electric resistance, surface resistivity, volume resistivity, swelling, ageing resistance, environmental stress cracking resistance.
G: Food Technology
Section 1: Food Chemistry and Nutrition
Carbohydrates: structure and functional properties of mono-, oligo-, & polysaccharides including starch, cellulose, pectic substances and dietary fibre, gelatinization and retrogradation of starch. Proteins: classification and structure of proteins in food, biochemical changes in post mortem and tenderization of muscles. Lipids: classification and structure of lipids, rancidity, polymerization and polymorphism. Pigments: carotenoids, chlorophylls, anthocyanins, tannins and myoglobin. Food flavours: terpenes, esters, aldehydes, ketones and quinines. Enzymes: specificity, simple and inhibition kinetics, coenzymes, enzymatic and nonenzymatic browning. Nutrition: balanced diet, essential amino acids and essential fatty acids, protein efficiency ratio, water soluble and fat soluble vitamins, role of minerals in nutrition, co-factors, anti-nutrients, nutraceuticals, nutrient deficiency diseases. Chemical and biochemical changes: changes occur in foods during different processing.
Section 2: Food Microbiology
Characteristics of microorganisms: morphology of bacteria, yeast, mold and actinomycetes, spores and vegetative cells, gram-staining. Microbial growth: growth and death kinetics, serial dilution technique. Food spoilage: spoilage microorganisms in different food products including milk, fish, meat, egg, cereals and their products. Toxins from microbes: pathogens and non-pathogens including Staphylococcus, Salmonella, Shigella, Escherichia, Bacillus, Clostridium, and Aspergillus genera. Fermented foods and beverages: curd, yoghurt, cheese, pickles, soya-sauce, sauerkraut, idli, dosa, vinegar, alcoholic beverages and sausage.
Section 3: Food Products Technology
Processing principles: thermal processing, chilling, freezing, dehydration, addition of preservatives and food additives, irradiation, fermentation, hurdle technology, intermediate moisture foods. Food packaging and storage: packaging materials, aseptic packaging, controlled and modified atmosphere storage. Cereal processing and products: milling of rice, wheat, and maize, parboiling of paddy, bread, biscuits, extruded products and ready to eat breakfast cereals. Oil processing: expelling, solvent extraction, refining and hydrogenation. Fruits and vegetables processing: extraction, clarification, concentration and packaging of fruit juice, jam, jelly, marmalade, squash, candies, tomato sauce, ketchup, and puree, potato chips, pickles. Plantation crops processing and products: tea, coffee, cocoa, spice, extraction of essential oils and oleoresins from spices. Milk and milk products processing: pasteurization and sterilization, cream, butter, ghee, icecream, cheese and milk powder. Processing of animal products: drying, canning, and freezing of fish and meat; production of egg powder. Waste utilization: pectin from fruit wastes, uses of by-products from rice milling. Food standards and quality maintenance: FPO, PFA, Agmark, ISI, HACCP, food plant sanitation and cleaning in place (CIP).
Section 4: Food Engineering
Mass and energy balance; Momentum transfer: Flow rate and pressure drop relationships for Newtonian fluids flowing through pipe, Reynolds number. Heat transfer: heat transfer by conduction, convection, radiation, heat exchangers. Mass transfer: molecular diffusion and Fick’s law, conduction and convective mass transfer, permeability through single and multilayer films. Mechanical operations: size reduction of solids, high pressure homogenization, filtration, centrifugation, settling, sieving, mixing & agitation of liquid. Thermal operations: thermal sterilization, evaporation of liquid foods, hot air drying of solids, spray and freeze-drying, freezing and crystallization. Mass transfer operations: psychrometry, humidification and dehumidification operations.
H. Atmospheric & Ocean Science
Section A: Atmospheric Science
Fundamental of Meteorology, Thermal structure of the atmosphere and its composition, Radiation Balance and Laws, Wind Belts, Monsoon, Climate. Atmospheric Thermodynamics. Hydrostatic equilibrium and: Hydrostatic equation, variation of pressure with height, geopotential, Tropical convection. Atmospheric Electricity. Cloud Physics. Observation Techniques of the Atmosepheric Properties.
Fundamental equations. Pressure, gravity, centripetal and Corolis forces, continuity equation in Cartesian and isobaric coordinates, Scale analysis, inertial flow, geostrophic and gradient winds, thermal wind, vorticity. Atmospheric turbulence, baroclinic instabiltiy. Atmosphreric Waves. Tropical meteorology: Trade wind inversion, ITCZ; monsoon trough tropical cyclones, their structure and development theory; monsoon depressions; Climate variability and forcings; Madden-Julian oscillation (MJO), ENSO, QBO (quasi-biennial oscillation) and sunspot cycles. Primitive equations of Numerical Weather Prediction. General Circulation and Climate Modelling. Synoptic weather forecasting, prediction of weather elements such as rain, maximum and minimum temperature and fog. Data Assimilation.
Section B: Ocean Sciences
Seawater Properties, T-S diagrams, Ocean Observations, Ocean Tide and Waves and their properties. Coastal processes and Estuary Dynamics. coastal zone management. Wind Driven Circulation: Ekman, Sverdrup, Stommel and Munk theories, Inertial currents; geostrophic motion; barotropic and baroclinic conditions; Oceanic eddies. Global conveyor belt circulation. Subtropical gyres; Western boundary currents; equatorial current systems; Current System in the Indian Ocean.
Momentum equation, mass conservation, vorticity. Ocean and Wave Modeling, Ocean State Forecasting. Data Assimilation. Ocean Turbulence. Chemical Property of seawater, major and minor elements, their behavior and chemical exchanges across interfaces and residence times in seawater, Element chemistry in atypical conditions-estuaries, Biochemical cycling of nutrients, trace metals and organic matter. Air-sea exchange of important biogenic dissolved gases; carbon dioxide-carbonate system; alkalinity and control of pH; biological pump. Marine Pollution. Primary and secondary production; factors controlling phytoplankton and zooplankton abundance and diversity; nekton and fisheries oceanography.
A: Engineering Mathematics (Compulsory) Section 1: Linear Algebra Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors; Diagona
Read MoreP: Chemistry (Compulsory)
Section 1: Atomic Structure and Periodicity
Planck’s quantum theory, wave particle duality, uncertainty principle, quantum mechanical model of hydrogen atom, electronic configuration of atoms and ions. Periodic table and periodic properties: ionization energy, electron affinity, electronegativity and atomic size.
Section 2: Structure and Bonding
Ionic and covalent bonding, MO and VB approaches for diatomic molecules, VSEPR theory and shape of molecules, hybridization, resonance, dipole moment, structure parameters such as bond length, bond angle and bond energy, hydrogen bonding and van der Waals interactions. Ionic solids, ionic radii and lattice energy (Born‐Haber cycle). HSAB principle.
Section 3: s, p and d Block Elements
Oxides, halides and hydrides of alkali, alkaline earth metals, B, Al, Si, N, P, and S. General characteristics of 3d elements. Coordination complexes: valence bond and crystal field theory, color, geometry, magnetic properties and isomerism.
Section 4: Chemical Equilibria
Colligative properties of solutions, ionic equilibria in solution, solubility product, common ion effect, hydrolysis of salts, pH, buffer and their applications. Equilibrium constants (Kc, Kp and Kx) for homogeneous reactions.
Section 5: Electrochemistry
Conductance, Kohlrausch law, cell potentials, emf, Nernst equation, Galvanic cells, thermodynamic aspects and their applications.
Section 6: Reaction Kinetics
Rate constant, order of reaction, molecularity, activation energy, zero, first and second order kinetics, catalysis and elementary enzyme reactions.
Section 7: Thermodynamics
First law, reversible and irreversible processes, internal energy, enthalpy, Kirchoff equation, heat of reaction, Hess’s law, heat of formation. Second law, entropy, free energy and work function. Gibbs‐Helmholtz equation, Clausius‐Clapeyron equation, free energy change, equilibrium constant and Trouton’s rule. Third law of thermodynamics.
Section 8: Structure-Reactivity Correlations and Organic Reaction Mechanisms
Acids and bases, electronic and steric effects, optical and geometrical isomerism, tautomerism, conformers and concept of aromaticity. Elementary treatment of S_{N}1, S_{N}2, E1 and E2 reactions, Hoffmann and Saytzeff rules, addition reactions, Markownikoff rule and Kharash effect. Aromatic electrophilic substitutions, orientation effect as exemplified by various functional groups. Diels‐Alder, Wittig and hydroboration reactions. Identification of functional groups by chemical tests.
Q: Biochemistry
Section 1:
Organization of life; Importance of water; Structure and function of biomolecules: Amino acids, Carbohydrates, Lipids, Proteins and Nucleic acids; Protein structure, folding and function: Myoglobin, Hemoglobin, Lysozyme, Ribonuclease A, Carboxypeptidase and Chymotrypsin.
Section 2:
Enzyme kinetics including its regulation and inhibition, Vitamins and Coenzymes ; Metabolism and bioenergetics; Generation and utilization of ATP; Metabolic pathways and their regulation: glycolysis, TCA cycle, pentose phosphate pathway, oxidative phosphorylation,gluconeogenesis, glycogen and fatty acid metabolism; Metabolism of Nitrogen containing compounds: nitrogen fixation, amino acids and nucleotides. Photosynthesis: Calvin cycle.
Section 3:
Biochemical separation techniques: ion exchange, size exclusion and affinity chromatography, Characterization of biomolecules by electrophoresis, UV-visible and fluorescence spectroscopy and Mass spectrometry.
Section 4:
Cell structure and organelles; Biological membranes; Transport across membranes; Signal transduction; Hormones and neurotransmitters.
Section 5:
DNA replication, transcription and translation; Biochemical regulation of gene expression; Recombinant DNA technology and applications: PCR, site directed mutagenesis and DNA-microarray.
Section 6:
Immune system: Active and passive immunity; Complement system; Antibody structure, function and diversity; Cells of the immune system: T, B and macrophages; T and B cell activation; Major histocompatibilty complex; T cell receptor; Immunological techniques: Immunodiffusion, immunoelectrophoresis, RIA and ELISA.
R: Botany
Section 1: Plant Systematics
Major systems of classification, plant groups, phylogenetic relationships and molecular systematics.
Section 2: Plant Anatomy
Plant cell structure and its components; cell wall and membranes; organization, organelles, cytoskeleton, anatomy of root, stem and leaves, floral parts, embryo and young seedlings, meristems, vascular system, their ontogeny, structure and functions, secondary growth in plants and stellar organization.
Section 3: Morphogenesis & Development
Cell cycle, cell division, life cycle of an angiosperm, pollination, fertilization, embryogenesis, seed formation, seed storage proteins, seed dormancy and germination.
Concept of cellular totipotency, clonal propagation; organogenesis and somatic embryogenesis, artificial seed, somaclonal variation, secondary metabolism in plant cell culture, embryo culture, in vitro fertilization.
Section 4: Physiology and Biochemistry
Plant water relations, transport of minerals and solutes, stress physiology, stomatal physiology, signal transduction, N2 metabolism, photosynthesis, photorespiration; respiration, Flowering: photoperiodism and vernalization, biochemical mechanisms involved in flowering; molecular mechanism of senencensce and aging, biosynthesis, mechanism of action and physiological effects of plant growth regulators, structure and function of biomolecules, (proteins, carbohydrates, lipids, nucleic acid), enzyme kinetics.
Section 5: Genetics
Principles of Mendelian inheritance, linkage, recombination, genetic mapping; extrachromosomal inheritance; prokaryotic and eukaryotic genome organization, regulation of gene expression, gene mutation and repair, chromosomal aberrations (numerical and structural), transposons.
Section 6: Plant Breeding and Genetic Modification
Principles, methods – selection, hybridization, heterosis; male sterility, genetic maps and molecular markers, sporophytic and gametophytic self incompability, haploidy, triploidy, somatic cell hybridization, marker-assisted selection, gene transfer methods viz. direct and vector-mediated, plastid transformation, transgenic plants and their application in agriculture, molecular pharming, plantibodies.
Section 7: Economic Botany
A general account of economically and medicinally important plants- cereals, pulses, plants yielding fibers, timber, sugar, beverages, oils, rubber, pigments, dyes, gums, drugs and narcotics. Economic importance of algae, fungi, lichen and bacteria.
Section 8: Plant Pathology
Nature and classification of plant diseases, diseases of important crops caused by fungi, bacteria,nematodes and viruses, and their control measures, mechanism(s) of pathogenesis and resistance, molecular detection of pathogens; plant-microbe beneficial interactions.
Section 9: Ecology and Environment
Ecosystems – types, dynamics, degradation, ecological succession; food chains and energy flow; vegetation types of the world, pollution and global warming, speciation and extinction, conservation strategies, cryopreservation, phytoremediation.
S: Microbiology
Section 1: Historical Perspective
Discovery of microbial world; Landmark discoveries relevant to the field of microbiology; Controversy over spontaneous generation; Role of microorganisms in transformation of organic matter and in the causation of diseases.
Section 2: Methods in Microbiology
Pure culture techniques; Theory and practice of sterilization; Principles of microbial nutrition; Enrichment culture techniques for isolation of microorganisms; Light-, phase contrast- and electron-microscopy.
Section 3: Microbial Taxonomy and Diversity
Bacteria, Archea and their broad classification; Eukaryotic microbes: Yeasts, molds and protozoa; Viruses and their classification; Molecular approaches to microbial taxonomy.
Section 4: Prokaryotic and Eukaryotic Cells: Structure and Function
Prokaryotic Cells: cell walls, cell membranes, mechanisms of solute transport across membranes, Flagella and Pili, Capsules, Cell inclusions like endospores and gas vesicles; Eukaryotic cell organelles: Endoplasmic reticulum, Golgi apparatus, mitochondria and chloroplasts.
Section 5: Microbial Growth
Definition of growth; Growth curve; Mathematical expression of exponential growth phase; Measurement of growth and growth yields; Synchronous growth; Continuous culture; Effect of environmental factors on growth.
Section 6: Control of Micro-organisms
Effect of physical and chemical agents; Evaluation of effectiveness of antimicrobial agents.
Section 7: Microbial Metabolism
Energetics: redox reactions and electron carriers; An overview of metabolism; Glycolysis; Pentose-phosphate pathway; Entner-Doudoroff pathway; Glyoxalate pathway; The citric acid cycle; Fermentation; Aerobic and anaerobic respiration; Chemolithotrophy; Photosynthesis; Calvin cycle; Biosynthetic pathway for fatty acids synthesis; Common regulatory mechanisms in synthesis of amino acids; Regulation of major metabolic pathways.
Section 8: Microbial Diseases and Host Pathogen Interaction
Normal microbiota; Classification of infectious diseases; Reservoirs of infection; Nosocomial infection; Emerging infectious diseases; Mechanism of microbial pathogenicity; Nonspecific defense of host; Antigens and antibodies; Humoral and cell mediated immunity; Vaccines; Immune deficiency; Human diseases caused by viruses, bacteria, and pathogenic fungi.
Section 8: Chemotherapy/Antibiotics
General characteristics of antimicrobial drugs; Antibiotics: Classification, mode of action and resistance; Antifungal and antiviral drugs.
Section 9: Microbial Genetics
Types of mutation; UV and chemical mutagens; Selection of mutants; Ames test for mutagenesis; Bacterial genetic system: transformation, conjugation, transduction, recombination, plasmids, transposons; DNA repair; Regulation of gene expression: repression and induction; Operon model; Bacterial genome with special reference to E.coli; Phage λ and its life cycle; RNA phages; RNA viruses; Retroviruses; Basic concept of microbial genomics.
Section 10: Microbial Ecology
Microbial interactions; Carbon, sulphur and nitrogen cycles; Soil microorganisms associated with vascular plants.
T: Zoology
Section 1: Animal world
Animal diversity, distribution, systematics and classification of animals, phylogenetic relationships.
Section 2: Evolution
Origin and history of life on earth, theories of evolution, natural selection, adaptation, speciation.
Section 3: Genetics
Basic Principles of inheritance, molecular basis of heredity, sex determination and sex-linked characteristics, cytoplasmic inheritance, linkage, recombination and mapping of genes in eukaryotes, population genetics.
Section 4: Biochemistry and Molecular Biology
Nucleic acids, proteins, lipids and carbohydrates; replication, transcription and translation; regulation of gene expression, organization of genome, Kreb’s cycle, glycolysis, enzyme catalysis, hormones and their actions, vitamins.
Section 5: Cell Biology
Structure of cell, cellular organelles and their structure and function, cell cycle, cell division, chromosomes and chromatin structure.
Section 6: Gene expression in Eukaryotes
Eukaryotic gene organization and expression (Basic principles of signal transduction).
Section 7: Animal Anatomy and Physiology
Comparative physiology, the respiratory system, circulatory system, digestive system, the nervous system, the excretory system, the endocrine system, the reproductive system, the skeletal system, osmoregulation.
Section 8: Parasitology and Immunology
Nature of parasite, host-parasite relation, protozoan and helminthic parasites, the immune response, cellular and humoral immune response, evolution of the immune system.
Section 9: Development Biology
Embryonic development, cellular differentiation, organogenesis, metamorphosis, genetic basis of development, stem cells.
Section 10: Ecology
The ecosystem, habitats, the food chain, population dynamics, species diversity, zoogerography, biogeochemical cycles, conservation biology.
Section 11: Animal Behaviour
Types of behaviours, courtship, mating and territoriality, instinct, learning and memory, social behaviour across the animal taxa, communication, pheromones, evolution of animal behaviour.
P: Chemistry (Compulsory) Section 1: Atomic Structure and Periodicity Planck’s quantum theory, wave particle duality, uncertainty principle, quantum mechanical model of hydrogen atom, electronic configuration of atoms and ions. Periodic tabl
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