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QUESTION: 1

**PART A**

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

**Q. **An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary,

secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

Solution:

Reaction proceeds through carbocation formation as 3^{0} carbocation is highly stable, hence reaction proceeds

through S_{N}1 with 3^{0} alcohol.

QUESTION: 2

The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na^{+} will be:

Solution:

here the backward reaction releases same amount of energy and known as Electron gain enthalpy.

QUESTION: 3

Stability of the species increases in the order of:

Solution:

is more stable than has more numbers of antibonding electrons

QUESTION: 4

The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M)HCl will be:

Solution:

QUESTION: 5

Which of the following is the wrong statement?

Solution:

(All the options are correct statements)

(2) Correct, as ozone is violet-black solid.

(3) Correct, as ozone is diamagnetic.

(4) Correct, as ONCl = 32 electrons and

ONO^{−} = 24 electron hence are not isoelectronic.

QUESTION: 6

Four successive members of the first row transition elements are listed below with atomic numbers. Which

one of them is expected to have the highest value?

Solution:

QUESTION: 7

A solution of (–) –1 – chloro –1 – phenylethane is toluene racemises slowly in the presence of a small

amount of SbCl_{5}, due to the formation of :

Solution:

QUESTION: 8

The coagulating power of electrolytes having ions Na^{+}, Al^{3+} and Ba^{2+} for arsenic sulphide sol increases in

the order:

Solution:

As_{2}S_{3} is an anionic sol (negative sol) hence coagulation will depend upon coagulating power of cation, which is directly proportional to the valency of cation (Hardy-Schulze rule).

QUESTION: 9

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an

aqueous solution with pH of 2?

Solution:

*Multiple options can be correct

QUESTION: 10

Which one of the following molecules is expected to exhibit diamagnetic behaviour?

Solution:

C_{2 }→ Dimagametic

QUESTION: 11

Which of the following arrangements does not represent the correct order of the property stated against it?

Solution:

The exothermic hydration enthalpies of the given trivalent cations are:

Sc^{+3} = 3960 kJ/mole

Fe^{+3} = 4429 kJ/mole

Co^{+3} = 4653 kJ/mole

Cr^{+3} = 4563 kJ/mole

Hence Sc^{+3} is least hydrated; so least stable (not most stable)

Fe^{+2} contains 4 unpaired electrons where as Mn^{+2} contains 5 unpaired electrons hence (4) is incorrect.

QUESTION: 12

Experimentally it was found that a metal oxide has formula M_{0.98}O. Metal M, is present as M^{2+} and M^{3+} in

its oxide. Fraction of the metal which exists as M^{3+} would be:

Solution:

Metal oxide = M_{0.98}O

If ‘x’ ions of M are in +3 state, then

3x + (0.98 – x) × 2 = 2

x = 0.04

So the percentage of metal in +3 state would be

QUESTION: 13

compound with molecular mass 180 is acylated with CH_{3}COCl to get a compound with molecular mass

390. The number of amino groups present per molecule of the former compound is:

Solution:

QUESTION: 14

Given

Based on the data given above, strongest oxidising agent will be:

Solution:

As per data mentioned

is strongest oxidising agent as it has maximum SRP value.

QUESTION: 15

Arrange the following compounds in order of decreasing acidity:

Solution:

Correct order of acidic strength is III > I > II > IV

QUESTION: 16

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such

a reaction will be:

(R = 8.314 JK^{–1} mol^{–1} and log 2 = 0.301)

Solution:

QUESTION: 17

Synthesis of each molecule of glucose in photosynthesis involves:

Solution:

QUESTION: 18

Which of the following complex species is not expected to exhibit optical isomerism?

Solution:

[Co(NH_{3})_{3}Cl_{3}] exists in two forms (facial and meridonial)

Both of these forms are achiral. Hence, [Co(NH_{3})_{3}Cl_{3}] does not show optical isomerism

QUESTION: 19

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant

temperature of 37.0^{0}C. As it does so, it absorbs 208J of heat. The values of q and w for the process will be:

(R = 8.314 J/mol K) ( l n 7.5 = 2.01)

Solution:

Process is isothermal reversible expansion, hence ΔU = 0.

q = −W

As q = +208 J

Hence W = −208 J

QUESTION: 20

A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO_{2}. The empirical formula of

the hydrocarbon is:

Solution:

QUESTION: 21

The order of stability of the following carbocations:

is

Solution:

Order of stability is III > I > II.

QUESTION: 22

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se

and Ar?

Solution:

Increasing order of first ionization enthalpy is

Ba < Ca < Se < S < Ar

QUESTION: 23

For gaseous state, if most probable speed is denoated by C*, average speed by and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

Solution:

QUESTION: 24

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

Solution:

It was methyl isocyanate (CH_{3}NCO)

QUESTION: 25

Consider the following reaction:

The values of x, y and z in the reaction are, respectively:

Solution:

QUESTION: 26

Which of the following exists as covalent crystals in the solid state?

Solution:

Silicon (Si) – covalent solid

Sulphur (S_{8}) – molecular solid

Phosphorous (P_{4}) – Molecular solid

Iodine (I_{2}) – Molecular solid

QUESTION: 27

Compound (A), C_{8}H_{9}Br, gives a white precipitate when warmed with alcoholic AgNO_{3}. Oxidation of (A)

gives a acid (B), C_{8}H_{6}O_{4}. (B) easily forms anhydride on heating. Identify the compound (A).

Solution:

QUESTION: 28

Energy of an electron is given by Wavelength of light required to excite an

electron in an hydrogen atom from level n = 1 to n = 2 will be

(h = 6.62 × 10^{−34} Js and c = 3.0 × 10^{8} ms^{−1})

Solution:

QUESTION: 29

An organic compound A upon reacting with NH3 gives B. On heating B gives C. C in presence of KOH

reacts with Br_{2} to give CH_{3}CH_{2}NH_{2}. A is

Solution:

QUESTION: 30

In which of the following pairs of molecules/ions, both the species are not likely to exist?

Solution:

Bond order of and He_{2} is zero, thus their existence is not possible.

QUESTION: 31

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point

Solution:

QUESTION: 32

ABCD is a trapezium such that AB and CD are parallel and BCCD. If ADB = q, BC = p and CD = q,

then AB is equal to

Solution:

QUESTION: 33

Given : A circle, 2x^{2} + 2y^{2} = 5 and a parabola, y^{2} = x.

Statement − I : An equation of a common tangent to these curves is y =

Statement − II : If the line, is their common tangent, then m satisfies m^{4 }- 3m^{2}+2=0

Solution:

QUESTION: 34

A ray of light along gets reflected upon reaching x-axis, the equation of the reflected rays is

Solution:

Slope of the incident ray is

So, the slope of the reflected ray must be

The point of incidence is √30 So, the equation of reflected ray is

QUESTION: 35

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10

to each of the students. Which of the following statistical measures will not change even after the grace

marks were given ?

Solution:

QUESTION: 36

If x, y, z are in A.P. and tan^{−1}x, tan^{−1}y and tan^{−1}z are also in A.P., then

Solution:

QUESTION: 37

if

Solution:

QUESTION: 38

The equation of the circle passing through the foci of the ellipse and having centre at (0, 3) is

Solution:

QUESTION: 39

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1)

(1, 1) and (1, 0) is

Solution:

QUESTION: 40

The intercepts on x-axis made by tangents to the curve, are parallel to the line

y = 2x, are equal to

Solution:

QUESTION: 41

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ….. , is

Solution:

QUESTION: 42

Consider :

Statement − I : is a fallacy.

Statement − II : is a tautology.

Solution:

QUESTION: 43

The area (in square units) bounded by the curves y = , 2y − x + 3 = 0 , x-axis, and lying in the first

quadrant is

Solution:

QUESTION: 44

The expression can be written as

Solution:

QUESTION: 45

The real number k for which the equation, 2x^{3} + 3x + k = 0 has two distinct real roots in [0, 1]

Solution:

If 2x^{3} + 3x + k = 0 has 2 distinct real roots in [0, 1], then f' (x) will change sign

but f'(x) = 6x^{2} + 3 > 0

So no value of k exists.

QUESTION: 46

is equal to

Solution:

QUESTION: 47

Let T_{n} be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If

T_{n+1} − T_{n} = 10, then the value of n is

Solution:

QUESTION: 48

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t.

additional number of workers x is given by . If the firm employs 25 more workers, then

the new level of production of items is

Solution:

QUESTION: 49

Statement − I : The value of the integral

Statement − II :

Solution:

QUESTION: 50

If is the adjoint of a 3 × 3 matrix A and |A| = 4, then α is equal to

Solution:

QUESTION: 51

The number of values of k, for which the system of equations

(k + 1)x + 8y = 4k

kx + (k + 3)y = 3k − 1

has no solution, is

Solution:

which means, k has only one value where the equation has no solution

QUESTION: 52

If is equal to

Solution:

QUESTION: 53

If the lines are coplanar, then k can have

Solution:

QUESTION: 54

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B

having 3 or more elements is

Solution:

QUESTION: 55

If the vectors are the sides of a triangle ABC, then the length of the

median through A is

Solution:

QUESTION: 56

A multiple choice examination has 5 questions. Each question has three alternative answers of which

exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

Solution:

P (correct answer) = 1/3

QUESTION: 57

If z is a complex number of unit modulus and argument θ, then arg equals

Solution:

QUESTION: 58

If the equations x^{2} + 2x + 3 = 0 and ax^{2} + bx + c = 0, a, b, c R, have a common root, then a : b : c is

Solution:

QUESTION: 59

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

Solution:

QUESTION: 60

The term independent of x in expansion of

Solution:

QUESTION: 61

**Q. No. 61 - 90 carry 4 marks each and 1 mark is deducted for every wrong answer**

**Q. In an LCR circuit as shown below both switches are open initially. Now switch S1 is closed, S2 kept open. (q is charge on the capacitor and t = RC is capacitive time constant). Which of the following statement is correct?**

Solution:

Charge on the capacitor at any time ‘t’ is

QUESTION: 62

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of

capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated

frequency which could be detected by it.

Solution:

QUESTION: 63

The supply voltage to a room is 120 V. The resistance of the lead wires is 6 W. A 60 W bulb is already

switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel

to the bulb?

Solution:

QUESTION: 64

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length

vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at

equilibrium position. The extension x_{0} of the spring when it is in equilibrium is:

Solution:

QUESTION: 65

Two charges, each equal to q, are kept at x = −a and x = a on the x-axis. A particle of mass m and charge

q_{0}= q/2 is placed at the origin. If charge q_{0} is given a small displacement along the y-axis, the net force acting on the particle is proportional to:

Solution:

QUESTION: 66

A beam of unpolarised light of intensity I_{0} is passed through a polaroid A and then through another polaroid

B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of

the emergent light is:

Solution:

QUESTION: 67

The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is

gradually changed. The plate current I of the photocell varies as follows:

Solution:

QUESTION: 68

Two coherent point sources S1 and S2 are separated by a small distance ‘d’ as

shown. The fringes obtained on the screen will be:

Solution:
C)

So, on a circle, path difference will be same locus of points having same path difference will be a circle, so fringes will make concentric circles.

So, on a circle, path difference will be same locus of points having same path difference will be a circle, so fringes will make concentric circles.

QUESTION: 69

A metallic rod of length ‘’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the

e.m.f. induced across the ends of the rod is:

Solution:

QUESTION: 70

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another

with quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to

Solution:

QUESTION: 71

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains

unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is

T, density of liquid is r and L is its latent heat of vaporization.

Solution:

QUESTION: 72

The graph between angle of deviation (d) and angle of incidence (i) for a triangular prism is represented by:

Solution:

QUESTION: 73

Let [ε_{0}] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time

and A = electric current, then:

Solution:

QUESTION: 74

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal

monoatomic gas. The amount of heat extracted from the source in a single cycle is

Solution:

Heat is extracted from the source in path DA and AB is

QUESTION: 75

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %.

What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10^{3} kg/m^{3} and

2.2 × 10^{11}N/m^{2} respectively?

Solution:

QUESTION: 76

This question has statement I and statement II. Of the four choices given after the statements, choose the

one that best describes the two statements.

Statement- I: Higher the range, greater is the resistance of ammeter.

Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

Solution:

For Ammeter, S

So for I to increase, S should decrease, so additional S can be connected across it.

QUESTION: 77

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass

M and radius R in a circular orbit at an altitude of 2R?

Solution:

QUESTION: 78

A projectile is given an initial velocity of is along the ground and is along the

vertical. If g = 10 m/s^{2}, the equation of its trajectory is

Solution:

x = t

y = 2t − 5t^{2}

Equation of trajectory is y = 2x − 5x^{2}

QUESTION: 79

Two capacitors C_{1} and C_{2} are charged to 120 V and 200 V respectively. It is found that by connecting

them together the potential on each one can be made zero. Then :

Solution:

120C_{1}= 200C_{2}

6C_{1}= 10C_{2}

3C_{1}= 5C_{2}

QUESTION: 80

A hoop of radius r and mass m rotating with an angular velocity ω_{0} is placed on a rough horizontal surface.

The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop

when it ceases to slip?

Solution:

From conservation of angular momentum about any fix point on the surface

QUESTION: 81

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The

piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the

gas is V_{0} and its pressure is P_{0}. The piston is slightly displaced from the equilibrium position and released.

Assuming that the system is completely isolated from its surrounding, the piston executes a simple

harmonic motion with frequency:

Solution:

QUESTION: 82

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric

potential at the point O lying at a distance L from the end A is:

Solution:

QUESTION: 83

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of

the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of

2.0 A flows through the smaller loop, then the flux linked with bigger loop is

Solution:

QUESTION: 84

If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature

θ_{0} the graph between the temperature T of the metal and time t will be closest to :

Solution:

The temperature goes on decreasing with time (non-linearly) The rate of decrease will be more initially which is depicted in the second graph.

QUESTION: 85

The I – V characteristic of an LED is

Solution:

For LED, in forward bias, intensity increases with voltage

QUESTION: 86

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the

one that best describes the two Statements.

Statement – I : A point particle of mass m moving with speed v collides with stationary point particle of

mass M. If the maximum energy loss possible is given as

Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the

collision.

Solution:

Loss of energy is maximum when collision is inelastic as in an inelastic collision there will be maximum deformation.

QUESTION: 87

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it

will decrease to α times its original magnitude, where α equals.

Solution:

QUESTION: 88

Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of

lens is 2 × 10^{8} m/s, the focal length of the lens is :

Solution:

QUESTION: 89

The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of

electric field strength is :

Solution:

QUESTION: 90

Two short bar magnets of length 1 cm each have magnetic moments 1.20 Am^{2} and 1.00 Am^{2} respectively.

They are placed on a horizontal table parallel to each other with their N poles pointing towards the South.

They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the

resultant horizontal magnetic induction at the mid - point O of the line joining their centres is close to

(Horizontal component of earth’s magnetic induction is 3.6 × 10^{–5} Wb/m^{2})

Solution:

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