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QUESTION: 1

The function is continuous everywhere except at

Solution:

QUESTION: 2

A classical particle has total energy E. The plot of potential energy (U) as a function of distance (r) from the centre of force located at r = 0 is shown in the figure. Which of the regions are forbidden for the particle?

Solution:

QUESTION: 3

In the thermal neutron induced fission of ^{235}U, the distribution of relative number of the observed fission fragments (Yield) versus mass number (A) is given by

Solution:

QUESTION: 4

Which one of the following crystallographic planes represent (101) Miller indices of a cubic unit cell?

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QUESTION: 5

The Fermi-Dirac distribution function [n(ε)] is (k_{B} is the Boltzmann constant, T is the temperature and ε_{F} is the Fermi energy)

Solution:

QUESTION: 6

If Ø (x,y,z) is a scalar function which satisfies the Laplace equation, then the gradient off is

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QUESTION: 7

In a heat engine based on the Carnot cycle, heat is added to the working substance at constant

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QUESTION: 8

Isothermal compressibility is given by

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QUESTION: 9

For using a transistor as an amplifier, choose the correct option regarding the resistances of base-emitter (R_{BE}) and base-collector (R_{BC}) junctions

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QUESTION: 10

A unit vector perpendicular to the plane containing and is

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QUESTION: 11

A thin lens of refractive index 3/2 is kept inside a liquid of refractive index 4/3. If the focal length of the lens in air is 10 cm, then its focal length inside the liquid is

Solution:

QUESTION: 12

The eigenvalues ofare

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QUESTION: 13

A quantum particle confined inside a cubic box of side L, the ground state energy is given by E_{0}. The energy of the first excited state is

Solution:

QUESTION: 14

A small spherical ball having charge q and mass m, is tied to a thin massless nonconducting string of length l. The other end of the string is fixed to an infinitely extended thin non-conducting sheet with uniform surface charge density σ . Under equilibrium, the string makes an angle 45° with the sheet as shown in the figure. Then σ is given by (g is the acceleration due to gravity and ε_{0 }is the permittivity of free space)

Solution:

QUESTION: 15

Consider the normal incidence of a plane electromagnetic wave with electric field given by ω over an interface at z = 0 separating two media [wave velocities v_{1} and v_{2} (v_{2} > v_{1}) and wave vectors k_{1} and k_{2}, respectively] as shown in figure. The magnetic field vector of the reflected wave is (ω is the angular frequency)

Solution:

QUESTION: 16

The output of following logic circuit can be simplified to

Solution:

QUESTION: 17

A red star having radius r_{R} at a temperature T_{R} and a white star having radius r_{W} at a temperature T_{W} , radiate the same total power. If these stars radiate as perfect black bodies, then

Solution:

QUESTION: 18

The mass per unit length of a rod (length 2 m) varies as ρ = 3x kg/m. The moment of inertia (in kg m^{2}) of the rod about a perpendicular-axis passing through the tip of the rod (at x = 0) is

Solution:

QUESTION: 19

For a forward biased p-n junction diode, which one of the following energy-band diagrams is correct?

(ε_{F} is the Fermi energy)

Solution:

QUESTION: 20

The amount of work done to increase the speed of an electron from c/3 to 2c/3 is (c = 3×10^{8} m/s and rest mass of electron is 0.511 MeV)

Solution:

QUESTION: 21

The location of Cs^{+} and Cl^{–} ions inside the unit cell of CsCl crystal is shown in the figure. The Bravais lattice of CsCl is

Solution:

QUESTION: 22

A γ-ray photon emitted from a ^{137}Cs source collides with an electron at rest. If the Compton shift of the photon is 3.25 × 10^{–13} m, then the scattering angle is closest to (Planck’s constant h = 6.626 × 10^{–34} J s, electron mass me = 9.109 × 10^{–31} kg and velocity of light in free space c = 3×10^{8} m/s)

Solution:

QUESTION: 23

During free expansion of an ideal gas under adiabatic condition, the internal energy of the gas

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QUESTION: 24

In the given phase diagram for a pure substance, regions I, II, III, IV, respectively represent

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QUESTION: 25

Light of wavelength λ (in free space) propagates through a dispersive medium with refractive index n(λ)=1.5 + 0.6λ. The group velocity of a wave travelling inside this medium in units of 10^{8} m/s is

Solution:

QUESTION: 26

The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be

Solution:

QUESTION: 27

During the charging of a capacitor C in a series RC circuit, the typical variations in the magnitude of the charge q(t) deposited on one of the capacitor plates, and the current i(t) in the circuit, respectively are best represented by

Solution:

QUESTION: 28

Which one of the following is an impossible magnetic field ?

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QUESTION: 29

If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle is

Solution:

QUESTION: 30

A ball of mass m is falling freely under gravity through a viscous medium in which the drag force is proportional to the instantaneous velocity v of the ball. Neglecting the buoyancy force of the medium, which one of the following figures best describes the variation of v as a function of time t?

Solution:

*Multiple options can be correct

QUESTION: 31

The relation between the nuclear radius (R) and the mass number (A), given by R = 1.2 A^{1/3} fm, implies that

Solution:

*Multiple options can be correct

QUESTION: 32

Consider an object moving with a velocity in a frame which rotates with a constant angular velocity . The Coriolis force experienced by the object is

Solution:

*Multiple options can be correct

QUESTION: 33

The gradient of a scalar field S(x,y,z) has the following characteristic(s).

Solution:

*Multiple options can be correct

QUESTION: 34

A thermodynamic system is described by the P, V, T coordinates. Choose the valid expression(s) for the system.

Solution:

*Multiple options can be correct

QUESTION: 35

Which of the following statement(s) is/are true?

Solution:

*Multiple options can be correct

QUESTION: 36

For an underdamped harmonic oscillator with velocity v(t),

Solution:

*Multiple options can be correct

QUESTION: 37

Out of the following statements, choose the correct option(s) about a perfect conductor.

Solution:

*Multiple options can be correct

QUESTION: 38

In the X-ray diffraction pattern recorded for a simple cubic solid (lattice parameter a = 1 Å) using X rays of wavelength 1 Å, the first order diffraction peak(s) would appear for the

Solution:

*Multiple options can be correct

QUESTION: 39

Consider a classical particle subjected to an attractive inverse-square force field. The total energy of the particle is E and the eccentricity is ε. The particle will follow a parabolic orbit if

Solution:

*Multiple options can be correct

QUESTION: 40

An atomic nucleus X with half-life TX decays to a nucleus Y, which has half-life TY. The condition(s) for secular equilibrium is(are)

Solution:

*Answer can only contain numeric values

QUESTION: 41

In a typical human body, the amount of radioactive ^{40}K is 3.24 × 10^{–5} percent of its mass. The activity due to ^{40}K in a human body of mass 70 kg is ________ kBq.

(Round off to 2 decimal places)

(Half-life of ^{40}K = 3.942 × 10^{16} s, Avogadro’s number N_{A} = 6.022 × 10^{23} mol^{–1})

Solution:

*Answer can only contain numeric values

QUESTION: 42

Sodium (Na) exhibits body-centered-cubic (BCC) crystal structure with atomic radius 0.186 nm. The lattice parameter of Na unit cell is ________ nm.

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 43

Light of wavelength 680 nm is incident normally on a diffraction grating having 4000 lines/cm. The diffraction angle (in degrees) corresponding to the third-order maximum is ________.

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 44

Two gases having molecular diameters D_{1} and D_{2}, and mean free paths λ_{1} and λ_{2}, respectively, are trapped separately in identical containers.

If D_{2} = 2D_{1}, then λ_{1}/λ_{2} = ________.

(Assume there is no change in other thermodynamic parameters)

Solution:

*Answer can only contain numeric values

QUESTION: 45

An object of 2 cm height is placed at a distance of 30 cm in front of a concave mirror with radius of curvature 40 cm. The height of the image is ________ cm.

Solution:

*Answer can only contain numeric values

QUESTION: 46

The flux of the function passing through the surface ABCD along is ________.

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 47

The electrostatic energy (in units of of a uniformly charged spherical shell of total charge 5 C and radius 4 m is ________.

(Round off to 3 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 48

An infinitely long very thin straight wire carries uniform line charge density 8π × 10^{–2} C/m. The magnitude of electric displacement vector at a point located 20 mm away from the axis of the wire is ______ C/m^{2}.

Solution:

*Answer can only contain numeric values

QUESTION: 49

The 7^{th} bright fringe in the Young’s double slit experiment using a light of wavelength 550 nm shifts to the central maxima after covering the two slits with two sheets of different refractive indices n_{1} and n_{2} but having same thickness 6 µm. The value of |n_{1}–n_{2}| is ________.

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 50

For the input voltage V_{i} = (200 mV) sin (400t), the amplitude of the output voltage (V_{0}) of the given OPAMP circuit is ________ V.

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 51

The value of emitter current in the given circuit is ________ µA.

(Round off to 1 decimal place)

Solution:

*Answer can only contain numeric values

QUESTION: 52

The value of , along the line 3 y=x , where z = x+ iy is ________.

(Round off to 1 decimal place)

Solution:

*Answer can only contain numeric values

QUESTION: 53

If the wavelength of Kα^{2} X-ray line of an element is 1.544Å, then the atomic number (Z) of the element is ________.

(Rydberg constant R = 1.097×10^{7}m^{–1} and velocity of light c = 3×10^{8} m/s)

Solution:

*Answer can only contain numeric values

QUESTION: 54

A proton is confined within a nucleus of size 10^{–13} cm. The uncertainty in its velocity is ________ × 10^{8} m/s.

(Round off to 2 decimal places)

(Planck’s constant h = 6.626 × 10^{–34} J s and proton mass mp = 1.672 × 10^{–27} kg)

Solution:

*Answer can only contain numeric values

QUESTION: 55

Given the wave function of a particle for 0 < x < L and 0 elsewhere, the probability of finding the particle between x = 0 and x =L/2 is _______.

(Round off to 1 decimal place)

Solution:

*Answer can only contain numeric values

QUESTION: 56

The Zener current I_{Z} for the given circuit is ________ mA.

Solution:

*Answer can only contain numeric values

QUESTION: 57

If the diameter of the Earth is increased by 4% without changing the mass, then the length of the day is ________hours.

(Take the length of the day before the increment as 24 hours. Assume the Earth to be a sphere with uniform density.)

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 58

A di-atomic gas undergoes adiabatic expansion against the piston of a cylinder. As a result, the temperature of the gas drops from 1150 K to 400 K. The number of moles of the gas required to obtain 2300 J of work from the expansion is ________.

(The gas constant R = 8.314 J mol^{–1}K^{–1}.)

(Round off to 2 decimal places)

Solution:

*Answer can only contain numeric values

QUESTION: 59

The decimal equivalent of the binary number 110.101 is ________.

Solution:

*Answer can only contain numeric values

QUESTION: 60

A surface current A/m flows on the surface z = 0,which separates two media with magnetic permeabilities µ1 and µ2 as shown in the figure. If the magnetic field in the region 1 is mT, then the magnitude of the normal component of will be ________ mT.

Solution:

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