Physics

Single correct answer type:

1. Two particles are moving on two concentric circles of radii and with equal

angular speed At their positions and direction of motion are shown in the

figure:

The relative velocity at

is given by:

(A) ( )

(B) ( )

(C) ( )

(D) ( )

Solution: (D)

( )

( )

( )

2. Let and represent inductance, resistance, capacitance and voltage,

respectively. The dimension of

is units will be:

(A) [ ]

(B) [ ]

(C) [ ]

(D) [ ]

Solution: (B)

*

+ *

+ *

+ *

+ *

+

[ ] *

+ *

+

*

+ *

+

3. When a certain photosensitive surface is illuminated with monochromatic light of

frequency the stopping potential for the photo current is

When the surface is

illuminated by monochromatic light of frequency

the stopping potential is The

threshold frequency for photoelectric emission is:

(A)

(B)

(C)

(D)

Solution: (B)

on solving we get,

4. To double the covering range of a TV transmittion tower, its height should be

multiplied by:

(A)

√

(B)

(C)

(D) √

Solution: (B)

√

To double the range have to be made times.

5. A long horizontal wire extends from North East to South West. It is falling with a

speed of at right angles to the horizontal component of the earth’s magnetic

field, of ⁄ The value of the induced emf in wire is:

(A)

(B)

(C)

(D)

Solution: (B)

√

6. Two satellite, has mass have masses and respectively. is in a circular

orbit of radius and is in a circular orbit of radius around the earth. The ratio of

their kinetic energies,

is:

(A)

(B)

(C)

(D) √

Solution: (D)

(√

)

7. A parallel plate capacitor with plates of area each, are at a separation of

If the electric field between the plates is ⁄ the magnitude of charge on each

plate is: (Take

)

(A)

(B)

(C)

(D)

Solution: (A)

⁄

8. A plano – convex lens (focal length , refractive index radius of curvature R) fits

exactly into a plano – concave lens (focal length refractive index radius of

curvature R). Their plane surfaces are parallel to each other. Then, the focal length of

the combination will be:

(A)

(B)

(C)

(D)

Solution: (A)

( ) (

)

( ) (

)

When joined together

9. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its

own vertical axis, the liquid rises up near the wall. If the radius of vessel is and its

rotational speed is rotations per second, then the difference in the heights between

the center and the sides, in will be:

(A)

(B)

(C)

(D)

Solution: (B)

When cylinder is rotated, water will rise at the edge and will dip at the centre. The

difference in pressure at and is Due to height difference.

pressure difference Due to rotation.

(

)

( )

( )

10. A block kept on a rough inclined plane, as shown in the figure, remains at rest upto

a maximum force down the inclined plane. The maximum external force up the

inclined plane that does not move the block is The coefficient of static friction

between the block and the plane is: [Take ⁄ ]

(A) √

(B)

(C)

(D) √

Solution: (D)

( )

( )

( √ ) ( √ )

√

√

11. Formation of real image using a biconvex lens is shown below:

If the whole set up is immersed in water without disturbing the object and the screen

positions, what will one observe on the screen?

(A) Image disappears

(B) Magnified image

(C) Erect real image

(D) No change

Solution: (A)

When we put our system in water, the focal length of lens is increased. Now image is

not formed on screen.

12. An ideal gas is enclosed in a cylinder at pressure of atm and temperature,

The mean time between two successive collisions is If the pressure is

doubled and temperature is increased to the mean time between two successive

collisions will be close to:

(A)

(B)

(C)

(D)

Solution: (D)

√

Where number of molecules per unit volume.

√

√

√

√

13. An alpha – particle of mass suffers dimensional elastic collision with a

nucleus at rest of unknown mass. It is scattered directly backwards losing, of its

initial kinetic energy. The mass of the nucleus is:

(A)

(B)

(C)

(D)

Solution: (B)

From momentum conservation ……..(1)

Using kinetic energy conservation

………….(2)

As it retain . Hence

On solving we get

14. A resonance tube is old and has jagged end. It is still used in the laboratory to

determine velocity of sound in air. A tuning fork of frequency produces first

resonance when the tube is filled with water to a mark below a reference mark,

near the open end of the tube. The experiment is repeated with another fork of

frequency which produces first resonance when water reaches a mark

below the reference mark. The velocity of sound in air, obtained in the experiment, is

close to:

(A)

(B)

(C)

(D)

Solution: (D)

…(i)

…(ii)

Equation (ii)-(i)

⁄

⁄

15. A vertical closed cylinder is separated into two parts by a frictionless piston of mass

and of negligible thickness. The piston is free to move along the length of the

cylinder. The length of the cylinder above piston is and that below the piston is

such that Each part of the cylinder contains moles of an ideal gas at equal

temperature If the piston is stationary, its mass, will be given by:

(R is universal gas constant and is the acceleration due to gravity)

(A)

*

+

(B)

*

+

(C)

*

+

(D)

*

+

Solution: (B)

(

)

(

)

16. A paramagnetic material has ⁄ Its magnetic susceptibility at

temperature is Its susceptibility at is:

(A)

(B)

(C)

(D)

Solution: (C)

From curie law

17. In the circuit shown, find if the effective capacitance of the whole circuit is to be

All values in the circuit are in

(A)

(B)

(C)

(D)

Solution: (C)

Let us take the equivalent circuit one by one.

= 0.5

18. The moment of inertial of a solid sphere, about an axis parallel to its diameter and at

a distance of from it, is ( ) Which one of the graphs represents the variation of

( ) with correctly?

(A)

(B)

(C)

(D)

Solution: (A)

Parabola opening upward

19. The mean intensity of radiation on the surface of the Sun is about ⁄ The

rms value of the corresponding magnetic field is closest to:

(A)

(B)

(C)

(D)

Solution: (D)

√

√

√

20. In the figure, given that supply can vary from to

and The minimum base current and the input

voltage at which the transistor will go to saturation, will be, respectively:

(A) and

(B) and

(C) and

(D) and

Solution: ()

When switched on,

using KVL at input side,

21. In a Frank – Hertz experiment, an electron of energy passes through

mercury vapour and emerges with an energy The minimum wavelength of

photons emitted by mercury atoms is close to:

(A)

(B)

(C)

(D)

Solution: (A)

When electron pass through the mercury vapor, it loses some of its energy. The loss in

of electron ( )

energy of radiation emitted

wavelength of radiation,

22. The charge on a capacitor plate in a circuit, as a function of time, is shown in the

figure:

What is the value of current at

(A)

(B)

(C) Zero

(D)

Solution: (C)

Since

|

Therefore current

23.

In the above circuit, √

√

and Current in

path is and in path it is The voltage of source is given by,

√ ( ) volts. The phase difference between and is:

(A)

(B)

(C)

(D)

Solution: ()

Inductive reactance √

√

Capacitive reactance

√

√

For , phase difference between & voltage,

√

√

current lagging

For , phase difference,

√

√

current leading.

difference in phase .

24. A galvanometer, whose resistance is , has divisions in it. When a current

of A passes through it, its needle (pointer) deflects by one division. To use this

galvanometer as a voltmeter of range it should be connected to a resistance of:

(A)

(B)

(C) 6

(D)

Solution: (B)

current for full scale deflection

Voltage for full scale deflection

Range is to be increased to

Additional resistance to be added in series ( )

Threshold frequency is more than incident frequency. Hence photoelectric will not be

emitted.

25. In the given circuit diagram, the currents, and

are flowing as shown. The currents and respectively, are:

(A)

(B)

(C)

(D)

Solution: (A)

It is problem of kirchhof’s current law.

( )

26. A simple harmonic motion is represented by:

( √ )

The amplitude and time period of the motion are:

(A)

(B)

(C)

(D)

Solution: (B)

( ) √

( √ )

27. A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in

volume, with time, at a constant rate. The graph that correctly depicts the time

dependence of pressure inside the bubble is given by:

(A)

(B)

(C)

(D)

Solution: (A)

(

)

(

)

28. A load of mass is suspended from a steel wire of length and radius

is Searle’s apparatus experiment. The increase in length produced in the wire

is Now the load is fully immersed in a liquid of relative density The relative

density of the material of load is The new value of increase in length of the steel wire

is:

(A)

(B) Zero

(C)

(D)

Solution: (D)

( )

29. A particle of mass is released with an initial velocity ⁄ along the curve

from the point as shown in the figure. The point is at height from point The

particle slides along the frictionless surface. When the particle reaches point its

angular momentum about will be: (Take ⁄ )

(A) ⁄

(B) ⁄

(C) ⁄

(D) ⁄

Solution: (C)

Applying conservation of energy

√

√

⁄

⁄

30. In a radioactive decay chain, the initial nucleus is At the end there are

particles and particles which are emitted. If the end nucleus is and are

given by:

(A)

(B)

(C)

(D)

Solution: (A)

Change in ( )

Change in

→

Chemistry Single correct answer type: 1. The major product of the following reaction is:

(A)

(B)

(C)

(D) Solution: (C)

is a strong reducing agent as it can reduce carboxylic acids, aldehydes, ketones and alcohols. But it cannot reduce double bonds. Also acts as a solvent in the above reaction and does not take part chemically. Hence, the reaction will be

2. The volume strength of is: (Molar mass of )

(A) (B) (C)

(D)

Solution: (C)

Volume strength

3. The two monomers for the synthesis of Nylon are: (A) ( ) ( )

(B) ( ) ( ) (C) ( ) ( ) (D) ( ) ( ) Solution: (B)

Nylon is made up by hexamethylene diamine ( ( ) ) and Adipic acid ( ( ) ) ( ) ( )

4. The element that does NOT show catenation is:

(A) (B) (C)

(D) Solution: (D)

atom has the tendency to link with one another through covalent bonds to form chavis and rings (catenation) this is because bonds are very strong. Down the group the size increases tendency to show catenation decreases. This is because of

bond enthalpy. The order of catenation is does not show catenation. 5. The major product of the following reaction is:

(A)

(B)

(C)

(D) Solution: (a)

6. The major product of the following reaction is:

(A)

(B)

(C)

(D) Solution: (D)

7. The major product of the following reaction is:

(A) (B)

(C) (D) Solution: (C)

8. The major product of the following reaction is:

(A)

(B)

(C)

(D) Solution: (C) In Fischer projection formula

present at leaving roup. sayzeff product will from. (more stable alkene)

9. The increasing order of the reactivity of the following with is:

( )

( )

( )

( )

(A) ( ) ( ) ( ) ( ) (B) ( ) ( ) ( ) ( ) (C) ( ) ( ) ( ) ( ) (D) ( ) ( ) ( ) ( ) Solution: (A)

In the mentioned, will get added to the carbon having slight positive charge. Presence of increases the positive charge whereas an electron donating group like

decreases the tendency. Hence, the correct order will be:

10. The compound that is a common component of photochemical smog is:

(A)

(B)

(C)

(D)

Solution: b is answer )

Photochemical smog, often refused to as summer smog consists of nitrogen oxides,

volatile organic

compounds, tropospheric ozone, etc., It is formed when there components react in the

presence of

sunlight.

, a chlorofluorocarbon, is not present in photochemical smog, but is a major

cause of ozone-layer

depletion.

11. Given:

( ) ( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

Based on the above thermochemical equations, find out which one of the following

algebraic relationship is correct?

(A)

(B)

(C)

(D)

Solution: (A)

We get above equation add n of and

12. The magnetic moment of an octahedral homoleptic ( ) complex is . The

suitable ligand for this complex is:

(A)

(B)

(C) ethylenediamine

(D)

Solution: (d)

will have configuration

√ ( )

or, as √

If has unpaired electron which are not getting paired up. This implies that the ligand

paired up. This implies that the ligand is a weak field ligand. Among the given options,

weak ligand is

13. Chlorine on reaction with hot and concentrated sodium hydroxide gives:

(A) and

(B) and

(C) and

(D) and

Solution: (B)

Ions will be

14. Molecules of benzoic acid ( ) dimerise in benzene. ‘ ’ of benzene

shows a depression in freezing point equal to . If the percentage association of the

acid to form dimer in the solution is , then is: (Given that , molar

mass of benzoic acid )

(A)

(B)

(C)

(D)

Solution: (B)

( )

because benzoic acid is dimerised mwy of

here (

)

(

)

Put the value in equation ( )

of benzoic acid

15. If the de Broglie wavelength of the electron in Bohr orbit in a hydrogenic atom is

equal to ( is Bohr radius), then the value of

is:

(A)

(B)

(C)

(D)0.75

Answer is (d)

16. of is dissolved in of . Mole fraction of in solution and

molality (in ) of the solution respectively are:

(A)

(B)

(C)

(D)

Solution: (A)

Mole fraction of

Molarity

17. If of is , the molar solubility of in is:

(A)

(B)

(C)

(D)

Solution: (D)

( )

or

18. The element that shows greater ability to form multiple bonds is:

(A)

(B)

(C)

(D)

Solution: (B)

Form most stable bonds

19. An open vessel at is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has heated is:

(A)

(B)

(C)

(D)

Solution: (D)

(

)

20. The correct order of atomic radii is:

(A)

(B)

(C)

(D)

Solution: (D)

21. The pair that does NOT require calcination is:

(A) and .

(B) and

(C) and

(D) and

Solution: (B)

Calcination is required for hydroxide carbonate and hydrated oxide ores

22. for and are and respectively. If the

conductivity of is , degree of dissociation of is

(A)

(B)

(C)

(D)

Solution: (0.125)

23. Among the following, the false statement is:

(A) Latex is a colloidal solution of rubber particles which are positively charged

(B) Tyndall effect can be used to distinguished between a colloidal solution and a true solution.

(C) It is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane.

(D) Lyophililc sol can be coagulated by adding an electrolyte.

Solution: (A)

Theory based

24. The combination of plots which does not represent isothermal expansion of an ideal gas is:

( )

( )

( )

( )

(A) ( ) and ( )

(B) ( ) and ( )

(C) ( ) and ( )

(D) ( ) and ( )

Solution: (C)

25. The correct statement( ) among to with respect to potassium ions that are

abundant within the cell fluids ⁄ :

They activate many enzymes

They participate in the oxidation of glucose to produce

Along with sodium ions, they are responsible for the transmission of nerve signals

(A) and

(B) only

(C) and only

(D) and only

Solution: (A)

Fact

26. The aldehydes which will not form Grignard product with one equivalent Grignard reagents are:

( )

( )

( )

( )

(A) ( ) ( )

(B) ( ) ( ) ( )

(C) ( ) ( )

(D) ( ) ( )

Solution: (D)

P and S will do acid base reaction with Grignard reagent rates.

27. The upper stratosphere consisting of the ozone layer protects us from the sun’s radiation that falls in the wavelengths region of:

(A)

(B)

(C)

(D)

Solution: (A)

28. The major product in the following conversion is:

(A)

(B)

(C)

(D)

Solution: (A)

29. For a reaction, consider the plot of versus ⁄ given in the figure. If the rate

constant of this reaction at is , then the rate constant at is:

(A)

(B)

(C)

(D)

Solution: (A)

30. The correct structure of histidine in a strongly acidic solution ( ) is:

(A)

(B)

(C)

(D)

Solution: (C)

Mathematics

Single correct answer type:

1. There are m men and two women participating in a chess tournament. Each

participant plays two games with every other participant. If the number of games played

by the men between themselves exceeds the number of games played between the

men and the women by 84, then the value of m is:

(A)

(B)

(C)

(D)

Solution: (B)

Since each compete two times with each other, hence boys Vs Boys total plays

Boys Vs Girls total plays

As per given condition

( )( )

2. If and are in then can be:

(A)

(B)

(C)

(D)

Solution: (B)

Since,

are in

( )

( )

( )

( )

( )( )

( )

( )

or

3. The expression ( ) is logically equivalent to:

(A)

(B)

(C)

(D)

Solution: (B)

As we know ( )

hence given expression

( )

4. The integral ∫

( ) is equal to: (where is a constant of integration)

(A)

( )

(B)

( )

(C)

( )

(D)

( )

Solution: (D)

The given integral can be written as

∫

( )

Let

( )

∫

( )

( )

5. If the sum of the first terms of the series .

/

.

/

.

/

.

/

is equal to then is equal to:

(A)

(B)

(C)

(D)

Solution: (B)

Given series can be written as

.

/

.

/

.

/

.

/

.

/

terms

( )

(

)

Since, given

6. The integral ∫ {.

/

.

/ }

is equal to:

(A)

(B)

(C)

(D)

Solution: (A)

Let ∫ .

/

Let .

/

∫

and ∫ .

/

Let .

/

∫ (

)

Hence required integral is .

/ ( )

7. .

/ is equal to:

(A)

(B) ( )

(C)

(D) ( )

Solution: (B)

( )

∑

∑

. /

∫

, -

8. Let be a differentiable function such that ( ) and ( ) ( ) for all . If

( ) ( ( )) then h’ (1) is equal to:

(A)

(B)

(C)

(D)

Solution: (C)

Given ( ) ( ( ))

( ) ( ( )) ( )

( ) ( ( )) ( ) (as ( ) ( ) ….(i)

Now ( ) ( )

( )

( )

( )

( )

From equation(i),

( )

.

/ (

)

( )

9. √ √

√ is equal to:

(A) √

(B) √

(C)

√

(D) √

Solution: (B)

Given limit can be written as

√ √

√

√ √

√ √

√ (√ √ )

√ (√ √ )

Let

√ put we get

√

√

√

√ √

10. The equation of a tangent to the parabola, which makes an angle with

the positive direction of x-axis, is

(A)

(B)

(C)

(D)

Solution: (C)

As we know, if the line is a tangent to then

So equation of tangent with slope is

….(i)

Since tangent is inclined at as with the positive axis, have

Equation of tangent is

11. The total number of irrational terms in the binomial expansion of .

/

is:

(A)

(B)

(C)

(D)

Solution: (C)

General term is .

/

.

/

We will get rational term when is multiple of and is multiple of

Number of irrational term Total term - Number of rational term

12. The mean and the variance of five observations are and respectively. If three

of the observations are and then the absolute value of the difference of the other

two observations, is:

(A)

(B)

(C)

(D)

Solution: (C)

Let rest two observations are &

….(i)

Variance,

( )

…………(ii)

from (i) & (ii),

( )

13. Let be the set of integers. If { ( )( ) } and *

+ then the number of subsets of the set is:

(A)

(B)

(C)

(D)

Solution: (D)

Given ( )( )( )

( )

Again,

( )

( )

number of subset of

14. If [

] then for all (

), det (A) lies in the interval:

(A) 5

1,2

(B) 5

,42

(C) 3

,32

(D) 3

0,2

Solution: (C)

( ) ( ) ( ) ( )

[

] [

]

( ) , - which is a subset of 3

,32

15. If a straight line passing through the point ( ) is such that its intercepted

portion between the coordinate axes is bisected at P, then its equation is:

(A)

(B)

(C)

(D)

Solution: (B)

Let the line passing through ( ) intersect the coordinate axes at &

Clearly

and

and

Hence equation of line is

16. If a circle of radius R passes through the origin O and intersects the coordinate axes

at A and B, then the locus of the foot of perpendicular from O on AB is:

(A) 2 2 2x y x y R xy

(B) 3

2 2 2 2 24x y R x y

(C) 2

2 2 2 2 24x y R x y

(D) 2

2 2 2 24x y Rx y

Solution: (B)

Since circle passing through origin intersect the coordinate axes at hence

must be diameter and

Now, let foot of the perpendicular from origin upon be ( )

Equation is

( ) .

/ & .

/

√(

)

(

)

( ) (

) ( )

Hence locus is ( )

17. Let S and S’ be the foci of an ellipse and B be any one of the extremities of its minor

axis. If is a right angled triangle with right angle at B and area ( ) sq.

units, then the length of a latus rectum of the ellipse is:

(A) √

(B)

(C)

(D) 4 2

Solution: (C)

Given

….(i)

Also, area ( )

….(ii)

From (i) and (ii)

and

√ and

Length of the latus rectum

18. The tangent to the curve , parallel to the line also

passes through the point:

(A) .

/

(B) .

/

(C) .

/

(D) .

/

Solution: (D)

Equation of line parallel to given line can be taken as Now this line touches

the curve hence roots of the equation must be

equal

Hence equation of tangent is

Clearly it passes through .

/

19. If an angle between the line,

and the plane, is

. √

/ then a value of k is:

(A) √

(B) √

(C)

(D)

Solution: (A)

cos ( )

( ) ( )

√ √

√

√ √

20. In a class of students, opted for NCC, opted for NSS and opted for both

NCC and NSS. If one of these students is selected at random, then the probability that

the student selected has opted neither for NCC nor for NSS is:

(A)

(B)

(C)

(D)

Solution: (A)

( ) ( ) ( )

( ) ( ) ( ) ( )

( )

( ) ( )

21. If the function given by ( ) ( ) , for some is

increasing in ( - and decreasing in , ) then a root of the equation, ( )

( ) (

) is:

(A)

(B)

(C)

(D)

Solution: (A)

At ( )

( ) ( )

( )

( )

( )

( )

22. If a curve passes through the point ( ) and has slope of the tangent at any point

( ) on it as

, then the curve also passes through the point:

(A) (√ )

(B) ( )

(C) ( √ )

(D) ( )

Solution: (A)

It is in linear form

∫

∫

at

( )

curve is

It passes through (√ )

23. The number of integral values of m for which the quadratic expression,

( ) ( ) ( ) is always positive, is

(A)

(B)

(C)

(D)

Solution: (A)

Quadratic expression is positive, hence and

and ( ) ( )( )

( )

( √ )( √ )

( √ √ )

number of integral values

24. If the angle of elevation of a cloud from a point P which is above a lake be

and the angle of depression of reflection of the could in the lake from P be then the

height of the cloud (in meters) from the surface of the lake is:

(A)

(B)

(C)

(D)

Solution: (A)

and

25. Let and be two complex numbers satisfying and .

Then the minimum value of is:

(A)

(B) √

(C)

(D)

Solution: (C)

( ) ( )

and circles touch each other internally

at the point of contact

26. In a game, a man wins Rs. if he gets or on a throw of a fair die and loses

Rs. for getting any other number on the die. If he decides to throw the die either till

he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in

rupees) is:

(A)

gain

(B)

gain

(C)

loss

(D)

Solution: (D)

P(success) ( )

expectations equal to

27. Let be the set of all real values of such that a plane passing through the points

( ) ( ) and ( ) also passes through the point ( ) Then

is equal to:

(A) *√ +

(B) * +

(C) * +

(D) {√ √ }

Solution: (D)

As we know, is four points P, A, B, C are planar, the vectors must be

coplanar

( )

|

|

√

28. The set of all values of for which the system of linear equations

has a non-trivial solution:

(A) is an empty set

(B) contains more than two elements

(C) is a singleton

(D) contains exactly two elements

Solution: (C)

For non-trivial solution

|

|

( )( ) ( ) ( )

( )

Singleton set

29. If √ , - then ( ) ( ) is

equal to:

(A)

(B) √

(C) √

(D)

Solution: (B)

( )

So

√

Hence

√ √

30. Let and be three unit vectors, out of which vectors and are non-parallel. If

and are the angles which vector makes with vectors and respectively and

( )

then is equal to:

(A)

(B)

(C)

(D)

Solution: (D)

( )

( ) ( )

is not parallel to

and