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QUESTION: 1

**Q. No 1- 30 carry 4 marks each and 1 mark is deducted for every incorrect answer.**

**Q.**

**The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is :**

**(For steel Young’s modulus is 2×1011 N m ^{–2} and coefficient of thermal expansion is 1.1×10^{–5} K^{–1})**

Solution:

QUESTION: 2

A conductor lies along the z-axis at –1.5 z < 1.5 m and carries a fixed current of

direction (see figure). For a field find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10^{-3} s. Assume parallel motion along the x-axis

Solution:

QUESTION: 3

A bob of mass m attached to an inextensible string of length is suspended from a vertical support. The

bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of

suspension :

Solution:

changes in direction not in magnitude

QUESTION: 4

The current voltage relation of diode is given by I = (e^{1000V/T} – 1) mA, where the applied voltage V is in

volts and the temperature T is in degree Kelvin. If a student makes an error measuring 0.01 V while

measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

Solution:

QUESTION: 5

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury

level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46

cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm

of Hg)

Solution:

(76) (8) = (54 – x) (76 – x)

x = 38 cm

Length of air column = 54 – 38 = 16 cm

QUESTION: 6

Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct

option from the choices given below the lists:

Solution:

2I

nfrared waves → To treat muscular strain

radio waves → for broadcasting

X-rays → To detect fracture of bones

Ultraviolet rays → Absorbed by the ozone layer of the atmosphere;

QUESTION: 7

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a

dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 10^{4} V/m,

the charge density of the positive plate will be close to :

Solution:

By formula of electric field between the plates of a capacitor=

QUESTION: 8

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

Solution:

Least count of vernier calliper is 1/10 mm = 0.1 mm = 0.01 cm

QUESTION: 9

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the

action of their mutual gravitational attraction. The speed of each particle is :

Solution:

QUESTION: 10

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The

voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

Solution:

QUESTION: 11

A particle moves with simple harmonic motion in a straight line. In first s, after starting from rest it travels

a distance a, and in next s it travels 2a, in same direction, then :

Solution:

QUESTION: 12

The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 x 103 Am^{-1}. The current

required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets

demagnetized when inside the solenoid, is:

Solution:

QUESTION: 13

The forward biased diode connection is:

Solution:

QUESTION: 14

During the propagation of electromagnetic waves in a medium:

Solution:

QUESTION: 15

In the circuit shown here, the point ‘C’ is kept connected to point ‘A’ till the current flowing through the circuit becomes constant. Afterward, suddenly, point ‘C’ is disconnected from point ‘A’ and connected to point ‘B’ at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to :

Solution:

QUESTION: 16

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

Solution:

For the mass m,

mg - T = ma

for the cylinder,

TR mR^{2} a/R

T = ma

mg = 2ma

a = g/2

QUESTION: 17

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct

statement:

Solution:

QUESTION: 18

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the

particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation

between H, u and n is:

Solution:

QUESTION: 19

A thin convex lens made from crown glass (μ= 3/2) has focal length f. When it is measured in two different

liquids having refractive indices 4/3 and 5/3 . it has the focal lengths f_{1 }and f_{2} respectively. The correct

relation between the focal lengths is:

Solution:

QUESTION: 20

Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross –

section of each rod = 4 cm^{2}. End of copper rod is maintained at 100^{o}C where as ends of brass and steel are

kept at 0^{o}C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are

thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are

0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

Solution:

QUESTION: 21

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air

column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

Solution:

Possible frequencies = 100 Hz, 300 Hz, 500 hz, 700 Hz, 900 Hz 1100 Hz below 1250 Hz.

QUESTION: 22

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d_{1} and d_{2} are filled in the tube. Each liquid subtends 900 angle at centre. Radius joining their interface makes an angle α with

vertical. ratio d_{1}/d_{2} is

Solution:

QUESTION: 23

A green light is incident from the water to the air - water interface at the critical angle (9). Select the correct statement

Solution:

As frequency of visible light increases refractive index increases. With the increase of refractive index critical angle decreases. So that light having frequency greater than green will get total internal reflection and the light having frequency less than green will pass to air

QUESTION: 24

Hydrogen (_{1}H^{1}), Deuterium (_{1}H^{2}), singly ionised Helium (_{2}He^{4})^{+} and doubly ionised lithium (_{3}Li^{6})^{++} all have

one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of

emitted radiation are λ_{1}, λ_{2}, λ_{3} and λ_{4} respectively then approximately which one of the following is

correct?

Solution:

QUESTION: 25

The radiation corresponding to 3 → 2 transition of hydrogen atom falls on a metal surface to produce

photoelectrons. These electrons are made to enter a magnetic field of 3 x 10^{-4}T. If the radius of the largest

circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

Solution:

QUESTION: 26

A block of mass m is placed on a surface with a vertical cross section given by y = x3/6. If the coefficient

of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping

is :

Solution:

QUESTION: 27

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx^{2} where a and b are constants. The work done in stretching the unstretched rubber band by L is :

Solution:

QUESTION: 28

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R, and the surface tension of water is T, value of r just before bubbles detach is : (density of water is ρ_{w})

Solution:

QUESTION: 29

Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen

through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero

intensity), a rotation of Polaroid through 300 makes the two beams appear equally bright. If the initial

intensities of the two beams are IA and IB respectively, then I_{A}/I_{B} equals :

Solution:

QUESTION: 30

Assume that an electric field exists in space. Then the potential difference V_{A} – V_{O}, where V_{O} is

the potential at the origin and V_{A} the potential at x = 2 m is :

Solution:

QUESTION: 31

**Q. No 31- 60 carry 4 marks each and 1 mark is deducted for every incorrect answer.**Q.

Q.

The image of the line in the plane 2x - y + z + 3 = 0 is the line

Solution:

Line is parallel to plane

Image of (1, 3, 4) is (- 3, 5, 2).

QUESTION: 32

If the coefficients of x^{3} and x^{4} in the expansion of in powers of x are both zero, then (a, b) is equal to

Solution:

QUESTION: 33

If a R and the equation (where [x] denotes the greatest integer x) has no integral solution, then all possible values of a lie in the interval

Solution:

QUESTION: 34

If , then λ is equal to

Solution:

QUESTION: 35

The variance of first 50 even natural numbers is

Solution:

QUESTION: 36

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is

45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from

O is reduced to 30°. Then the speed (in m/s) of the bird is

Solution:

QUESTION: 37

The integral equals

Solution:

QUESTION: 38

The statement

Solution:

QUESTION: 39

If A is an 3 x 3 non-singular matrix such that equals

Solution:

QUESTION: 40

The integral is equal to

Solution:

QUESTION: 41

If z is a complex number such that |z| 2, then the minimum value of

Solution:

Hence, minimum distance between z and

QUESTION: 42

If g is the inverse of a function f and then g'(x) is equal to

Solution:

QUESTION: 43

If α, β 0, and f (n) = α" + β" and

then K is equal to

Solution:

QUESTION: 44

Let Then f_{4}(x) - f_{6}(x) equals

Solution:

QUESTION: 45

Let α and β be the roots of equation px^{2 }+ qx + r = 0, p 0. If p, q, r are in A.P. and hen the value of |α - β| is

Solution:

QUESTION: 46

Let A and B be two events such that stands for the complement of the event A. Then the events A and B are

Solution:

QUESTION: 47

If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some

Solution:

Let h(f) = f(x) – 2g(x)

as h(0) = h(1) = 2

Hence, using Rolle’s theorem

h'(c) = 0

f'(c) = 2g'(c)

QUESTION: 48

Let the population of rabbits surviving at a time t be governed by the differential equation If p(0) = 100, then p(t) equals

Solution:

QUESTION: 49

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to

Solution:

QUESTION: 50

The area of the region described by A = {(x, y) : x^{2} + y^{2} 1 and y^{2} 1 - x} is

Solution:

QUESTION: 51

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 lies in the fourth quadrant and is equidistant from the two axes then

Solution:

Let point of intersection is (h, –h)

so -c/2a= -d/3b

3bc – 2ad = 0

QUESTION: 52

Let PS be the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3). The equation of the line

passing through (1, -1) and parallel to PS is

Solution:

QUESTION: 53

Solution:

QUESTION: 54

If where N is the set of natural numbers, then XY

Solution:

QUESTION: 55

The locus of the foot of perpendicular drawn from the centre of the ellipse x^{2} + 3y^{2} = 6 on any tangent to it

is

Solution:

Let the foot of perpendicular be P(h, k)

Equation of tangent with slope m passing P(h, k) is

QUESTION: 56

Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

Solution:

QUESTION: 57

If (10)^{9} + 2(11)^{1} (10)^{8} + 3(11)^{2} (10)^{7} + ….. + 10(11)^{9} = k(10)^{9}, then k is equal to

Solution:

QUESTION: 58

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l^{2} = m^{2} + n^{2} is

Solution:

QUESTION: 59

The slope of the line touching both the parabolas y^{2} = 4x and x^{2} =-32y is

Solution:

QUESTION: 60

If x = -1 and x = 2 are extreme points of f(x) = αlog |x| + βx^{2} + x, then

Solution:

QUESTION: 61

Which one of the following properties is not shown by NO?

Solution:

NO is paramagnetic in gaseous state due to the presence of unpaired electron in its structure

QUESTION: 62

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

Solution:

at low pressure, terms Pb & ab/V^{2}

will be negligible as compared to RT

QUESTION: 63

The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is:

Solution:

During the electrolysis of aqueous solution of s-block elements, H_{2} gas is obtained at cathode

QUESTION: 64

Resistance of 0.2 M solution of an electrolyte is 50 ?. The specific conductance of the solution is 1.4 S m^{-1}.

The resistance of 0.5 M solution of the same electrolyte is 280 ?. The molar conductivity of 0.5 M solution

of the electrolyte in S m^{2} mol^{-1} is:

Solution:

QUESTION: 65

CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following

expressions is correct?

Solution:

In CsCl structure, Cs^{+} ion is in contact with Cl^{–} ion at the nearest distance which is equal to

QUESTION: 66

Consider separate solutions of 0.500 M C_{2}H_{5}OH(aq), 0.100 M Mg_{3}(PO_{4})_{2}(aq), 0.250 M KBr(aq) and 0.125

M Na_{3}PO_{4}(aq) at 25^{o}C. Which statement is true about these solutions, assuming all salts to be strong

electrolytes?

Solution:

QUESTION: 67

In which of the following reactions H_{2}O_{2} acts as a reducing agent?

Solution:

A reducing agent loses electrons during redox reaction.

Hence (b, d) is correct.

QUESTION: 68

In S_{N}2 reactions, the correct order of reactivity for the following compounds:

CH_{3}Cl, CH_{3}CH_{2}Cl, (CH_{3})_{2}CHCl and (CH_{3})_{3}CCl is:

Solution:

QUESTION: 69

The octahedral complex of a metal ion M^{3+} with four monodentate ligands L_{1}, L_{2}, L_{3} and L_{4} absorb

wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand

strength of the four ligands is:

Solution:

Strong field ligands cause higher magnitude of crystal field splitting which is accompanied by the absorption of higher energy radiation.

QUESTION: 70

For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the

evolved ammonia was absorbed in 60 mL of M/10 sulphuric acid. The unreacted acid required 20 ml of M/10 sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is:

Solution:

QUESTION: 71

The equivalent conductance of NaCl at concentration C and at infinite dilution are λ_{C} and λ_{∞}, respectively.

The correct relationship between λ_{C} and λ_{∞} is given as:

(where the constant B is positive)

Solution:

1

According to Debye Huckel’s Theory for a strong electrolyte,

QUESTION: 72

For the reaction where the symbols have usual meaning then the value of x is: (assuming ideality)

Solution:

For reaction

QUESTION: 73

In the reaction,

the product C is:

Solution:

QUESTION: 74

Sodium phenoxide when heated with CO_{2} under pressure at 125^{o}C yields a product which on acetylation

produces C.

The major product C would be:

Solution:

QUESTION: 75

On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic

compound formed is:

Solution:

QUESTION: 76

The correct statement for the molecule, CsI3 is:

Solution:

QUESTION: 77

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

Solution:

Equation – 1 is not balanced w.r.t. charge.

Equation – 2 gives K_{3} [Cu(CN)_{4}] as product.

Equation – 3 reaction is unfavourable in the forward direction (K_{2}O is unstable, while Li_{2}O is stable).

Equation – 4 is correct & balanced.

QUESTION: 78

For which of the following molecule significant μ 0?

a) b) c) d)

Solution:

Due to infinite possible conformations in the above cases (of which only one has zero ?); a weighted ? will

finally exist.

QUESTION: 79

For the non – stoichiometre reaction 2A+B →C+D , the following kinetic data were obtained in three

separate experiments, all at 298 K.

The rate law for the formation of C is:

Solution:

QUESTION: 80

Which series of reactions correctly represents chemical reactions related to iron and its compound?

Solution:

n Eq. (1) FeCl_{3} cannot be reduced when heated in air.

In Eq. (3) Fe_{2}(SO_{4})_{3} cannot convert to Fe on heating; instead oxide(s) will be formed.

In Eq. (4) FeSO_{4} cannot be converted to Fe on heating; instead oxide(s) will be formed.

Hence Eq. (2) is correct.

QUESTION: 81

Considering the basic strength of amines in aqueous solution, which one has the smallest pK_{b} value?

Solution:

Aliphatic amines are more basic than aromatic amines.

(CH_{3})_{2}NH > CH_{3}NH_{2} > (CH_{3})_{3}N (among aliphatic amines in water).

QUESTION: 82

Which one of the following bases is not present in DNA?

Solution:

Adenine, Thymine, Cytosine, Guanine are bases present in DNA.

Quinoline an aromatic compound is NOT present in DNA

QUESTION: 83

The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:

Solution:

QUESTION: 84

The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:

Solution:

QUESTION: 85

Given below are the half-cell reactions:

Solution:

QUESTION: 86

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of

their molecule is:

Solution:

QUESTION: 87

Which one is classified as a condensation polymer?

Solution:

Teflon, Acrylonitrile and Neoprene are addition polymers while Dacron is a condensation polymer.

QUESTION: 88

Among the following oxoacids, the correct decreasing order of acid strength is:

Solution:

HClO < HClO_{2} < HClO_{3} < HClO_{4}

Increasing acid strength due to increase in oxidation state of central atom.

QUESTION: 89

For complete combustion of ethanol, the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol^{–1} at 25^{0}C. Assuming ideality the Enthalpy of combustion, ΔCH, for the reaction will be: (R = 8.314 kJ mol^{–1})

Solution:

QUESTION: 90

The most suitable reagent for the conversion of R -CH_{2} -OH→R -CHO is:

Solution:

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