A H-shaped frame of uniform flexual rigidity EI is loaded as shown in the figure. The relative outward displacement between points K and O is
\(\frac { RL{ h }^{ 2 } }{ EI } \)
b)\(\frac { { RL }^{ 2 }h }{ EI } \)
c)\(\frac { RL{ h }^{ 2 } }{ EI } \)
d)\(\frac { { RL }^{ 2 }h }{ 3EI } \)
Pick the incorrect statement from the following four statements.
On the plane which carries maximum normal stress, the shear stress is zero
b)Principal planes are mutually orthogonal
c)On the palne which carries maximum shear stress, the normal stress is zero
d)Principal planes are inclined at 450 with plane of maximum shear stress
Solution of recurrence relation
ar - 5ar-1 + 8ar-2 - 4ar-3 = 0 is
ar = A1(1)r + (A2 + A3r) (2)r
b)ar = (A1 + A2r2 + A3r3) (3)r
c)ar = (A1 + A2r + A3 r2) (-2)r
d)None of the above
What is the possible number of reflexive relations on a set of 5 elements?
210
b)215
c)220
d)225
Let P, Q and R be three atomic propositional assertions. Let X denotes (P V Q) \(\rightarrow\) R and Y denotes \((P\rightarrow R)\nu (Q\rightarrow R)\). Which one of the following is a tautology?
\(X\equiv Y\)
b)\(X\rightarrow Y\)
c)\(Y\rightarrow X\)
d)\(\rightharpoondown Y\rightarrow X\)
A numerical solution of the equation \(f(x)=x+\sqrt { x-3 } \) can be obtained using Newton-Raphson method. If the starting value of x = 2 for ten iterations, the value of x that is to be used in the next step
0.306
b)0.739
c)1.694
d)2.306
If mode of a data is 18 and mean is 24, then median
18
b)24
c)22
d)21
The value of the \(\oint { \frac { -3z+4 }{ { z }^{ 2 }+4z+5 } } dz\) where C is the circle |z|=1 is given by
0
b)\(\frac { 1 }{ 10 } \)
c)\(\frac { 4 }{ 5 } \)
d)1
The order of the differential equation \(\frac { { d }^{ 2 }y }{ dt^{ 2 } } +\left( \frac { dy }{ dt } \right) ^{ 3 }+{ y }^{ 4 }=e^{ -t }\)
1
b)2
c)3
d)4
The value of \(l=\int _{ 0 }^{ a }{ \int _{ \frac { { x }^{ 2 } }{ a } }^{ 2a-z }{ xy\quad dx\quad dy } } \)is
\(\frac { 3 }{ 8 } { a }^{ 4 }\)
b)\(\frac { 5 }{ 8 } { a }^{ 4 }\)
c)\(\frac { 7 }{ 8 } { a }^{ 4 }\)
d)\({ a }^{ 4 }\)
How many equations does the following system of linear equations have ?
-x+5y = -1
x-y = 2
x+3y = 3
Infinitely many
b)Two distinct solutions
c)Unique
d)None of these
If the first and fourth terms of a GP are 1 and 27 the common ratio is
1
b)\(\frac { 1 }{ 3 } \)
c)3
d)\(\frac { 1 }{ 27 } \)
If logx \(\frac { 9 }{ 16 } =-\frac { 1 }{ 2 } ,\)then x is
\(-\frac { 1 }{ 2 } \)
b)\(\frac {2 }{3 } \)
c)\(\frac { 81 }{ 256 } \)
d)\(\frac { 256 }{81 } \)
In a flight of 800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/h and the time of flight increased by 20 min. The duration of the flight is
\(\frac { 3 }{ 5 } h\)
b)\(\frac { 1 }{ 2 } h\)
c)1 h
d)\(1\frac { 1 }{ 2 } h\)
There is a leak in the bottom of a cistern. Before the leak, it could be filled in \(4\frac { 1 }{ 2 } h\) . It now takes \(\frac { 1 }{ 2 } h\) longer. If the cistern is full, in how much time would the leakage empty the full cistern?
45 h
b)40 h
c)36 h
d)56 h
A person invests money in three different schemes for 5 yr, 10 yr and 15 yr at 8%, 10 % and 12% simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investments is
45:9:5
b)45:18:10
c)25:18:10
d)25:9:5
The order of a leaf node in a B+ tree is the maximum number of (value, data recoed pointer) pairs it can hold. Given that the block size in 1 Kbytes, data record pointer is 7 nytes long, the value field is 9 byte long and a block pointer is 6 bytes long, what is the order of the leaf node?
63
b)64
c)67
d)68
A trader professes to sell his goods at cost price but he uses a false weight of 800g for 1 kg. Find his gain per cent
25%
b)21%
c)18%
d)16%
p is 5 times as large as q, the percent that q is less than p is
70%
b)75%
c)80%
d)85%
Which among the following is the least number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, when divided by 8 leaves a remainder of 7, when divided by 7 leaves a remainder of 6, when divided by 6 leaves a remainder of 5, when divided by 5 leaves a remainder of 5, when divided by 4 leaves a reaminder 3, when divided by 3 leaves a remainder of 2, when divided by 2 leves a reaminder of 1 ?
7559
b)839
c)5039
d)None of these
Each of the answer choice has a combination of three statements from the given set of six statements .You are required to identify the answer choice in which the statements are logically related.
A. A is taller than B.
B. A and B play golf.
C. C is shorter than B, but taller than D.
D. Golf and cricket are outdoor games.
E. C is the second shortest.
F. All outdoor games require energy.
ABC
b)ACE
c)ADF
d)FBD
Four girls are sitting on a bench to be photographed. Shikha is to the left of Reena. Manju is to the right of Reena. Rita is between Reena and Manju. Who would be the second from the left in the photograph?
Reena
b)Shikha
c)Manju
d)Rita
Read the following information carefully and answer the questions.
Five dramas A,B,C,D, and E have to be staged in 6 h where 1 h needs to be given per drama.
(1) A break of 1 has to be taken in the third or fourth hour.
(2) Drama show cannot be started with A and has to end in C.
(3) D has to follow B immediately with no break in between.
(4) A cannot be done immediately after D.
(5) A has to precede E immediately with no break in between.
Which drama is staged immediately after D?
B
b)E
c)C
d)None of these
A worker may claim Rs 15 for each km which he travels by taxi and Rs. 5 for each km which he drives his own car. If in one week he claimed Rs 500 for travelling 80 km, how many km did he travel by taxi?
10
b)20
c)30
d)40
Select the pair of Words, Which exhibits the same relationship between each other as the given pair of words.
Quixotic : practicable ::
Eulogize : praise
b)Ethos : spirit
c)Ethics : morality
d)Raucous : quiet
Choose the most appropriate option to fill in the blank.
Companies that try to improve employees performane by .............. rewards encourage negative kinds of behaviour instead of ........ a genuine interest in doing the work well.
conferring, discrediting
b)bestowing, discouraging
c)giving, seeking
d)withholding fostering
Choose the correct meaning of the given word.
Debilitate
Argue
b)Engage
c)Soothe
d)Enfeeble
The length and bearings of a closed traverse PQRSP are given below
Line | Length(m) | Bearing(WLB) |
PQ | 200 | \({ 0 }^{ \circ }\) |
QR | 1000 | \({ 45 }^{ \circ }\) |
RS | 907 | \({ 180 }^{ \circ }\) |
SP | ? | ? |
The missing length and bearing, respectively of the line SP are
207m and \({ 270 }^{ \circ }\)
b)707 m and \({ 270 }^{ \circ }\)
c)707 m and \({ 180 }^{ \circ }\)
d)907m and \({ 270 }^{ \circ }\)
A horizontal curve of 480 m radius for 7.5 m two lane road is to be designed for a speed of 80 km/h.The raising of the outer edge of pavement with respect to the centre line to cater the mixed traffic condition is
0.14 m
b)0.22 m
c)0.24 m
d)0.44 m
A 2% solution of sewage sample is kept at an incubation temperature of 200 C. If the inital DO and final DO values after 5 days incubation period are 8.5 mg/L and 5.5 mg/L respectively, then BOD will be
50 mg/L
b)150 mg/L
c)250 mg/L
d)350 mg/L
An outlet irrigates an area of 20 ha. The discharge (litre/s) required at outlet to meet the evapotranspiration requirement of 20 mm occurring uniformly in 20 days neglecting the other field losses is
2.52
b)2.31
c)2.01
d)1.52
The probability that a 100 yr flood is equalled or exceeded at once in 100 yr is
99%
b)64%
c)36%
d)1%
If the specific energy at the upstream section of a rectangular channel is 3m and minimum specific energy is 2.5 m, the maximum height of jump without causing afflux will be
0.50 m
b)1.20 m
c)2.50 m
d)5.50 m
The fall velocity of a sand grain in water is to be modelled by using particles of the same relative density as sand and a liquid whose kinematic viscosity is 100 times larger than that of water.The diameters of the particles in the model that will have the same fall velocity as the prototype will be
10 times smaller
b)10 times larger
c)100 times smaller
d)100 times larger
An excavation is proposed for a site consisting of homogenous, isotopic layer of silty clay, 10 m thick above a deep deposit of sand. The ground water is 1 m below ground level. Given, e = 0.60 and G = 2.70. The limiting depth of excavation to avoid heaving will be (see figure)
4.85 m
b)5.15 m
c)6.15 m
d)7.85 m
Match List I (Shape of structure ) with List II (Shape factor) and select the correct answer using the codes given below the lists
List I | List II |
P.Rectangular | 2.0 |
QCircular | 2.1.1 to 1.2 |
R.I-section | 3.1.5 |
S.Diamond | 4 1.7 |
P | Q | R | S |
3 | 1 | 3 | 1 |
P | Q | R | S |
2 | 4 | 3 | 1 |
P | Q | R | S |
3 | 4 | 2 | 1 |
P | Q | R | S |
2 | 1 | 3 | 4 |
A bar of 20 mm diameter in a axially loaded short column is to be spliced with 16 mm diameter bar, the lap length required for proper transfer for the load in (mm) is (\(\tau_{bd}=1.2\) MPa and grade of steel Fe 415)
752.18
b)553.6
c)576
d)601.75
For a linear elastic frame, if stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will be
twice the existinq value
b)halt the existing value
c)the same as existing value
d)indeterminate value
A simply supported beam is made of two wooden planks of same width resting upon the one another without friction and connection.The upper plank is of half the thickness as compared to lower plank .The assembly is loaded by a uniformly distributed load on th entire span. The ratio of maximum stress developed between top and bottom planks will be
1 : 16
b)1 : 8
c)1 : 4
d)1 : 2
The solution of the recurrence relation ar = ar-1 + 2ar-2 with a0 = 2,a1 = 7 is
ar = (3)r + (1)r
b)2ar = \(\frac { (2{ ) }^{ r } }{ 3 } \)- (1)r
c)ar = 3r+1 - (-1)r
d)ar = 3(2)r - (-1)r
Let (S,\(\le \)) be a partial order with two minimal elements and a and b and a, c maximum element. Let P : S \(\Rightarrow\){True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\Rightarrow\) P(y), \(\forall \)x, y\(\epsilon \)S satisfying x \(\le \)y, where \(\Rightarrow\) stands for logical implication .Which of the following statement cannot be true?
P(x) = True for all x\(\epsilon \)S such that x\(\epsilon \)0 such that x\(\neq\) b
b)P(x) = False for all x\(\epsilon \)S Such that x\(\neq\)a and x\(\neq\)c
c)P(x) = False for all x\(\epsilon \)S Such that b\(\le \)x such tht x\(\neq\)c
d)P(x) = False for all x\(\epsilon \)S Such that a\(\le \)x and b\(\le \)x
The following resolution rulwe is used in logic programming .Drive clause ( P \(\wedge \) Q ) from clauses ( P \(\vee \) R ) \(\wedge \) (Q \(\vee \neg \) R ).
Which of the following statements related to this rule is false?
P \(\vee \) R \(\wedge \) (Q \(\vee \neg \) R ) \(\Rightarrow\) (P \(\vee \) R ) is logically valid
b)(P \(\vee \) Q ) \(\Rightarrow\) ( P \(\vee \) R ) \(\wedge \) (Q \(\vee \neg \) R ) is logically valid
c)(P \(\vee \) Q ) is satisfiable if and only if ( P \(\vee \) R ) \(\wedge \) (Q \(\vee \neg \) R ) is satisfiable
d)(P \(\vee \) Q ) \(\Rightarrow\) False if and only if both P anmd Q are unsatisfiable
Let \({ X }^{ 2 }-117=0.\) The iterative steps for the solution using Newton-Raphson's method is given by
\({ X }_{ k+1 }=\frac { 1 }{ 2 } \left( { X }_{ k }+\frac { 117 }{ { X }_{ k } } \right) \)
b)\({ X }_{ k+1 }={ X }_{ k }-\frac { 117 }{ { X }_{ k } } \)
c)\({ X }_{ k+1 }={ X }_{ k }-\frac { { X }_{ k } }{ 117 } \)
d)\({ X }_{ k+1 }={ X }_{ k }-\frac { 1 }{ 2 } ({ X }_{ k }+\frac { 117 }{ { X }_{ k } } )\)
A loaded dice has following probability distribution of occurrences
Dice value | 1 | 2 | 3 | 4 | 5 | 6 |
Probability | \(\frac { 1 }{ 4 } \) | \(\frac { 1 }{ 8 } \) | \(\frac { 1 }{ 8 } \) | \(\frac { 1 }{ 8 } \) | \(\frac { 1 }{ 8 } \) | \(\frac { 1 }{ 4 } \) |
If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is
same as that of occurrence 3, 4, 5
b)same as that of occurrence 1, 2, 5
c)\(\frac { 1 }{ 128 } \)
d)\(\frac { 5 }{ 8 } \)
For an analytic function f(x+iy)=\(\mu \) (x,y) + iv(x,y), \(\mu \) is given by \(\mu \) = 3x2-3y2 expression for v considering K to be at constant is
3y2-3x2+K
b)6x-6y+K
c)6x+6y+K
d)6xy+K
The Blasius equation \(\frac { d^{ 3 }f }{ d\eta ^{ 3 } } +\frac { f }{ 2 } \frac { d^{ 2 }f }{ d\eta ^{ 2 } } =0\) is a
second order non-linear differential equation
b)third order non-linear ordinary differential equation
c)third order linear ordinary differential equation
d)mixed order non-linear ordinary differential equation
Assuming i=\(\sqrt { -1 } \)and t is a real number \(\int _{ 0 }^{ \pi }{ { e }^{ it } } dt\) is
\(\frac { \sqrt { 3 } }{ 2 } +\frac { i }{ 2 } \)
b)\(\frac { \sqrt { 3 } }{ 2 } -\frac { i }{ 2 } \)
c)\(\frac { 1 }{ 2 } +i\frac { \sqrt { 3 } }{ 2 } +\frac { 1 }{ 2 } +i\left( 1-\frac { \sqrt { 3 } }{ 2 } \right) \)
d)0
Let AX = b be a system of linear equations, where A is an n\(\times\)n matrix, b is m\(\times\)1 column vector and X is a n\(\times\)1 column vector of unknowns. Which of the following statements is false?
The system has a solution if and only idf both A and the augmented matrix [A b] have the same rank
b)If m<n and b is the zero vector, then the system has infinitely many solutions
c)If m = n and b is a non- zero vector, then the system has a unique solution
d)The system will have only a trivial solution when m= n,b is zero vector and rank(A) = n
Find the tenth term of the GP \(\frac { 1 }{ \sqrt { 2 } } ,-1,\sqrt { 2 } ,.....\)
-16
b)16
c)\(16\sqrt { 2 } \)
d)\(-16\sqrt { 2 } \)
If a, b, c are three consecutive integers,, then log(ac+1) is equal to
log(2b)
b)x =2
c)2 log b
d)None of these
Two trains start from A and B respectively and travel towards each other at the speeds of 60 km/h and 45 km/h respectively. By the time they meet, the first train has travelled 30 km more than the second. The distance between A and B is
240 km
b)180 km
c)210 km
d)175 km
Pipe A can fill a tank in 30 mihn and pipe C can empty the full tank in 1 h. If all the pipes are opened togethyer, how much time will be needed to mak tank full?
14 min
b)12 min
c)15 min
d)18 min
If the simple interest for 5 yr be equal to 40 % of the principal , it will be equal to the principal after.
12 yr 3 months
b)12 yr 6 months
c)12 yr 4 months
d)12 yr 9 months
There are two classes I and II consisting of 42 and 52 students respectively. If the average weight of class I is 45 kg and that of class II is 40 kg. Find the average weight of all the students of class I and II.
42.17kg
b)41.25 kg
c)43.50 kg
d)39.75 kg
A trader mixes three varies of tea costing Rs.50, Rs. 30 and Rs. 20/kg in the ratio of 2 : 4 : 3 in terms of weight and sells the mixture at Rs.35/kg. What percentage of profit or loss does he make?
12.5%
b)12%
c)10%
d)10.5%
If the numerator of a fraction is increased by 20% and its denominator is decreased by 20%, the value of fraction is 3/7. Find the original fraction.
100.8
b)0.2
c)0.8
d)100.2
Findthe HCF of \(\frac { 2 }{ 5 } ,\frac { 12 }{ 11 } ,\frac { 1 }{ 3 } \)
\(\frac { 1 }{ 165 } \)
b)\(\frac { 5 }{ 165 } \)
c)\(\frac { 2 }{ 165 } \)
d)\(\frac { 12 }{ 165 } \)
Each of the answer choice has a combination of three statements from the given set of six statements .You are required to identify the answer choice in which the statements are logically related.
A. Actors know English.
B. He does not know English.
C. He is an actor.
D. He is not an actor.
E. He knows Hindi.
F. He should know English.
ABD
b)AEF
c)DEA
d)ACF
Answer the questions below based on the following information.
Each of seven objects T, U, V, W, X, Y and Z is placed either on the tower, middle or top shelf of the three-shelf bookcase that contains no other objects.
(i) At least two objects are on the top shelf.
(ii) No more than four objects are on any shelf.
(iii) T and U are on different shelves.
(iv) V is either on one shelf or two shelves above the shelf that X is on.
(v) W is either on one shelf or two shelves above the shelf that X is on.
If V and T are the only objects on one of the shelves, which of the following must be true?
W is on the top shelf
b)X is on the bottom shelf
c)U is on either the middle or top shelf
d)If U and Y are on different shelves, Z is on the top shelf
Read the following information carefully and answer the questions.
Five dramas A,B,C,D and E have to be staged in 6 h where 1 h needs to be given per drama.
(1) A break of 1 has to be taken in the third or fourth hour.
(2) Drama show cannot be started with A and has to end in C.
(3) D has to follow B immediately with no break in between.
(4) A cannot be done immediately after D.
(5) A has to precede E immediately with no break in between.
Which drama is staged immediately after E?
A
b)E
c)C
d)None of these
These Questions are based on the following information for an examination.
A. Candidates appeares | 10500 |
B. Passed in all the five sbjects | 5685 |
C. Passed in three subjects only | 1498 |
D. Passed in two subjects only | 1250 |
E. Passed in one subjects only | 835 |
F. Failed in Wnglish only | 78 |
G. Failed in Mathematics only | 275 |
H. Failed in Physics only | 149 |
I. Failed in Chemistry only | 147 |
J. Filed in Biology only | 221 |
How many candidates failed because of having failed in four or less subjects?
4815
b)4453
c)3618
d)2368
Select the pair of Words, Which exhibits the same relationship between each other as the given pair of words.
Demote : Promote :: Deplorable :
explicable
b)shameful
c)disgraceful
d)admirable
Choose the most appropriate option to fill in the blank.
This paper intends to .......... fearlessly all a forms of corruption and falsehood in public life.
present
b)unveil
c)uncover
d)expose
Guess the meaning of the underlined words in the context and choose the antonym for the same.
Disreputable: Corrupt ways of earning money left them undignified and disreputable.
Dishonourable
b)Unkempt
c)Respectable
d)Untrustworthy
The whole circle bearings of line OP and OQ are \({ 18 }^{ \circ }{ 15 }^{ ' }\)and \({ 335 }^{ \circ }{ 45 }^{ ' }\)respectively. What is the value of the included angle QOP?
\(307^{ \circ }{ 30 }^{ ' }\)
b)\(42^{ \circ }{ 30 }^{ ' }\)
c)\(354^{ \circ }{ 00 }^{ ' }\)
d)\(177^{ \circ }{ 00 }^{ ' }\)
A horizontal circular curve with a centre line radius of 200m is provided on a 2-lane 2-way SH section.The width of the 2-lane road is 7.0m.Design speed for this section is 80km/h.The brake reaction time is 2.4s and the coefficient of friction in longitudinal and lateral direction are 0.355 and 0.15 respectively.The set back distance from the centre line of the inner lane is
7.93m
b)8.10
c)9.60
d)9.77m
TCO is equivalent to the colour produced by
1 mg/L of chloroplatinate ion
b)1 mg/L of platinum ion
c)1 mg/L platinum is form of chloroplatinate ion
d)1 mg/L of organo-platinate ion
With the increase in supplied irrigation water, the yield of crops
increase continuously
b)decrease continuously
c)Increase upto a certain limit and then becomes constant
d)Increase upto a certain limit and then decrease
For a given storm, other factors remaining same
basins having two drainage density give smaller peak in flood hydrograph
b)Basins with larger drainage density gives smaller flood peak.
c)low drainage density basins gives shorter tune bases of hydrograph
d)the flood peak is independent of the drainage density
The flow in rectangular channel is subercritical . If the width is expanded at a certain section, the water surface
at a downstream section will drop
b)at the downstream section will rise
c)at the upstream section will rise
d)at the upstream section will drop
In a steady, incompressible, fluid flow with uniform velocity distribution the momentum flux in a given X-direction past a given section is expressed as Mx is equal to
pQv
b)pQvx
c)\(Q^2\over A\)
d)\(pv^2\over2\)
The width and depth of a footing are 2 m and 1.5 m respectively.The water table at the site is at a depth of 3 m below the ground level.The water table correction factor for the calculation of the bearing capacity of the soil is
0.875
b)1.000
c)0.925
d)0.500
A moment M of magnitude of 150 KN-m is transmitted to a column flange through a bracket using four 20 mm diameter bolts as shown in figure
The shear force included in the bolt A is
530.3 KN
b)265.2 KN
c)176.7 KN
d)158.2 KN
A beam is designed for udl causing compression in the supporting column. Where is the critical section for shear?
A distance of \(\frac{d}{2}\) from the face of the support
b)A distance d from the face of the support
c)At the centre of support
d)At the face of support
For the truss shown in the figure, the force in the member QR is
zero
b)\(\frac { P_{ 0 } }{ \sqrt { 2 } } \)
c)P0
d)\(\sqrt { 2 } P_{ 0 }\)
The resultant stress on a certain plane makes an angle of 200 with the normal to the plane. On the plane perpendicular to the above plane, the resultant stress makes an angle of \(\theta \) with normal. The value of \(\theta \) can be
00 and 200
b)any value other than 00 and 900
c)any value between 00 and 200
d)200 only