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A.

B.

C.

D.

The time for half life period of a certain reaction products is 1 hour. When the initial concentration of the reactant â€˜Aâ€™, is , how much time does it take for its concentration to come from to if it is a zero order reaction ?

A. 4 h

D .0.5 h

C. 0.25 h

B. 1 h

A solution containing is passed through a cation exchanger. The chloride ions obtained in solution were reated with excess of to give . The formula of the complex is (At. Mass of Ag = 108 u)

(A) (B)

A. B only

B. Both A and B

C. Neither A nor B

D. A only

If of water is introduced into a flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ? (Given : Vapour pressure of

One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is

A. propene

B. 1â€“butene

C. 2â€“butene

D. ethene

If sodium sulphate is considered to be completely issociated into cations and anions in aqueous solution, the change in freezing point of water , when of sodium sulphate is dissolved in 1 kg of water, is

A. 0.0372 k

B. 0.0558 k

C. 0.0744 k

D. 0.0186 k

From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous , is

A. 2â€“Butanol

B. 2â€“Methylpropanâ€“2â€“ol

C. 2â€“Methylpropanol

D. 1â€“Butanol

In the chemical reactions,

the compounds â€˜Aâ€™ and â€˜Bâ€™ respectively are

A. nitrobenzene and fluorobenzene

B. phenol and benzene

C. benzene diazonium chloride and fluorobenzene

D. nitrobenzene and chlorobenzene

A. 59.0

B. 47.4

C. 23.7

D. 29.5

The energy required to break one mole of bonds in is . The longest wavelength of light capable of breaking a single bond is

A. 594 nm

B. 640 nm

C. 700 nm

D. 494nm

Ionisation energy of . The energy of the first stationary state (n = 1) of is

Consider the following bromides :

The correct order of reactivity is

A. B > C > A

B. B > A > C

C. C > B > A

D. A > B > C

Which one of the following has an optical isomer ?

On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa espectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane and 35 g of octane will be (molar mass of and of

A. 72.0 kPa

B. 36.1 kPa

C. 96.2kPa

D. 144.5 kPa

The main product of the following reaction is

Three reactions involving are given below: (i) (ii) (iii) In which of the above does $$

A. (ii) only

B. (i) and (ii)

C. (iii) only

D. (4) (i) only

Select the correct statement for a saturated 0.034 M solution of the carbonic acid.

A. The concentration of is 0.034 M.

B. The concentration of is greater than that of .

C. The concentration of and are approximately equal.

D. The concentration of is double that of

The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is

A. 288 pm

B. 398 pm

C. 618 pm

D. 144 pm

The correct order of increasing basicity of the given conjugate bases is

The correct sequence which shows decreasing order of the ionic radii of the elements is

Solubility product of silver bromide is . The quantity of potassium bromide (molar mass taken as ) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is

A. 4.5 V

B. 3.0 V

C. 2.5 V

D. 5.0 V

At the solubility product of is . At which pH, will ions start precipitating in the form of from a solution of ions ?

A. 9

B. 10

C. 11

D. 8

Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

A. 30% and 26%

B. 26% and 32%

C. 32% and 48%

D. 48% and 26%

Out of the following, the alkene that exhibits optical isomerism is

A. 3â€“methylâ€“2â€“pentene

B. 4â€“methylâ€“1â€“pentene

C. 3â€“methylâ€“1â€“pentene

D. 2â€“methylâ€“2â€“pentene

Biuret test is not given by

A. carbohydrates

B. polypeptides

C. Urea

D. proteins

The correct order of values with negative sign for the four successive elements Cr, Mn, Fe and Co is

The polymer containing strong intermolecular forces e.g. hydrogen bonding, is

A. teflon

B. nylon 6,6

C. polystyrene

D. natural rubber

For a particular reversible reaction at temperature and were found to be both . If is the temperature at equilibrium, the reaction would be spontaneous when

C. is 5 times T

A rectangular loop has a sliding connector PQ of length and resistance and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents and are

Let C be the capacitance of a capacitor discharging through a resistor R. Suppose is the time taken for the energy stored in the capacitor to reduce to half its initial value and is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio will be

A. 1

B. 1/2

C. 1/4

D. 2

Directions: Questions contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.

A. Statement-1 is true, statement-2 is true; Statement-2 is the correct explanation of Statement-1.

B. Statement-1 is true, statement-2 is true; Statement-2 is not the correct explanation of Statement -1

C. Statement-1 is false, Statement-2 is true.

D.Statement-1 is true, Statement-2 is false.

Directions: Questions contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements

Statement-1 : When ultraviolet light is incident on a photocell, its stopping potential is and the maximum kinetic energy of the photoelectrons is When the ultraviolet light is replaced by Xrays,both and increase.

Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

A. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

B. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement -1

D. Statement-1 is true, Statement-2 is false.

A ball is made of a material of density where with and representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position ?

A particle is moving with velocity , where K is a constant. The general equation for its path is

A. constant

B. constant

C. xy = constant

D. Constant

Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX’ is given by

In the circuit shown below, the key K is closed at t = 0. The current through the battery is

A. and

B. and

The figure shows the position – time (x – t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

A. 0.4 Ns

B. 0.8 Ns

C. 1.6 Ns

D. 0.2 Ns

Directions : Following Questions are based on the following paragraph. A nucleus of mass M + Dm is at rest and decays into two daughter nuclei of equal mass each. Speed of light is c.

The binding energy per nucleon for the parent nucleus is and that for the daughter nuclei is . Then

Directions : Following Questions are based on the following paragraph.

A nucleus of mass M + Dm is at rest and decays into two daughter nuclei of equal mass each. Speed of light is c.

The speed of daughter nuclei is

A radioactive nucleus (initial mass number A and atomic number Z) emits 3 – particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field at the centre O is

The combination of gates shown below yields

A. OR gate

B. NOT gate

C. XOR gate

D. NAND gate

A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is

A. 0.5

B. 0.75

C. 099

D. 0.25

If a source of power 4 kW produces photons/second, the radiation belong to a part of the spectrum called

A. Xâ€“rays

B. ultraviolet rays

C. microwaves

D. – rays

The respective number of significant figures for the numbers and are

A. 5, 1 , 2

B. 5, 1, 5

C. 5, 5, 2

D. 4, 4, 2

In a series LCR circuit and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by . On taking out the inductor from the circuit the current leads the voltage by . The power dissipated in the LCR circuit is

A. 305 W

B. 210 W

C. Zero W

D. 242 W

Let there be a spherically symmetric charge distribution with charge density varying as upto r = R, and for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D is

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of with each other. When suspended in a liquid of density , the angle remains the same. If density of the material of the sphere is , the dielectric constant of the liquid is

A. 4

B. 3

C. 2

D. 1

Two conductors have the same resistance at but their temperature coefficients of resistance are and . The respective temperature coefficients of their series and parallel combination are nearly

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of â€˜Pâ€™ is such that it sweeps out a length , where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of â€˜Pâ€™ when t = 2 s is nearly

Two fixed frictionless inclined plane making an angle and with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ?

A. in horizontal direction

B. $9.8\; ms^\{-2\}\; in\; vertical\; direction$

C. Zero

D. in vertical direction

For a particle in uniform circular motion the acceleration at a point P(R, q) on the circle of radius R is (here q is measured from the xâ€“axis)

An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

As the beam enters the medium, it will

A. diverge

B. converge

C. diverge near the axis and converge near the periphery

D. travel as a cylindrical beam

The initial shape of the wave front of the beam is

A. convex

B. concave

C. convex near the axis and concave near the periphery

D. planar

The speed of light in the medium is

A. minimum on the axis of the beam

B. the same everywhere in the beam

C. directly proportional to the intensity

D. maximum on the axis of the beam

A small particle of mass m is projected at an angle q with the x-axis with an initial velocity in the x-y plane as shown in the figure. At a time the angular momentum of the particle is

The equation of a wave on a string of linear mass density is given by . The tension in the string is

A. 4.0 N

B. 12.5 N

C. 0.5 N

D. 6.25 N

Let and let , where , then

A. 56/33

B. 19/12

C. 20/7

D. 25/16

Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number such that x > 0. Which of the following statements is the negation of the statement P ?

A. There is no rational number such that .

B. Every rational number satisfies

C. and is not rational

There is a rational number such that

Let and . Then vector satisfying and is

C. .

The equation of the tangent to the curve , , that is parallel to the x-axis, is

A. Y=1

B. Y=2

C. Y=3

D. Y=0

Solution of the differential equation is

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and is

If two tangents drawn from a point P to the parabola are at right angles, then the locus of P is

If the vectors and are mutually orthogonal, then

A. (2, â€“3)

B. (â€“2, 3)

C. (3, â€“2)

D. (â€“3, 2)

Consider the following relations:

R = {(x, y) | x, y are real numbers and x = wy for some rational number w};

A. neither R nor S is an equivalence relation

B.S is an equivalence relation but R is not an equivalence relation

C. R and S both are equivalence relations

D. R is an equivalence relation but S is not an equivalence relation

Let be defined by If f has a local minimum at x = -1, then a possible value of k is

A. 0

B. -1/2

C. -1

The number of non-singular matrices, with four entries as 1 and all other entries as 0, is

A. 5

B. 6

C. at least 7

D. less than 4

Statement-1: (Assertion) and Statement-2: (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}.

Statement – 1: The probability that the chosen numbers when arranged in some order will form an AP is .

Statement – 2: If the four chosen numbers from an AP, then the set of all possible values of common difference is

A. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

B. Statement-1 is true, Statement-2 is false

C. Statement-1 is false, Statement-2 is true

D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x â€“ y + z = 5.

Statement-2: The plane x â€“ y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4).

Let and

Statement-1: Statement-2: and

Let A be a matrix with non-zero entries and let , where I is identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.

Statement-1: Tr(A) = 0 Statement-2: |A| = 1

Let be a continuous function defined by . Statement-1: , for some . Statement-2: for all

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

A. There is a regular polygon with

B. here is a regular polygon with

C. here is a regular polygon with

D. here is a regular polygon with

If a and b are the roots of the equation then

A. -1

B. 1

D. -2

The number of complex numbers z such that equals

B. 2

D. 0

A line AB in three-dimensional space makes angles and with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle with the positive z-axis, then equals

The line L given by passes through the point (13, 32). The line K is parallel to L and has the equation . Then the distance between L and K is

4.

A person is to count 4500 currency notes. Let an denote the number of notes he counts in the minute. If and are in A.P. with common difference -2, then the time taken by him to count all notes is

A. 34 minutes

B. 125 minutes

C. 135 minutes

D. 24 minutes

Let f: be a positive increasing function with Let f: be a positive increasing function with Then

A. 2/3

B. 3/2

C. 3

Let p(x) be a function defined on R such that for all and .Then p(x) dx equals

A. 21

B. 41

C. 42

Let be a differentiable function with and . Let Then g’(0) =

A. -4

B. 0

C. -2

D. 4

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

A. 36

B. 66

C. 108

D. 3

A. exactly 3 solutions

B. a unique solution

C. no solution

D. infinite number of solutions

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

A. 2/7

B. 1/21

C. 2/23

D. 1/3

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

A. 11/2

C. 13/2

D. 5/2

The circle intersects the line at two distinct points if

A. $-35\; <\; m\; <\; 15$ $$

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