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QUESTION: 1

The magnetic field of a plane electromagnetic wave is given by:

The rms value of the force experienced by a stationary charge Q =10^{–4}C at z = 0 is

Solution:

QUESTION: 2

A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ‘3a’ from the centre will be:

Solution:

Field at

Field =

QUESTION: 3

A moving coil galvanometer has resistance 50Ω and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a 5 kΩ resistance.The maximum voltage, that can be measured using this voltmeter, will be close to:

Solution:

QUESTION: 4

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127ºC. At 2 atm pressure and at 227ºC, the rms speed of the molecules will be:

Solution:

QUESTION: 5

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2^{nd} Balmer line (n = 4 to n = 2) will be:

Solution:

1^{st} line Balmer

QUESTION: 6

The pressure wave, P = 0.01sin[1000t – 3x]Nm^{–2} , corresponds to the sound produced

by a vibrating blade on a day when atmospheric temperature is 0ºC. On some other day when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336ms^{–1} . Approximate value of T is:

Solution:

QUESTION: 7

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane :

(i) a ring of radius R,

(ii) a solid cylinder of radius R/2 and

(iii) a solid sphere of radius R/4. If, in each case, the speed of the center of mass at the bottom of the incline is same, theratio of the maximum heights they climb is:

Solution:

QUESTION: 8

An NPN transistor is used in common emitter configuration as an amplifier with1kΩ load resistance. Signal voltage of 10 mV is applied across the base-emitter. Thisproduces a 3 mA change in the collector current and 15μ A change in the basecurrent of the amplifier. The input resistance and voltage gain are:

Solution:

Voltage gain

Voltage gain = 300

QUESTION: 9

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum – height (p-h) diagram is:

Solution:

v^{2} - u^{2} = -2 gh

v^{2} = v^{2} - 2 gh

p^{2} = A - Bh

QUESTION: 10

The electric field of light wave is given as .

The light falls on a metal plate of work function 2eV. The stopping potential of the

photo-electrons is:Given, E (in eV)

Solution:

hv = hv_{0} + s. potential

= w + s potential

2.48 = 2ev + s. potential

stop potential = 0.4eV

QUESTION: 11

A string is clamped at both the ends and it is vibrating in its 4^{th} harmonic. The equation of the stationary wave is Y= 0.3sin(0.157x)cos(200π) . The length of the string is: (All quantities are in SI units.)

Solution:

ln 4^{th} harmonic

QUESTION: 12

A signal Acosωt is transmitted using ν_{0} sin ω_{0}t as carrier wave. The correct amplitude modulated (AM) signal is:

Solution:

Mododulater wave =

QUESTION: 13

In the density measurement of a cube, the mass and edge length are\ measured as (10.00 ± 0.10) kg and ( 0.10 ± 0.01) m, respectively. The error in the measurement of density is:

Solution:

mass = (10 ± 0.1) kg

Length = ( 0.1 ± 0.01) m

Denisty ==D

=0.01+0.3

= 0.31 kg/m^{3}

QUESTION: 14

A simple pendulum oscillating in air has period T. The bob of the pendulum is

completely immersed in a non-viscous liquid. The density of the liquid is of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

Solution:

QUESTION: 15

If ‘M’ is the mass of water that rises in a capillary tube of radius ‘r’, then mass of

water which will rise in a capillary tube of radius ‘2r’ is:

Solution:

mass α r^{2}h

mass α r

So final mass rise = 2M

QUESTION: 16

Following figure shows two process A and B for a gas. If ΔQ_{A} and ΔQ_{B} are the amount of heat absorbed by the system in two cases, and ΔU_{A} and ΔU_{B }are changes in internal energies, respectively, then:

Solution:

QUESTION: 17

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

Solution:

WKT

Self inductance L = μn^{2} x(volume)

Self inductance

QUESTION: 18

A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such

that its part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

Solution:

The resultant is the centre of mass of the part AB is shifter to top i.e.

QUESTION: 19

A body of mass 2 kg makes an elastic collision with a second body at rest andcontinues to move in the original direction but with one fourth of its original speed.What is the mass of the second body?

Solution:

Momentum conservation

Elatic collision

Energy conservation

QUESTION: 20

A capacitor with capacitance 5μF is charged to5μC. If the plates are pulled apart to reduce the capacitance to 2μF , how much work is done?

Solution:

⇒work done by force ⇒ F×S

QUESTION: 21

A rectangular coil (Dimension5cm × 2.5cm) with 100 turns, carrying a current of 3A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45º about Z-axis, then the torque on the coil is

Solution:

Torque = M×B

= Nxi×A×B×sin 4J

= 100×3×12.5×10^{–4} ×1×

τ =0.265

QUESTION: 22

The figure shows a Young’s double slit experimental setup. It is observed that when

a thin transparent sheet of thickness t and refractive index µ is put in front of one

of the slits, the central maximum gets shifted by a distance equal to n fringe widths.

If the wavelength of light used is λ,t will be:

Solution:

S_{1} P–S_{2} P+(µ–1) t = 0

(µ–1) = S_{1} P–S_{2}

(µ–1) t =nl

QUESTION: 23

A wire of resistance R is bent to form a square ABCD as shown in the figure. The

effective resistance between E and C is: (E is mid-point of arm CD)

Solution:

QUESTION: 24

A rigid square loop of side ‘a’ and carrying current I_{2} is lying on a horizontal surface near a long current I_{1} carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

Solution:

QUESTION: 25

The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

Solution:

to cross the river straight, V _{along the river}=0

Vsteam = Vswimmer cos θ

2 = 4cos θ ⇒ cos θ =

⇒ θ = 60º

Direction w.r.t flow of river = 180º-60º = 120º

QUESTION: 26

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ , where θ is the angle by which it has rotated, is given as kθ^{2} . If its moment of inertia is I then the angular acceleration of the disc is:

Solution:

KE = Kθ^{2
}

QUESTION: 27

A system of three charges are placed as shown in the figure:

If D > > d, the potential energy of the system is best given by:

Solution:

The potential energy of +q, -q system is

The system of +q, -q act as an electric dipole as d<<D

Hence, Potential energy between Q and dipole is

Hence,

QUESTION: 28

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is , m is its mass and K_{B}is Boltzman constant, then its temperature will be :

Solution:

QUESTION: 29

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

Solution:

QUESTION: 30

Determine the charge on the capacitor in the following circuit:

Solution:

QUESTION: 31

Among the following, the set of parameters that represents path functions, is:

A) q+w

B) q

C) w

D) H-TS

Solution:

Except q, w all other thermodynamic variables are state functions q, w are path functions.

QUESTION: 32

The correct IUPAC name of following compound is

Solution:

NO - Nitro Cl - Chloro CH_{3} - Methyl

QUESTION: 33

The degenerate orbitals of [Cr (H_{2}O)_{6}]^{3+} are

Solution:

d_{zx} , d_{yz} are degenerate in octahedral splitting.

QUESTION: 34

The organic compound that gives following qualitative analysis is:

Solution:

insoluble in Dil. HCl, Soluble in NaOH solution , & Decolourization of Br_{2} / water

QUESTION: 35

Excessive release of CO_{2} into the atmosphere results in

Solution:

Excessive release of CO_{2} into the atmosphere results in global warming.

QUESTION: 36

The element having greatest difference between its first and second ionization energies, is

Solution:

In given options k has greatest difference between its first & second ionisation energies.

QUESTION: 37

The major product of the following reaction is:

Solution:

QUESTION: 38

The number of water molecules not coordinated to copper ion directly in CuSOl 4.5H_{2} O, is

Solution:

In CnSO_{4} .5H_{2}O , four water molecules are coordinates to Cu^{2+} ion and one water molecules is outside the coordinate sphere.

Number of water molecules not coordinated to copper ion is

QUESTION: 39

C_{60} , an allotrope of carbon contains:

Solution:

In C_{60} , hexagonal, 12 pentagonal

⇒ 20 hexagonal, 12 petagonal

QUESTION: 40

Aniline dissolved in dilute HCl is reacted with sodium nitrite at 0ºC. this solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is

Solution:

In equimolar mixture of aniline, phenol in dil.HCl, amiline in more reactive, as slightly acidic medium supports.

QUESTION: 41

The major product of the following reaction is

Ch_{3}Cº =CH

Solution:

QUESTION: 42

The standard Gibbs energy for the given cell reaction in kJ mol^{-1} at 298 K is:

Zn (s) + Cu^{2+} (aq) ® Zn^{2+} (aq) + Cu (s), Eº = 2V at 298K

Solution:

ΔGº = -nFEº_{cell}

= -2 x 96000 x 2

= -4 x 96kJ = -384kJ

QUESTION: 43

The given plots represent the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are

Solution:

T is proportional [R] it is 1^{st} order t is proportional to [R] it is 0^{th} order

QUESTION: 44

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is

Solution:

B > C > A > D(dueto + M, Directing)

QUESTION: 45

The correct order of the oxidation states of nitrogen in NO, N_{2}O, NO_{2} and N_{2}O_{3} is

Solution:

QUESTION: 46

Match the catalysts (colum I) with products (column II).

Solution:

QUESTION: 47

Which of the following statement is not true about sucrose?

Solution:

QUESTION: 48

The aerosol is a kind of colloid in which:

Solution:

aerosol is a kind of colloid is disersion phase(s) dispersion medium(g)

QUESTION: 49

The major product of the following reaction is

Solution:

QUESTION: 50

Consider the van der walls constants, a and b, for the following gases

Q. Which gas is expected to have the highest critical temperature

Solution:

To have highest critical temperature a should be high b should below so, it is Kr

QUESTION: 51

Among the following, the molecule expected to be stabilized by anion formation is:

Solution:

C_{2} has vacant and if e^{—}enters into this if will be stabilized

QUESTION: 52

The ore that contains the metal in the form of fluoride is

Solution:

Cryolife → Na_{3}AlF_{6}

Malachite → CuCO_{3}.CU(OH)_{2}

Magnetite → Fe_{3}O_{4}

Sphalarite ®ZnS

QUESTION: 53

The one that will show optical activity is:

(en = ethane – 1,2, -diamine)

Solution:

Given which will show optical activity

The Compound should not have plans of symmetry only compounds in options

QUESTION: 54

For any given series of spectral lines of atomic hydrogen, let be the difference in maximum and minimum frequencies in cm^{-1} . The ratio is:

Solution:

QUESTION: 55

The major product of the following reaction is:

Solution:

QUESTION: 56

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M BaCl_{2} in water. Assuming complete dissociation of the given ionic compounds is water, the concentration of XY (in mol L^{-1}) in solution is

Solution:

2 – Chloro – 1 – methyl - 4 – nitro benzene

C = 0.06 M

QUESTION: 57

For a reaction, n_{2}(g)+H_{2} (g) →2NH_{3}(g): identify dihydrogen ( H_{2} ) as a limiting reagent in the following reaction mixtures.

Solution:

N_{2} + 3H_{2} → 2NH_{3}

56g 10g

2 mol 5 mol

Actually 6 mol of H_{2} is required but only 5 mol present so it is limiting reagent.

QUESTION: 58

Magnesium powder burns in air to give:

Solution:

Mh + O_{2} → MgO + Mg_{3} N_{2}

QUESTION: 59

The major product of the following reaction is

CH_{3} CH = CHCO_{2} CH_{3}

Solution:

QUESTION: 60

Liquid ‘M’ and liquid ‘N’ form an ideal solution. The vapour pressures of pure liquids ‘M’ and ‘N’ are 450 and 700mmHg, respectively, at the same temperature. Then correct statement is:

(x_{M} = Mole fraction of ‘M’ is solution;

x_{N} = Mole fraction of ‘N’ in solution ;

y_{M} = Mole fraction of ‘M’ in vapour phase;

y_{N} = Mole fraction of ‘N’ in vapour phase)

Solution:

QUESTION: 61

Let S = {θ ∈ [ -2π, 2π] : 2 cos^{2} θ + 3sin θ = 0} . Then the sum of the elements of S is:

Solution:

solving the trigonometric equation, we get sin θ

QUESTION: 62

If the standard deviation of the numbers -1, 0,1, k is √5 where k > 0 , then k is equal to:

Solution:

QUESTION: 63

All the points in the set lie on a:

Solution:

So x^{2} + y^{2} = 1, is a circle of radius 1

QUESTION: 64

For any two statements p and q, the negation of the expression p V ( ~ p ∧ q ) is:

Solution:

pV(~ p ∧ q) = (pV ~ p) ∧ (p V q) = T∧ (p V q) = p V q

So ~ ( p V ( ~ p ∧ q ) ) =~ ( p V q ) =~ p∧ ~ q (or) draw truth tables

QUESTION: 65

If the function f : R - {1, -1} → A defined by , is surjective, then A is equal to:

Solution:

x^{2} (1 + y) = y

y (y + 1)≥ 0 ⇒ y ∈(-∝, -1) ∪ [0, ∝)

So A = R - [ -1, 0)

QUESTION: 66

If the fourth term in the Binomial expansion of , then a value of x is:

Solution:

equate T_{4} = 20 × 8^{7
Take logaritham on both side to base 8, we get
}

QUESTION: 67

Slope of a line passing through P ( 2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is:

Solution:

QUESTION: 68

If f ( x ) is a non-zero polynomial of degree four, having local extreme points at x = -1, 0,1 ; Then the set S = {x ∈ R : f ( x ) = f ( 0)} contains exactly:

Solution:

QUESTION: 69

Let is parallel to is perpendicular to is equal to:

Solution:

QUESTION: 70

If the function f defined on is continuous, then k is equal to:

Solution:

QUESTION: 71

Let α and β be the roots of the equation x^{2} + x + 1 = 0 . Then for y ≠ 0 in R,

is equal to:

Solution:

R_{1} → R_{1} + R_{2} + R_{3} & take common ( y + 1 + α + β )

Given determinant expanding simplify = y ( y^{2} ) = y^{3}

QUESTION: 72

If the line y = mx + 7√3 is normal to the hyperbola , then a value of m is:

Solution:

Simplify we get m = 2/√5

QUESTION: 73

The value of

Solution:

Simplify we get, given integral

QUESTION: 74

If the line, meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is:

Solution:

Let P(2t + 1, 3t - 1, 4t + 2) be any point on the line, P lies on plane also

QUESTION: 75

Let = 16(2^{10} - 1), where the function f satisfies f ( x + y ) = f ( x ) f ( y ) for all natural numbers x, y and f (1) = 2 . Then the natural number 'a' is

Solution:

f ( x ) = 2^{x} & simplify (using G.P formula) we get a = 3

QUESTION: 76

If one end of a focal chord of the parabola, y^{2} = 16x is at (1, 4 ) , then the length of this focal chord is:

Solution:

So Q(16, -16 ) , ( P (1, 4) given ) PQ = 25

QUESTION: 77

The solution of the differential equation with y (1) = 1, is:

Solution:

QUESTION: 78

If the tangent to the curve, y = x^{3} + ax - b at the point (1, -5) is perpendicular to the line, - x + y + 4 = 0 , then which one of the following points lies on the curve?

Solution:

f (1) = -5 ⇒ 1 + a - b = -5 ⇒ a - b = -6 ......(1)

f^{1}(x) = 3x^{2} +a f^{1}(1) = 3+a = -1⇒ a = -4

b = a + 6 = 2

f ( x ) = x^{3} - 4 x - 2 check options (( 2, -2) satisfies )

QUESTION: 79

If then the inverse of is

Solution:

(n -1) n =156 = 13 × 2 ⇒ n =13 (n ∈ N)

So increase of

QUESTION: 80

The value of is cos^{2} 10^{0} - cos10^{0} cos 50^{0} + cos^{2} 50^{0} is :

Solution:

cos^{2} A + cos^{2} B - cos A cos B** **= 3/4, A + b = 60^{0}** **

QUESTION: 81

Let the sum of the first n terms of a non-constant A.P., a_{1} , a_{2} , a_{3} , ... be A, where A is a constant, If d is the common difference of this A.P., then the ordered pair ( d, a_{50} ) is equal to:

Solution:

d = A, a_{50} = 46A + 50

QUESTION: 82

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

Solution:

m = ^{8}C_{6} . ^{5}C_{5} + ^{8}C_{7} . ^{5}C_{4} + ^{8}C_{8} . ^{5}C_{3} = 28 + 40 + 10 = 78

n = ^{8}C_{6} . ^{5}C_{3} + ^{8}C_{7} . ^{5}C_{4} + ^{8}C_{6} . ^{5}C_{5} = 78

QUESTION: 83

Four persons can hit a target correctly with probabilities

respectively. If all hit at the target independently, then the probability that the target would be hit, is:

Solution:

1 P ( no one hiting the t arg et )

QUESTION: 84

Let S be the set of all values of x for which the tangent to the curve y = f ( x ) = x^{3} - x^{2} - 2x at ( x, y ) is parallel to the line segment joining the points (1, f (1) ) , and ( -1, f ( -1) ) , then S is equal to:

Solution:

(1, f (1) ) = (1, -2 ) , ( -1, f ( -1) ) = ( -1, 0)

slope = -1 ⇒ 3x^{2} - 2x - 2 = -1

3x^{2 }- 2x -1 = 0 ⇒ x -1)(3x +1) = 0

QUESTION: 85

The integral is equal to (Here C is a constant of integration)

Solution:

put

QUESTION: 86

Let p, q ∈ R. If 2 - √3 is a root of the quadratic equation, x^{2} + px + q = 0, then :

Solution:

2 + √3 also root, S.R = 2 + √3 + 2 - √3 = -P ⇒ p = -4

P.R = 4-3=q ⇒ q =1

So p^{2} - 4q - 12 = 16 - 4 - 12 = 0

QUESTION: 87

If a tangent to the circle x^{2} + y^{2} = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:

Solution:

Let P ( cos θ, sin θ ) be any point on circle, tangent at P is x cos θ + y sin θ = 1

P x_{1} , y_{1} ) be mid point of AB =

QUESTION: 88

The area (in sq. units) of the region A = {( x, y ) : x^{2} ≤ y ≤ x + 2} is:

Solution:

x^{2} ≤ y ≤ x + 2

x^{2} - x - 2 = 0

Draw diagram and find

QUESTION: 89

Let f ( x ) = 15 - |x - 10|; x ∈ R. Then the set of all values of x, at which the function, g ( x ) = f ( f ( x ) ) is not differentiable, is:

Solution:

f ( x) = 15 - x -10 , x ∈ R

QUESTION: 90

A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:

Solution:

is the equation of plane ……(1)

y - z = 0 ..........(2)

So plane equation is

Check options ( √2,1, 4 ) satisfies second equation

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