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QUESTION: 1

In the following ‘I’ refers to current and other symbols have their usual meaning.

Choose the option that corresponds to the dimensions of electrical conductivity:

Solution:

QUESTION: 2

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F =−kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

Solution:

QUESTION: 3

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle θ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction µmin between the mass and the inclined surface such that the mass does not move is :

Solution:

QUESTION: 4

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force W/20 on the car. While moving uphill on the road at a speed of 10 ms^{−1}, the car needs power P. If it needs power P/2 while moving downhill at speed v then value of v is :

Solution:

QUESTION: 5

A cubical block of side 30 cm is moving with velocity 2 ms^{−1} on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

Solution:

QUESTION: 6

Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is 1/4 the area of the ellipse. (Seefigure) With db as the semimajor axis, and ca as the semiminor axis. If t_{1} is the time taken for planet to go over path abc and t_{2 }for path taken over cda then :

Solution:

QUESTION: 7

Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure.

If the radius of the cross-section of water stream when it hits the ground is x. Then :

Solution:

QUESTION: 8

200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water=4184 J/kg/K) :

Solution:

QUESTION: 9

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

Solution:

QUESTION: 10

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time t=0 one particle has displacement A while the other one has displacement -A/2 and they are moving towards each other. If they cross each other at time t, then t is :

Solution:

QUESTION: 11

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec :

Solution:

QUESTION: 12

The potential (in volts) of a charge distribution is given by

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume ρ0 (in units of ∈_{o}) which is spread over a certain region, then choose the correct statement.

Solution:

QUESTION: 13

Three capacitors each of 4 µF are to be connected in such a way that the effective capacitance is 6 µF. This can be done by connecting them :

Solution:

QUESTION: 14

In the circuit shown, the resistance r is a variable resistance. If for r = f R, the heat generation in r is maximum then the value of f is:

Solution:

QUESTION: 15

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30º with this field. The magnitude of the other field (in mT ) is close to :

Solution:

QUESTION: 16

A 50 Ω resistance is connected to a battery of 5V. A galvanometer of resistance 100 Ω is to be used as an ammeter to measure current through the resistance, for this a resistance r_{s} is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of the current without the ammeter in the circuit ?

Solution:

QUESTION: 17

A series LR circuit is connected to a voltage source with V(t)=V_{0} sinΩt. After very large time, current I(t) behaves as :

Solution:

QUESTION: 18

Microwave oven acts on the principle of :

Solution:

QUESTION: 19

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of :

Solution:

QUESTION: 20

In Young’s double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance d0 between the slits. If the angular resolution of the eye is 1º/60 the value of d_{0} is close to :

Solution:

QUESTION: 21

When photons of wavelength λ_{1} are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength λ_{2} are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength λ_{3} is used then find the stopping potential for this case:

Solution:

QUESTION: 22

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z=3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

Solution:

QUESTION: 23

The truth table given in fig. represents :

Solution:

QUESTION: 24

An audio signal consists of two distinct sounds : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal bandwidth required to send both the signals together to the AM signal bandwidth required to send just the human speech is:

Solution:

QUESTION: 25

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :

Solution:

QUESTION: 26

A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

Solution:

QUESTION: 27

To know the resistance G of a galvanometer by half deflection method, a battery of emf V_{E} and resistance R is used to deflect the galvanometer by angle θ. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

Solution:

QUESTION: 28

To find the focal length of a convex mirror, a student records the following data :

The focal length of the convex lens is f_{1} and that of mirror is f_{2}. Then taking index correction to be negligibly small, f_{1} and f_{2} are close to :

Solution:

QUESTION: 29

An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of R=100 Ω, and a maximum power of dissipation rating of 1 W. The minimum voltage range of the DC source in the circuit is :

Solution:

QUESTION: 30

An unknown transistor needs to be identified as a npn or pnp type. A multimeter, with +ve and −ve terminals, is used to measure resistance between different terminals of transistor. If terminal 2 is the base of the transistor then which of the following is correct for a pnp transistor ?

Solution:

QUESTION: 31

The most appropriate method of making egg-albumin sol is :

Solution:

QUESTION: 32

The amount of arsenic pentasulphide that can be obtained when 35.5 g arsenic acid is heated with excess H_{2}S in the presence of cone. HC1 ( assuming 100% conversion) is:

Solution:

QUESTION: 33

At very high pressures, the compressibility factor of one mole of a gas is given by :

Solution:

QUESTION: 34

The total number of orbitals associated with the principal quantum number 5 is :

Solution:

QUESTION: 35

Which intermolecular force is most responsible in allowing xenon gas to liquefy ?

Solution:

QUESTION: 36

A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following :

Solution:

QUESTION: 37

The solubility of N_{2} in water at 300 K and 500 torr partial pressure is 0.01 g L^{−1}. The solubility (in g L^{−1}) at 750 torr partial pressure is :

Solution:

QUESTION: 38

For the reaction,

A(g)+B(g)→C(g)+D(g), ∆Hº and ∆Sº are, respectively, −29.8 kJ mol^{−1} and −0.100 kJ K^{−1} mol^{−1} at 298 K. The equilibrium constant for the reaction at 298 K is :

Solution:

QUESTION: 39

What will occur if a block of copper metal is dropped into a beaker containing a solution of 1M ZnSO_{4} ?

Solution:

QUESTION: 40

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below :

The closest rate constant for the overall reaction O_{3}(g)+O•(g) → 2 O_{2}(g) is

Solution:

QUESTION: 41

A particular adsorption process has the following characteristics :

(i) It arises due to van der Waals forces and

(ii) it is reversible. Identify the correct statement that describes the above adsorption process :

Solution:

QUESTION: 42

The non-metal that does not exhibit positive oxidation state is :

Solution:

The non-metal that does not exhibit positive oxidation state is fluorine. It shows -1 oxidation state only. other halogens show −1 and positive oxidation states of +1,+3,+5 and +7. Oxygen shows positive oxidation state of +2 in oxygen difluoride (OF2).

QUESTION: 43

The plot shows the variation of −ln K_{p} versus temperature for the two reactions.

and

Identify the correct statement :

Solution:

QUESTION: 44

Identify the incorrect statement regarding heavy water :

Solution:

QUESTION: 45

The correct order of the solubility of alkaline-earth metal sulphates in water is :

Solution:

QUESTION: 46

Match the items in Column I with its main use listed in Column II :

Solution:

QUESTION: 47

The group of molecules having identical shape is :

Solution:

QUESTION: 48

Which one of the following species is stable in aqueous solution ?

Solution:

QUESTION: 49

Which one of the following complexes will consume more equivalents of aqueous solution of Ag(NO_{3}) ?

Solution:

QUESTION: 50

Identify the correct trend given below : (Atomic No.=Ti : 22, Cr : 24 and Mo : 42)

Solution:

QUESTION: 51

BOD stands for :

Solution:

QUESTION: 52

An organic compound contains C, H and S. The minimum molecular weight of the compound containing 8% sulphur is : (atomic weight of S=32 amu)

Solution:

QUESTION: 53

The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is :

Solution:

QUESTION: 54

5L of an alkane requires 25 L of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is :

Solution:

QUESTION: 55

The gas evolved on heating CH_{3}MgBr in methanol is :

Solution:

QUESTION: 56

Bouveault-Blanc reduction reaction involves :

Solution:

QUESTION: 57

The test to distinguish primary, secondary and tertiary amines is :

Solution:

QUESTION: 58

Assertion : Rayon is a semisynthetic polymer whose properties are better than natural cotton.

Reason : Mechanical and aesthetic properties of cellulose can be improved by acetylation.

Solution:

QUESTION: 59

Consider the following sequence for aspartic acid

:

The pI (isoelectric point) of aspartic acid is:

Solution:

QUESTION: 60

The artificial sweetener that has the highest sweetness value in comparison to cane sugar is :

Solution:

QUESTION: 61

Let P = {θ : sinθ − cosθ = √2 cosθ } and Q = {θ : sinθ + cosθ = √2 sinθ } be two sets. Then :

Solution:

QUESTION: 62

If x is a solution of the equation, , then is equal to :

Solution:

QUESTION: 63

Let z = 1+ai be a complex number, a > 0, such that z^{3} is a real number. Then the sum 1+z+z^{2}+.....+z^{11} is equal to :

Solution:

QUESTION: 64

Let A be a 3 × 3 matrix such that A^{2}−5A+7I=O.

Statement - I :

Statement - II : The polynomial A^{3}−2A^{2}−3A+I can be reduced to 5(A−4I). Then :

Solution:

QUESTION: 65

If A = ,then the determinant of the matrix (A^{2016}−2A^{2015}−A^{2014}) is:

Solution:

QUESTION: 66

If = 11, then n satisfies the equation :

Solution:

QUESTION: 67

If the coefficients of x^{−2 }and x^{−4} in the expansion of , (x > 0), are m and n respectively, then m/n is equal to :

Solution:

QUESTION: 68

Let a_{1}, a_{2}, a_{3}, ......, a_{n}, ..... be in A.P. If a_{3 }+ a_{7 }+ a_{11 }+ a_{15 }= 72, then the sum of its first 17 terms is equal to :

Solution:

QUESTION: 69

The sum is equal to :

Solution:

QUESTION: 70

is:

Solution:

QUESTION: 71

Let a, b ∈ R, (a ≠ 0). If the function f defined as is continuous in the interval [0, ∞), then an ordered pair (a,b) is :

Solution:

QUESTION: 72

Let f (x) = sin^{4}x + cos^{4}x . Then f is an increasing function in the interval :

Solution:

QUESTION: 73

Let C be a curve given by If P is a point on C, such that the tangent at P has slope 2/3, then a point through which the normal at P passes, is:

Solution:

QUESTION: 74

The integral is equal to :

(where C is a constant of integration.)

Solution:

QUESTION: 75

The value of the integral where [x] denotes the greatest integer less than or equal to x, is:

Solution:

QUESTION: 76

For x ∈ R, x ≠ 0, if y(x) is a differentiable function such that then y(x) equals : (where C is a constant)

Solution:

QUESTION: 77

The solution of the differential equation where and y(0)=1, is given by :

Solution:

QUESTION: 78

A ray of light is incident along a line which meets another line, 7x−y+1=0, at the point (0, 1). The ray is then reflected from this point along the line, y+2x=1. Then the equation of the line of incidence of the ray of light is :

Solution:

QUESTION: 79

A straight line through origin O meets the lines 3y=10−4x and 8x+6y+5=0 at points A and B respectively. Then O divides the segment AB in the ratio :

Solution:

QUESTION: 80

Equation of the tangent to the circle, at the point (1, −1), whose centre is the point of intersection of the straight lines x−y=1 and 2x+y=3 is :

Solution:

QUESTION: 81

P and Q are two distinct points on the parabola, y^{2 }= 4x, with parameters t and t_{1} respectively. If the normal at P passes through Q, then the minimum value of is

Solution:

QUESTION: 82

A hyperbola whose transverse axis is along the major axis of the conic, and has vertices at the foci of this conic. If the eccentricity of the hyperbola is 3/2, then which of the following points does NOT lie on it ?

Solution:

QUESTION: 83

ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, µ). If the median through A is equally inclined to the coordinate axes, then the value of (λ^{3 }+ µ^{3} + 5) is :

Solution:

QUESTION: 84

The number of distinct real values of λ for which the lines and are coplanar is :

Solution:

QUESTION: 85

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are and respectively, then the position vector of the orthocentre of this triangle, is :

Solution:

QUESTION: 86

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

Solution:

QUESTION: 87

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

Solution:

QUESTION: 88

If A > 0, B >0 and Α + B = π/6, then the minimum value of tanA + tanB is :

Solution:

QUESTION: 89

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45º.The angle of elevation of the top of the same tower from a point B, due south of A is 30º. If the distance between A and B is 54√2 m , then the height of the tower (in metres), is

Solution:

QUESTION: 90

The contrapositive of the following statement,

“If the side of a square doubles, then its area increases four times”, is :

Solution:

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