Which one of the following is an analgesic?

Ripe graphs contain

Caprolactum is used to prepare for which of the following polymer?

\(CH_{ 3 }CH_{ 2 }COOH\overset { { Cl_{ 2 } }/{ Fe } }{ \longrightarrow } X\overset { alc }{ \underset { KOH }{ \longrightarrow } } Y\) Compound Y is

Which one of the following products is obtained on treatment of aniline with nitrous acid?

Which one of the following acids reduces Tollens' reagent?

The order for the acidic strength of 1^o, 2^o, 3^o alcohols, H₂O and \(RC\equiv CH\) is 

The veriety of coal having the highest percentage of carbon content is

A mixture of butane,ethylene and dimethyl acetylene is passed through acidified permanganate solution.The gas that comes out is

Isomers of a substance must have the same 

The oxidation state of Pt [(en)H₂O)₄(NO₂)Cl]²⁺ is 

For the process\(Cu\quad (g)\rightarrow { Cu }^{ + }\quad (g)+e\), the electron is removed from

\(KO_2\) is used in space and submarines because it

Which one of the following is the outer electronic configuration of an element belonging to the d-block of the periodic table ?

The formula of carnalite is

A hydrocarbon (C₅H₈) cannot have 

Which one of the following halogens has the highest electron affinity?

Which one of the following is not a method of concentraction of metals?

The hydrogen phosphate  of  certain metal has formula MHPO_{4. The formula of metal chloride would be} 

The empirical formula of a compound is CH2, 1 mole of the compound has mass 14 g.its moleculer formula is

Which of the radioactive isotopes is used for temperature control in blood disease?

Which of the following electrolytes will have maximum coagulating value for AgI/Ag⁺ sol?

For a unimolecular reaction

How many grams of H₂SO₄ is to be dissolved to prepare 200 mL aqueous solution having concentration of H₃O⁺ ions is 1 M at 25^o C temperature ?

In the reaction \({ 2I }^{ - }+{ Cl }_{ 2 }\longrightarrow { I }_{ 2 }+2C{ l }^{ - }\) the reductant is

The standard electrode potentials for the reactions, 
\({ Ag }^{ + }(aq)+{ e }^{ - }\longrightarrow Ag(s)\) \({ S }n^{ 2+ }(aq)\ +\ 2{ e }^{ - }\longrightarrow Sn(s)\) at \({ 25 }^{ \circ }C\) are 0.80 V and -0.14 V, respectively.

The emf of the cell, \(Sn\ |\ { S }n^{ 2+ }(1M)\ ||\ Ag^{ + }(1M)\ |Ag\ \) is

The solubility product of mercurous chloride is 1.0*10^-18 mol3 l^-3. The solubility of the compound in formula weight per litre is about

Ice and water are in equilibrium at 273K, which of the following statement is correct?

Given \(\Delta H\) = 177.9 kJ and \(\Delta S\) = 160.4 kJ mole^-1 for the reaction. \(Ca{ CO }_{ 2 }(s)\rightarrow Cao(s)+{ CO }_{ 2 }(s)\) at 298 K; the free energy change per mole for the above reaction would be

A compound formed by elements A and B crystallises in the cubic structure, where A atoms are at the corners of a cube, while B atoms are at the face ventres. the formula of the compound would be?

The maximum possible number of hydrogen bonds in which a water molecule can participate is

Which set of elements have strongest tendency to form anions?

The equation y = a sin 2π\(\left( \frac { t }{ T } -\frac { x }{ \lambda } \right) \) of a simple harmonic wave gives us:

In an experiment, the angles are required to be measured by an instrument having 29 divisions of main scale coincide with 30 divisions of the mirror scale.  If the smaller division of the main scale is half of a degree \((=0.5^o)\).  then the least count of the instrument is

A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by,

A nuclear transformation is denoted by X(n,\(\alpha\))\(\rightarrow ^7_3Li\). Which of the following is the nucleus of element X?

A proton, a neutron, an electron and an \(\alpha \)- particle have same energy. Then, their de-Broglie wavelengths compare as

If a magnetising field of 1600 A/m C. Horizontal produces a magnetic flux of 1.4X10^-5 Wb in an iron bar of cross- sectional area 0.2 cm² . Then, 

The displacement of an object attached to a spring and executing simple harmonic motion is given by \(x=2 \times10^{-2} \ cos \ \pi t\) metre. The time at which the maximum speed first occurs

The air density at Mount Everest is less than that at sea level. It is found by mountaineers that for one trip lasting a few hours, the extra oxygen needed by them corresponds to 30,000 cc at sea level (pressure = 1 atmosphere, temperature = 27°C). Assuming that the temperature around Mount Everest is -73° e and that the oxygen cylinder has capacity of 5.2 litres, the pressure at which oxygen be filled (at site) in the cylinder is:

A black body radiates heat energy at the rate of 3X10⁶ W at 127^oC. The temperature at which it would radiate heat energy at 243X10⁶ W is 

When a number of small droplets combine to form a large drop, then

Which of the following correctly gives the elastic energy stored in the metal bar? ( \(\sigma \) =stress, \(\varepsilon \) =strain, Y=Young's modulus, L=length, \(\Delta l\) =extension, F=load, A=cross- sectional area).

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field \(B={ B }_{ o }\hat { k } \) 

In earth's atmosphere, for F₁- layer; the virtual height and critical frequency are 

In a halfwave rectifier, the r.m.s value of the a.c. component of the wave is

An electron in Bohr's theory of hydrogen atom has an energy of -3.4eV. The angular momentum of the electron is

The de Brogile wavelength \(\lambda \) of an electron in the \(n^{th}\) Bohr orbit is related to the radius R of the orbit as

Match List-I (electromagnetic wave type) with List-II (its association/application) and select the correct option from the choices given below the lists

In young's experiment, if the slit separation is amde 3 folds, the fringes width becomes

While viewing a distant object with a telescope, suddenly a housefly sits on objective lens. The correct statement is that

A closed planar wire loop of area A and arbitrary shape is placed in a uniform magnetic field of magnitude B, with its plane perpendicular to magnetic field.  The resistance of the wire loop is R.  The loop is now turned upside down by \(180^O\) so that its plane again becomes perpendicular to the magnetic field.  The total charge that must have flowed through the wire ring in the process is

A circular loop of radius 0.0157 m carries a current of 2.0 A. The magnetic field at the centre of the loop is \(\left[ { \mu }_{ 0 }=4\pi \times { 10 }^{ -7 }\quad weber/amp-m \right] \)

The e.m.f. in a thermocouple one junction of which is kept at 0⁰C, is given by E = at + bt². The value of the Thomson coefficient is

For making standard resistances such as 1.00 ohm, the material of the wire should best have a temperature coefficient of resistance which is

Figure shows a charge +Q at a distance 2d away from a charge -Q and a point P at a distance d from -Q.The total potential at P due to the charges +q and -Q, using S.I.units is

The presence of gravitational field is required for the heat transfer by

A solid body of constant heat capacity 1 J/oC is being heated by keeping it in contact with reservoirs in two ways:
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature 100 K to final temperature 200 K. Entropy change of the body in the two cases respectively is :

In the production of beats by two progressive waves of nearly the same frequency,

A particle moving along a straight line vibrates to and fro about the origin of a cartesian system. While passing through the origin it has

Two waterpipes P and Q having diameters 2 x 10^-2 m and 4 x 10^-2 m respectively are joined in series with the main supply line of water.The velocity of water flowing in pipe P is

The mass of a planet is six times that ofthe earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is:

When a ceiling fan is switched-off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before corning to rest?

A bullet having a speed of 100 m/sec crashes through a plank of wood. After passing through a plank, its speed is 80 m/sec. Another bullet of the same mass and size, but travelling at 80 m/sec, is fired at the plank. The speed of the second bullet after travelling through the plank is: (Assume that resistance of the plank is independent of the speed of the bullet)

Consider the statements:
A. An astronaut in an orbiting artificial satellite is weightless
B. Both the satellite and the astronaut undergo free fall
C. If the cable that supports the elevator were to break, the elevator would be in free fall
Mark if :

If retardation produced by air resistance is g/10, then time of flight of projectile will nearly

Two trains A and B initially 120 km apart, start moving towards each other on the same track with a velocity of 60 km/h each. At the moment of start A blows a whistle,
which reflects on B and subsequently reflects from A and so on. Take the velocity of sound waves in air as 1200 km/hr. The distance travelled by sound waves before the trains crash will be:

The random error in the arithmetic mean of 100 observations is x, then random error in the arithmetic mean
of 400 observations would be:

Find the distance between the line 3x+4y=9 and 6x+8y=15.

Let f : A\(\rightarrow \)B be a function defined by y = f(x) such that f is both one-one (Injective) and onto (surjective)(ie, bijective), then there exists a unique function g: B\(\rightarrow \)A such that \(f\left( x \right) =y\Leftrightarrow g\left( y \right) =x,\ \forall x\epsilon A\ y\epsilon B\), then g is said to be inverse of f. Thus, g = f^-1: B\(\rightarrow \)A = \(\left[ \left\{ f\left( x \right) ,x \right\} :\left\{ x,\ f(x) \right\} \epsilon { f }^{ -1 } \right] \).If no branch of an inverse trigonometric function is mentioned, then it means the principal value branch of that function. On the basis of above information, answer the following question: If \(\frac { 3\pi }{ 2 } \le x\le \frac { 5\pi }{ 2 } \) then sin^-1(sin x) is equal to

Let f(x) be a continuous function such that the area bounded by the curve y = f(x), the x-axis and the two ordinates x = 0 and x = a is \(\left( \frac { { a }^{ 2 } }{ 2 } +\frac { a }{ 2 } sina+\frac { \pi }{ 2 } cosa \right) \)sq unit, then f\(\left\{ \frac { \pi }{ 2 } \right\} \)is

A cubic f(x)=ax³+bx²+cx+d vanishes at x=-2 and has relative minimum/maximum at x = - 1 and x=\(\frac{1}{3}\) and if \(\int _{ -1 }^{ 1 }{ f(x)dx=\frac { 14 }{ 3 } } \)
The value of d is

The third derivative of a function f(x) vanishes for all x. If f(0) = 1, f' (1) = 2 and f" (1) = - 1, then f(x) is equal to

If x¹⁸=y²¹=z²⁸, then 3,3log_yx, 3log_zy,7log_xz are in

If a be a positive integer, the number of values of a satisfying  \(\int _{ 0 }^{ \pi /2 }{ \left[ { a }^{ 2 }\left( \frac { cos\quad 3x }{ 4 } +\frac { 3 }{ 4 } cos\quad x \right) +a\quad sin\quad x-20\quad cos\quad x \right] } dx\le -\frac { { a }^{ 2 } }{ 3 } \) is

Which among the following is a conjunction? 

Three vertical poles of height h₁, h₂ and h₃ at the vertices A,B and C of a \(\Delta ABC\) subtend angles \(\alpha ,\beta \quad and\quad \gamma \) respectively, at the circumcentre of the triangle. If \(cot\alpha ,cot\beta ,cot\gamma \) are in AP, then h₁, h₂ and h₃ are in 

\(sin^{-1}(\frac{2x}{1+x^2})=2tan^{-1}x\) for

The value of sin \(\frac { \pi }{ 18 } sin\frac { \pi }{ 9 } +sin\frac { 2\pi }{ 9 } +sin\frac { 5\pi }{ 18 } \) is given

The eccentric angle of a point on the ellipse X² + 3y² = 6 at point on the ellipse X² + 3Y² = 6 at a distance 2 unit from origin is

The tangents drawn from the origin to the circle x² + y² - 2px - 2qy + q² = 0 are perpendicular, if

If p is the length of perpendicular from origin to the line whose intercept on the axes are a and b, then \(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } \) is equal to

\(\int _{ -1/2 }^{ 1/2 }{ \sqrt { \left\{ \left( \frac { x+1 }{ x-1 } \right) ^{ 2 }+\left( \frac { x-1 }{ x+1 } \right) ^{ 2 }-2 \right\} } } dx\)  is 

If \(\int{f(x)\over log\ sin\ x}dx\)=log log sin x, the f(x) is equal to

If the line ax + by + c = 0 is normal to curve xy + 5 = 0, then

\(\frac { d }{ dx } \left( x\sqrt { { a }^{ 2 }-{ x }^{ 2 } } +{ a }^{ 2 }{ sin }^{ -1 }\left( \frac { x }{ a } \right) \right) \) is equal to 

The function \(f:R-\left\{ 0 \right\} \rightarrow R\) given by \(f(x)={1\over x}-{2\over e^{2x}-1}\)can be made continuous at x=0 by defining f(0) as

\(\underset { x\rightarrow 0 }{ lim } \cfrac { { x }^{ m }-1 }{ { x }^{ 2 }-1 } \) is

The period of \({ sin }^{ 2 }\theta \) is 

A particle is projected vertically upwards and is at a height h after \({ t }_{ 1 }\)seconds and again after \({ t }_{ 2 }\)seconds. Then h equals

If the resultant of two forces each of a unit magnitude,acting at a point ,is of unit magnitude, then angle between these forces, is

Statement-I: 'x' is not an integrating factor for the differential equation \(x\frac { dy }{ dx } +2y={ e }^{ x }\).
Statement-II: \(x\left( x\frac { dy }{ dx } +2y \right) =\frac { d }{ dx } \left( { x }^{ 2 }y \right) \).

\(\int { \frac { dx }{ (x+2)\sqrt { x+3 } } , } \) equals

If \(f\left( x \right) =x{ e }^{ x\left( 1-x \right) }\), then \(f\left( x \right) \) is

Three numbers are chosen from 1 to 20. Find the probability that they are not consecutive.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to eah of the students. Which of the following statistical measures will not change even after the grace marks were given?

A line segment has length 63 and direction ratios 3,-2,6. If the line makes an obtuse angle with X-axis, then the components of vector are

The vector \(\hat{i}+x\hat{j}+3\hat{k}\) is rotated through an angle \(\theta\) and doubled in magnitude, then it becomes \(4\hat{i}+(4x-2)\hat{j}+2\hat{k}\) The values of x are

If the lines represented by 2x² - 5xy + 2y² = 0 be the two sides of a parallelogram and the line 5x + 2y = 1 be one of its diagonal.
On the basis of above information, answer the following questions:
The equation of the other diagonal is

The radical center of the circles x²+y²+4x+7=0, 2x²+2y²+3x+5y+9=0, and x²+y²+y=0, is

If \(\sin { \theta } +\sin { \phi } =a\) and \(\cos { \theta } +\cos { \phi } =b\), then

Write the first three terms of the sequence whose general term is \(a_n={n-3\over4}\)

Write the first three terms of the sequence whose general term is \(a_n={n-3\over4}\)

If n is a positive integer and a₁ ,a₂, a₃, ... , am ∊ C, then
(a₁ ,a₂, a₃+......+a_m)ⁿ = \(\sum { \frac { n! }{ { n }_{ 1 }!{ n }_{ 2 }!{ n }_{ 3 }!...{ n }_{ m }! } . } { a }_{ 1 }^{ { n }_{ 1 } }.{ a }_{ 2 }^{ { n }_{ 2 } }.{ a }_{ 3 }^{ { n }_{ 3 } }....{ a }_{ 1 }^{ { n }_{ m } }\) where n₁ , n₂, n₃, ... , n_m are all non negative integers subject to the condition n₁ + n₂ + n₃ + ... + n_m = n
The number of distinct terms in the expansion of (x₁ + x₂ + x₃ + ... + x_n)⁴ is

If x and y are distinct integers, then (xⁿ-yⁿ) is divisible by

Let N denote the greatest number of points in which m straight lines and n circles intersect, then

The value of 'a' for which one root of the quadratic equation (a²-5a+3)x²+(3a-1)x+2=0 is twice as large as the other, is 

Find the adjoint of the matrix A=\(\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \)

Number of solutions of the equation |z|²+7\(\overline { z } \)=0

Let A={a,b,c} and B={4,5}. Consider a relation R defined from set A to set B, then R is equal to

If we separate the cell organelles of a living cell, which part should be alive?

Match column I with column II and select the correct option from the given codes

Method of producing microbe and pest resistant plants include

Stains commercially used as blood cholesterol lowering agents are produced by

In monohybrid cross, number of pure line plants in F₂ will be

The 'symptomless' period or latent period in case of syphilis may last for

The organic nutrients are

The initial slow growing phase is called

The water loss due to transpiration is prevented by

Protein consists mainly of

Stirred-tank bioreactors have been designed for

Following are some statements regarding the primary and secondary antibody response in humans. All the statements are correct except

Match the following

The animal in which Lampbrush chromosomes were first observed was

Which of the muscles are attached to bones?

Phycology deals with the study of

For the functioning of electro static precipitators to remove dust particles
1. Electrode wires are maintained at several thousand volts
2. A corona must be produced that releases electrons to attach dust
3. The velocity of air between the plates must be low enough to allow the particles to fall on them

The hybridisation of orbitals of N atom in NO₃^-, NO₂⁺ and NH₄⁺ respectively are 

Which of the following can act as both as an antiseptic and disinfectant?

The outer electron configuration of Gd (Atomic number 64) is

Sphalerite and siderite are the ores of the metals

Who among the following was the first to organise the elements according to same behavioural trends of elements?

When a gas expands from 1.5 L to 6.5 L against a constant pressure of 0.50 atm and during this process, the gas also absorbs 100 J of heat.  The change in internal energy is

The coordination number of hexagonal closest packed (hep) structure is

20% \(N_2O_4\) molecules are dissociated in a sample of gas at \(27^oC\) and 760 torr pressure.  What is the density of equilibrium mixture?

In the following reaction, 
     \({ N }_{ 2 }(g)+3{ H }_{ 2 }(g)\rightarrow 2{ NH }_{ 3 }(g)\) 
Calculate the moles of NH₃ obtained when 2 moles of N₂ react with 3 moles of H₂ .

Compounds having same empirical formula always have same

Which air pollutant is not released by automobiles?

Which one of the following is a vat dye?

The equation which is balanced and represents the correct product (s) is 

By the Hydrolysis of 1,1,1-trichloro ethane the product formed is

Which one of the following reagents will convert acetamide into methyl amine?

Which one of the following is known to exist?

Which has the highest calorific value?

The compressed gas (know as LPG)available in cooking gas cylinders is a mixture

How many mono derivatives will br formed when

\({ 1 }^{ 0 }\quad \quad \quad { 3 }^{ 0 }\quad \quad { 2 }^{ 0 }\quad \quad { 1 }^{ 0 }\quad \\ { CH }_{ 3 }-{ CH }.{ CH }_{ 2 }-{ CH }_{ 3 }\\ \quad \quad \quad \quad \quad \parallel \\ \quad \quad \quad \quad \quad { CH }_{ 3\\ } \) (isopentane)

is reacted with bromine?

The substance represented by the formulae

\(\quad\quad COOH\\ \quad \quad \quad \quad |\\ { H }_{ 2 }N-C-H\\ \quad \quad \quad \quad |\\ H\quad -C-\quad OH\\ \quad \quad \quad \quad |\\ \quad \quad \quad C{ H }_{ 3 }\)     and \(\quad\quad\quad COOH\\ \quad \quad \quad \quad |\\ { H }-\quad C \quad -N{ H }_{ 2 }\\ \quad \quad \quad \quad |\\ HO-\quad C-H\\ \quad \quad \quad \quad |\\ \quad \quad \quad C{ H }_{ 3 }\)

The coordination number of copper in cuprammonium sulphate is

which one of the following transition metal iones has the least magnetic moment?

Which of the following equation is incorrect?

Metallic silver may be obtainedform AgCl by

which one of the following anhydrous halides can be prepared by heating its hydrated form?

The color of the blue glass is due to the prersence of 

Which of the following annulenes is antiaromatic?

In metallurgical processes the flux used for removing acidic inpurities is

1.55 g of an oil saponified with 28 ml of N/2 alcoholic KOH. The mix requires 15 ml of N/2 HCl. The saponification value of oil is 

When petroleum is heated gradually, first batch of vapours evolved will be rich in

The end product of (4n+2) disintegration series is

Which of the following electrolytes will have maximum coagulating value for AgI/Ag⁺ sol?

Activation energy of a chemical reaction can be determined by

What is the total number of moles of H₂SO₄ required to prepare 5.0 L of a 2.0 M solution of H₂SO₄ ?

The oxidation state of chemical carbon is

A solution containing one mole \(l^{-1}\) each of \(Cu(NO_3)_2,AgNO_3,Hg_2(NO_3)_2 \) and \(Mg(NO_3)_2\) is electrolysed using inert electrodes.\(E^o\) in volt are: with increasing voltage,the sequence of deposition of metals on the cathode will be

The strength of an acid depends in its tendency to

At 700 K, the equilibrium constant for the reaction \(H_{2}(g)+I_{2}(g)\rightleftharpoons 2HI(g)\) is 54.8.  If 0.5  mol \(l^{-1}\) of HI(g) is present at equilibrium at 700 K, assuming that we initially started with HI(g) and allowed to reach equilibrium at 700 K.  the concemtration of \(H_{2}\) or \(I_{2}\) each would be

For the chamical reaciton in forward direction at 25\(?\). A + B \(\rightarrow\) AB

A student forgot to add the reaction mixture to the round bottomed flask at \({ 27 }^{ \circ }C\) but put it on the flame. After a lapse of time, he realised his mistake; using a pyrometer he found the temperature of the flask was \({ 477 }^{ \circ }C.\) The fraction of air expelled would be

The velocity of electron in the first Bohr orbit of hydrogen atom would be (radius of the first orbit given as 0.53X10^-10m)

The length of the string of a simple pendulum is mmeasured with a meter scale to be 92.0cm, the radius of the bob plus the hook is measured with the help of vernier callipers to be 2.17cm.Mark out the correct statement(s).

A nucleus of mass M+\(\Delta m\) is at rest and decays into two daughter nuclei of equal mass  \(M\over 2\)  each . The speed of daughter nuclei is

The inner and the outer radii of a toroid are 9 cm and 11 cm respectively and the number of turns in it is 3140. A magnetic field of 2.5 T is produced in it when a current of 0.5 A is passed in it. The permeability of core material is (in H/m)

A particle executing SHM with frequency v. The frequency with which kinetic energy oscillate is

The value of molar specific heat at constant pressure for one mole of triatomic gas (triangular arrangement)of temperature TK is(R=universal gas constant)

If a cylinder of radius R having thermal conductivity K₁ is surrounded by other cylindrical shell of radius 2R having thermal conductivity K₂ . Two ends are maintained at two different temperatures. In steady state, the effective thermal conductivity of system is (assume no heat loss)

The terminal speed of a sphere of gold (density=19.5 kg m^-3) is 0.2 ms^-1 in a viscous liquid (density=1.5kg m^-3). The terminal speed of a sphere of silver (density = 10.5 kg/m³) of the same size in the same liquid will be 

A mass of 10 kg tied to the string which is fixed to the ceiling of the elevator. If the elevator is moving up with an acceleration of 5 m/s² . Then the elastic energy stored in the wire is (given, area and length of wire are 5cm² and 20 cm respectively and Young's modulus is 2X10¹¹ N/m² and use g=10 m/s²)

A length L of a wires carriers a steady current I. It is bent first to form circular plane coil of one turn. The same length is now bent more sharply to give a double loop of small radius. The magnetic field field at the centre caused by the same current is

A male voice after modulation transmission sounds like that of female to the receiver. The problem is due to

In p-type semiconductor

When a particle and an anti-particle combine the result is the emission of

In a photoelectric experiment, the stopping potential \(V_{s}\) is plotted against the frequancy \(\upsilon \), of the incident light.  The resulting curve is a straight line which makes an angle \(\theta \) with the \(\upsilon \)-axis.  Then tan \(\theta \) is equal to

The phase of velocity (v_p) of travelling wave is 

Light is incident normally on a diffraction grating through which the first order diffraction is seen at \({ 32 }^{ \circ }\). the second order diffraction will be seen at

An achromatic combination of lenses produces

The LRC circuit has L=10 mH,C=1\(\mu F\),R=3.3\(\Omega \) and a.c supply as E(t)=\(\cos { \omega t } \). The average power dissipated per period at resonance is

A certain amount of current when flowing in a properly set tangent galvanometer produces a deflection of \(45º\). If the current be reduced by a factor of \(\sqrt { 3 } \), the deflection would

How long will it take a current of 50A to produce 32g of oxygen by the electrolysis of water? Oxygen has an atomic mass of 16 and a valence of 2.

The conductivity of superconductor is 

Two points P and Q are maintained at the potentials of 10 V and - 4V, respectively. The work done in moving 100 electron from P to Q is

The substance having lowest thermal conductivity is

Lowest temperature close to 0 K can be achieved by experimental technique like

A seconds pendulum is placed in an elevator at rest. When the elevator ascends with an acceleration \(4.9m{ s }^{ 2 }\),the pendulum will have time period (in s)

Two steel wires have their lengths and diameters in the ratio of 1 : 2.  Their elongation for the same stretching force will be in the ratio

if g is accelaration due to gravity on the  surface of earth

A gramophone turn table have the angular speed 150 rpm slows down uniformly and stops in 10 s after breaking the supply to the motor. The angular acceleration in rad per square second is

A force F varies simultaneously with time.  The average force is ( \(F_{o} \) is peak value of force )

A body is projected at an angle of 30° with the horizontal and with a speed of 30 ms^-1. What is the angle with the horizontal after 1.5 seconds? (Take g = 10ms^-2)

hat is the angle between \(\overrightarrow { A } +\overrightarrow { B } \) and \(\overrightarrow { A } \times \overrightarrow { B } \) ?

Find the new coordinates of the point (1,1)if the origin is shifted to the point (-3,-2)by a translation of axes.

\(2{ cot }^{ -1 }7+{ cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \) is equal to

Four points A, B, C and D lie in that order on the parabola y = ax²+bx+c and the coordinates of A, Band D are known A(- 2, 3); B(- 1, 1); D(2, 7).
If area of quadrilateral ABCD is greatest, then the coordinates of Care

The third derivative of a function f(x) vanishes for all x. If f(0) = 1, f' (1) = 2 and f" (1) = - 1, then f(x) is equal to

The value of {log_ba.log_cb.log_dc.log_ad} is

If ∝,β,\(\gamma \) be the roots of the equation ax³+bx²+cx+d=0. To obtain the equation whose are f(∝),f(β),f(\(\gamma \)), where f is a function, we put y=f(∝) and obtain ∝=f^-1(y)
Now, ∝ is a root of the equation ax³+bx²+cx+d=0, then we obtain the desired equation which is a {f^-1(y)}³+b{f^-1(y)}²+c{f^-1(y)}+d=0
For example, if ∝,β,\(\gamma \)  are the roots of ax³+bx²+cx+d=0. To find equation whose are ∝²,β²,\(\gamma \)², we put y=∝²
⇒ ∝=\(\sqrt { y } \)
As ∝ is a root of ax³+bx²+cx+d=0
we get ay^3/2+by+c\(\sqrt { y } \)+d=0
or \(\sqrt { y } \)(ay+c)=-(by+d)
On squaring both sides, then y(a²y²+2acy+c²)=b²y²+2bdy+d² or a²y³+(2ac-b²)y²+(c²-2bd)y-d²=0 This is desired equation
If ∝,β,\(\gamma \) are the roots of the equation x³-x-1=0, then the value of \(\prod { \left( \frac { 1+\alpha }{ 1-\alpha } \right) } \) is equal to

The negation of the statement "72 is divisible by 2 and 3" is

If in a \(\Delta ABC\) ,  the tangent of half the difference of two angles is one-third the tangent of half the sum of the angles. Then, the ratio of the sides opposite to the angles is 

4 tan^-1\(\frac{1}{5}\)-tan^-1\(1\over70\)+tan^-1\(1\over99\) is equal to

Lex x be a real number different from Zero.
Statement -I : \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) cannot be less than 2.
Statement - II : \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) is not equal to cos\(\theta\)

Let us define a region R in xy-plane as a set of points (x, y) satisfying [x²] = [y] (where [x] denotes greatest integer \(\le \)x), then the region R defines

A circle of the coaxial system with limiting points (0, 0) and (1, 0) is

Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4aX + 2aY + c = 0 and 5bX + 2bY + d = 0 lie in the fourth quadrant and is equidistant from the two axes, then

\(\int{x^2-1\over x^4+x^2+1}dx\) is equal to

The function \(f(x) = tan^{-1}(sin\ x + cos x)\) is an increasing function in

If y² = ax² + bx + c, then \(\frac { d }{ dx } ({ y }^{ 3 }{ y }_{ 2 })\)=

The number of points at which the function \(f(x)={1\over x-[x]}\)([.] denotes the greatest integer function) is not continuous, is

If y=f(x)=-cosecx.cosx,then \(\left( { \cfrac { dy }{ dx } } \right) _{ x=\cfrac { \pi }{ 2 } }\) is equal to 

Let F(x)=f(x)+g(x), G(x)=f(x)-g(x) and H(x)=\(\frac { f(x) }{ g(x) } \), where f(x)=1-2sin²x and g(x)=cos 2x, ∀ f: R⟶ [-1,1] and g : R⟶ [-1,1]. If the solutions of F(x)-G(x)=0 are x₁,x₂,x₃,...,x_n where x∈[0,5π], then

A particle is projected vertically upwards and is at a height h after \({ t }_{ 1 }\)seconds and again after \({ t }_{ 2 }\)seconds. Then h equals

Solve the differential equation \(X\frac { dY }{ dX } =Y\left( \log { Y-\log { X+1 } } \right) \) 

The length of the tangent at the point \(t=\frac { \pi }{ 2 } \) on the curve \(x=\left( t+\sin { t } \right) ,y=\left( 1-\cos { t } \right) \) is

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively; then P(X=1), is

The frequency distribution table is given here.

Find the standard deviation.

A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is
y²z² + z²x² + x²y² = kx² y² z², where k is equal to

The position vectors of the points A, B and C are \(\hat { i } +\hat { j } +\hat { k } +,\hat { i } +5\hat { j } -\hat { k } \) and \(2\hat { i } +3\hat { j } +5\hat { k } \) respectively. The greatest angle of the triangle ABC is

The line x + y = 1 meets the lines represented by the equation y³ - 6xy² + 11x²y - 6x³ = 0 at the points P, Q, R. If O is the origin, then (OP)² + (OQ)² + (OR)² is equal to

Consider the straight lines x + 2y + 4 = 0 and 4x + 2y - 1 = O.The line 6x + 6y + 7 = 0 is

If \(\cos { \alpha } +\cos { \beta } =\sin { \alpha } +\sin { \beta } \), then \(\cos { 2\alpha } +\cos { 2\beta } \) is equal to

The minimum value of the expression \({ 3 }^{ X }+{ 3 }^{ 1-X },X\epsilon R,\) is

The expression (¹⁰C₀)² - (¹⁰C₁)² + .... - (¹⁰C₉)² + (¹⁰C₁₀)² equals

For all n∈N, 41ⁿ-14ⁿ is a multiple of 

The sum of the digits in the unit's place of all the numbers formed with the digits 5, 6,7,8 when taken all at a time, is

The value of 'a' for which one root of the quadratic equation (a²-5a+3)x²+(3a-1)x+2=0 is twice as large as the other, is 

If matrix A =\(\left[ \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right] \)where a,b,c are real positive numbers, abc =1 and A^TA =I, then the value of a³+b³+c³ is

The value of x³+7x2-x+16 when x=1+2i is,

Which of the following is a finite set?