## IIT JAM PHYSICS 2021

Previous Year Question Paper with Solution.

1. An experiment with a Michelson interferometer is performed in vacuum using a laser of wavelength 610 nm. One of the beams of the interferometer passes through a small glass cavity 1.3 cm long. After the cavity is completely filled with a medium of refractive index n, 472 dark fringes are counted to move past a reference line. Given that the speed of light is 3 × 10^{8} m/s, the value of n is

(a) 1.06

(b) 1.01

(c) 1.04

(d) 1.10

Ans. (b)

Sol.

2. A planet is in a highly eccentric orbit about a star. The distance of its closest approach is 300 times smaller than its farthest distance from the star. If the corresponding speeds are v_{c} and v_{f}, then is

(a) 300

(b)

(c)

(d)

Ans. (a)

Sol. Using conservation of angular momentum

3. Let M be a 2 × 2 matrix. its trace is 6 and its determinant has value 8. Its eigenvalues are

(a) 2 and 6

(b) 2 and 4

(c) 3 and 3

(d) –2 and –3

Ans. (b)

Sol. M is a 2 × 2 matrix

We know trace = sum of eigenvalues

and determinant = product of eigenvalues

4. Arrange the following telescopes, where D is the telescope diameter and is the wavelength, in order of decreasing resolving power:

I. D = 100 m, = 21 cm

II. D = 2 m, = 500 nm

III. D = 1 m, = 100 nm

IV. D = 2 m, = 10 mm

(a) III, II, I, IV

(b) III, II, IV, I

(c) II, III, I, IV

(d) IV, III, II, I

Ans. (a)

Sol.

RP_{III} > RP_{II} > RP_{I} > RP_{IV}

5. The moment of inertia of a solid sphere (radius R and mass M) about the axis which is at a distance of from the center is

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

Moment of inertia of solid sphere about an axis passing through centre

Now moment of inertia about an axis from R/2 from centre

Correct option is (a)

6. Metallic lithium has bcc crystal structure. Each unit cell is a cube of side a. The number of atoms per unit volume is

(a)

(b)

(c)

(d)

Ans. (a)

Sol. There are 8 atom at corner contributing of its whole volume and one atom at centre. So total number of atom in bcc crystal structure

Number of atom per unit volume

Correct option is (a)

7. An object of density is floating in a liquid with 75% of its volume submerged. The density of the liquid is

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Let us assume total volume of object = 100m^{3}

weight of displaced liquid = weight of object

Correct option is (c)

8. For a semiconductor material, the conventional flat band energy diagram is shown in the figure. The variables Y, X, respectively, are

(a) Momentum, Energy

(b) Energy, Distance

(c) Energy, Momentum

(d) Distance, Energy

Ans. (b)

Sol. Along the y-axis energy varies while along x-axis distance is variable.

9. For the given circuit, V_{D} is the threshold voltage of the diode. The graph that best depicts the variation of V_{0} with V_{i} is

(a)

(b)

(c)

(d)

Ans. (c)

Sol. In this case diode become reverse bias so it behave like open circuit so now ckt will be

Now apply KCL

V_{i} = –V_{0}

Correct option is (c)

10. The function e^{cos x} is Taylor expanded about x = 0. The coefficient of x^{2} is

(a)

(b)

(c) Zero

(d)

Ans. (a)

Sol. Taylor expansion of a function around x = 0

Correct option is (a)

11. Four charges are placed very close to each other, as shown. The separation between the two charges on the y-axis is a. The separation between the two charges on the x-axis is also a. The leading order (non-vanishing) form of the electrostatic potential, at point P, at a distance r from the origin (r >> a), is

(a)

(b)

(c)

(d)

Ans. (a)

Sol.

12. The radial component of acceleration in plane polar coordinates is given by

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

13. A thin circular disc lying in the xy-plane has a surface mass density , given by

where r is the distance from its center. its moment of inertia about the z-axis, passing through its center is

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

Equation (2) put in equation (1)

Correct option is (b)

14. For the given circuit, the output Y is

(a) 0

(b) A

(c)

(d) 1

Ans. (c)

Sol.

This is given combination of EX NOR gate

As we know EXNOR gate

Correct option is (c)

15. A system undergoes a thermodynamic transformation from state S_{1} to state S_{2} via two different paths 1 and 2. The heat absorbed and work done along path I are 50 J and 30 J, respectively. If the heat absorbed along path II is 30 J, the work done along path II is

(a) 30 J

(b) 10 J

(c) 20 J

(d) Zero

Ans. (b)

Sol. For path (1)

dU_{1} = dQ_{1} – dW_{1} = (50 – 30)J = 20J

For the path (2)

dW_{2} = dQ_{2} – dU_{2}

= (30 – 20)J ....(dU_{1} = dU_{2}.state function

= 10 J

Correct option is (b)

16. The total charge contained within the cube (see figure), in which the electric field is given by , where is the permittivity of free space, is

(a) Zero

(b)

(c)

(d)

Ans. (c)

Sol.

Gauss's Law

Correct option is (c)

17. Let (x, y) denote the coordinates in a rectangular Cartesian coordinate system C. Let (x', y') denote the coordinates in another coordinate system C', defined by

x' = 2x + 3y

y' = –3x + 4y

the area element in C', is

(a)

(b) 12dx' dy'

(c) dx' dy'

(d) x' dx' dy'

Ans. (a)

Sol. Let there be a transformation

Which is defined as

x' = 2x + 3y

y' = –3x + 4y

The area element is |J| such that

dx'dy' = |J|dx dy

Correct option is (a)

18.

(a)

(b)

(c) (–V, –V)

(d)

Ans. (a)

Sol. At time , The velocity of the particle is v_{i} along x-axis in frame s relative velcoity of particle in frame s observed by s'-frame

as frame s' is moving anticlockwise instantaneously the relative velocity of the particle will be along –y axis. So final velocity co-ordinates are in frame s.

Correct option is (a)

19.

(a) a parabola

(b) a circle

(c) a straight line

(d) an ellipse

Ans. (d)

Sol.

This is a separable differential equation

ydy = –3xdx

y^{2} + 3x^{2} = 2C

Applying the boundary condition

Then, y^{2} + 3x^{2} = 3

Which is an equation of ellipse.

Correct option is (d)

20.

(a)

(b)

(c)

(d)

Ans. (a)

Sol. Using principle of superposition

y = y_{1} + y_{2}

_{ }

_{ }

_{ }

_{ }

_{ }

_{ }

_{ }Correct option is (a)

21. In the figure below, point A is the object and point B is the image formed by the lens. Let *l*_{1}, *l*_{2} and *l*_{3} denote the optical path lengths of the three rays 1, 2 and 3, respectively. Identify the correct statement.

(a) *l*_{1}= *l*_{2} = *l*_{3}

(b) *l*_{1} = *l*_{3} > *l*_{2}

(c) *l*_{1} > *l*_{2} < *l*_{3}

(d) *l*_{1} = *l*_{3} < *l*_{2}

Ans. (a)

Sol. For a perfect optical system, the optical path or distance, from an object point to a corresponding image point will be equal for all rays i.e. *l*_{1} = *l*_{2} = *l*_{3}

Correct option is (a)

22.

(a)

(b)

(c)

(d)

Ans. (b)

Sol. Given that

At t = 0 N = N_{0}

disintegration of nuclei A is given by

its solution is given by

At t = 0 N_{1} = N_{0} ... (2)

Equation (2) reduces to

Nuclei B is forming as well as disintegrating simultaneously

On integration we get

At t = 0, N_{2} = 0 so

Correct option is (b)

23. The rms velocity of molecules of oxygen gas is given by v at some temperature T. The molecules of another gas have the same rms velocity at temperature . The second gas is

(a) Neon

(b) Helium

(c) Hydrogen

(d) Nitrogen

Ans. (c)

Sol.

m = 2

Indicate hydrogen atom

Correct option is (c)

24. Three events, E_{1}(ct = 0, x = 0), E_{2}(ct = 0, x = L) and E_{3}(ct = 0, x = –L) occur, as observed in an inertial frame S. Frame S' is moving with a speed v along the positive x-direction with respect to S. In S', let t'_{1}, t'_{2}, t'_{3} be the respective times at which E_{1}, E_{2}, and E_{3} occurred. Then,

(a) t'_{3} < t'_{2} < t'_{1}

(b) t'_{3} < t'_{1} < t'_{2}

(c) t'_{1} = t'_{2} = t'_{3}

(d) t'_{2} < t'_{1} < t'_{3}

Ans. (d)

Sol.

For event E_{1}

t = 0, x = 0

For event E_{2}

t = 0, x = L

For event event E_{3}

t = 0, x = –L

t'_{2} < t'_{1} < t'_{3}

Correct option is (d)

25. A linearly polarized light falls on a quarter wave plate and the emerging light is found to be elliptically polarized. The angle between the fast axis of the quarter wave plate and the plane of polarization of the incident light, can be

(a) 45º

(b) 30º

(c) 180º

(d) 90º

Ans. (b)

Sol. When it emerges from the first polarizer the light is linearly polarised at 50º.

The angle between this and the transmission axis of the second polarizer is 30º.

Correct option is (b)

26.

(a)

(b)

(c)

(d)

Ans. (b)

Sol. f_{1} = 4t^{2} + 3 f_{2} = 6t^{3} + 7t

There we can deduce that f_{1} is an even function and f_{2} is an odd function.

Correct option is (b)

27. A mass m is connected to a massless spring of spring constant k, which is fixed to a wall. Another mass 2m, having kinetic energy E, collides collinearly with the mass m completely inelastically (see figure). The entire set up is placed on a frictionless floor. The maximum compression of the spring is

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Kinetic energy of block mass (2m) = E

Linear momentum is conserved before and after collision

Total energy is also conserved after collision

Correct option is (c)

28.

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

Correct option is (b)

29.

(a)

(b) Zero

(c)

(d)

Ans. (d)

Sol.

at z = 0, t = 0

Correct option is (d)

30. A semiconductor pn junction at thermal equilibrium has the space charge density ρ(x) profile as shown in the figure. The figure that best depicts the variation of the electric field E with x is (W denotes width of the depletion layer)

(a)

(b)

(c)

(d)

Ans. (b)

Sol. It is given

So it will become parabola

Correct option is (b)

31. Consider the following differential equation that describes the oscillations of a physical system:

(a) the frequency of oscillations decreases

(b) the frequency of oscillations increases

(c) the oscillations decay faster

(d) the oscillations decay slower

Ans. (a)

Sol.

General solution is given by

Correct option is (a)

32. Identify the Correct statement(s) regarding nuclei

(a) ^{56}Fe is the most stable nucleus

(b) The volume of a nucleus grows linearly with the number of nucleons in it

(c) The uncertainty in the momentum of a proton in a nucleus is roughly 10^{5} times the uncertainty in the momentum of the electron in the ground state of hydrogen atom

(d)

Ans. (a, b, c, d)

Sol. Correct options are (a, b, c, d)

33. A particle of mass m is in an infinite square well potential of length L. It is in a superimposed state of the first two energy eigenstates, as given by

Identify the correct statement(s). h is Planck's constant.

(a)

(b)

(c)

(d)

Ans. (b, c, d)

Sol.

(c) In particle in box average momentum of particle is always zero.

We can write

This function is normalized function

Correct options are (b, c, d)

34. A gaseous system, enclosed in an adiabatic container, is in equilibrium at pressure P_{1} and volume V_{1}. Work is done on the system in a quasi – static manner due to which the pressure and volume change to P_{2} and V_{2}, respectively, in the final equilibrium state. At every instant, the pressure and volume obey the and C is a constant. If the work done is zero, then identify the correct statement(s).

(a)

(b)

(c) P_{2}V_{2} = P_{1}V_{1}

(d)

Ans. (c)

Sol. Workdone = 0

is not possible because work done is zero.

P_{1}V_{1} = P_{2}V_{2}

Correct option is (c)

35. A beam of light traveling horizontally consists of an unpolarized component with intensity I_{0} and a polarized component with intensity I_{p}. The plane of polarization is oriented at an angle with respect to the vertical. The figure shows the total intensity I_{total} after the light passes through a polarizer as a function of the angle , that the axis of the polarizer makes with respect to the vertical. Identify the correct statements(s)

(a)

(b) I_{p} = 5 W/m^{2}

(c) I_{0} = 10 W/m^{2} ; I_{p} = 20 W/m^{2}

(d) I_{0} = 17.5 W/m^{2}

Ans. (c)

Sol. I_{0} = 10W/m^{2}, I_{p} = 20W/m^{2}

Correct option is (c)

36. A carnot engine operates between two temperatures, T_{L} = 100 K and T_{H} = 150 K. Each cycle of the engine lasts for 0.5 seconds during which the power delivered is 500 J/second. Let Q_{H} be the corresponding heat absorbed by the engine and Q_{L} be the heat lost. Identify the correct statement(s).

(a) The change in entropy of the engine in 0.5 seconds in zero.

(b) Q_{H} = 750 J

(c) The change in entropy of the engine and the hot bath in a cycle is 5 J/K

(d)

Ans. (a, b, c)

Sol. Workdone in one cycle

W = 500 × 0.5 = 250J

we know that

Q_{L} = Q_{H} – W = 750 – 250 = 500 J

Correct options are (a, b, and c)

37. An isolated ideal gas is kept at a pressure P_{1} and volume V_{1}. The gas undergoes free expansion and attains a pressure P_{2} volume V_{2}. Identify the correct statement(s).

(a) This is an adiabatic process

(b) This is an isobaric process

(c) P_{1}V_{1} = P_{2}V_{2}

(d)

Ans. (a, c)

Sol. An isolated ideal gas is kept a pressure and volume constant in adiabatic process and for free expansion P_{1}V_{1} = P_{2}V_{2}.

Correct options are (a and c)

38. The figure show the corss – section of a hollow cylindrical tank, 2.2 m in diameter, which is half filled with water (refractive index of 1.33). The space above the water is filled with a gas of unknown refractive index. A small laser move along the bottom surface and aims a light beam towards the center (see figure). When the laser moves a distance of S = 1.09 m or beyond from the lowest point in the water, no light enters the gas. Identify the correct statement(s) (speed of light is 3 × 10^{8} m/s).

(a) The critical angle for the water – gas interface is 56.77 º

(b) The time taken for the light beam to travel from the laser to the rim of the tank when S > 1.09 m is 9.7 ns

(c) The time taken for the light beam to travel from the laser to the rim of the tank when S < 1.09 m is 8.9 ns

(d) The refractive index of the gas is 1.05

Ans. (a)

Sol.

Using Snell's law

= 56.77º

Correct option is (a)

39. For the given circuit, identify the correct statement(s).

(a) V_{0} = 3V

(b) I_{0} = 1 mA

(c) If R_{L} is doubled, V_{0} will change to 6V

(d) If R_{L} is doubled, I_{0} will change to 0.5 mA

Ans. (a, b, d)

Sol.

(a) Apply KCL on upper current value

V_{0} = 2V_{x}

Now apply on Non-Inverting Terminal

Now

15 – 15V_{x} = 10V_{x} + 15V_{x} – 15V_{0}

15 – 40V_{x} = –15V_{0}

15 – 40 V_{x} = –15 *2V_{x} (V_{0} = 2V_{x})

15 – 40 V_{x} = –30V_{x}

15 = 10V_{x}

V_{x} = 1.5 V_{0} = 2V_{x} = 3V

(d) If R_{L} is doubled

Correct options are (a, b, d)

40.

(a) 3x + 8

(b) 2x + 8 cos y

(c)

(d) 2x + 8 (y – 1)^{2}

Ans. (a, c)

Sol.

Correct options are (a, c)

41. A particle with positive charge 10^{–3} C and mass 0.2 kg is thrown upwards from the ground at an angle 45º with the horizontal with a speed of 5 m/s. The projectile moves through a horizontal electric field of 10 V/m, which is in the same direction as the horizontal component of the initial velocity of the particle. The acceleration due to gravity is . The range is ______m.(Round off to three decimal places.)

Ans. (2.512)

Sol.

R = 2.5125 = 2.512

R = 2.512

Correct answer is (2.512)

42.

Ans. (0.04)

Sol.

Correct answer is (0.04)

43. Consider N_{1} number of ideal gas particles enclosed in a volume V_{1}. If the volume is changed in V_{2} and the number of particles is reduced by half, the mean free path becomes four times of its initial value. The ratio is ______ (Round off to one decimal place.)

Ans. (0.5)

Sol.

Correct answer is (0.5)

44. A small conducting square loop of side *l* is placed inside a concentric large conducting square loop of side L(L >> *l*). The value of mutual inductance of the system is expressed as . The value of n is ______ (Round off of two decimal places).

Ans. (2.84)

Sol.

Eq. (1) put in eq. (2)

From equation (3) and (4)

n = 2.84

Correct answer is (2.84)

45.

Ans. (16)

Sol.

Correct answer is (16)

46. An ideal blackbody at temperature T, emits radiation of energy density u. The corresponding value for a material at temperature Its emissivity is _____ (Round off to three decimal places).

Ans. (0.060 to 0.065)

Sol.

e = 0.062

Correct answer is (0.060 to 0.065)

47. The following Zener diode voltage regulator circuit is used to obtain 20 V regulated output at load resistance R_{L} from a 35 V dc power supply. Zener diodes are rated at 5W and 10V. The value of the resistance R is ______

Ans. (30)

Sol.

I_{S} = I_{Z} + I_{L}

Apply KVL

–35 + I_{S*R} + 20 = 0

I_{S*R} = 15

We have to find I_{s}.

Power at zener diode = 5W

and potential is 10V

P_{z} = I_{z} V_{z}

5W = I_{z} * 10 V

Working to zener diode is find when I/P voltage is less than its cut in voltage then it behave as open circuit when it crosses its cut in voltage then it become a wire which have nearly zero resistance. In this as

I_{s} = I_{z} = 0.5A

Correct answer is (30)

48.

Ans. (1.67)

Sol.

So net velocity measured in frame S'

Energy of particle in S' frame

Correct answer is (1.67)

49. One of the roots of the equation, z^{6} – 3z^{4} – 16 = 0 is given by z_{1} = 2. The value of the product of the other five roots is _______.

Ans. (–8)

Sol. z^{6} – 3z^{4} – 16 = 0

Let z_{1}z_{2}z_{3} .... z_{6} are the roots of this equation.

z^{6} – (sum of roots)z^{5} + (sum of roots in group of 2)z^{4} – .....+ (product of roots) = 0

Then z_{1}z_{2}z_{3}z_{4}z_{5}z_{6} = –16

when z_{1} = 2

z_{2}z_{3}z_{4}z_{5}z_{6} = –8

Correct answer is (–8)

50. A laser beam shines along a block of transparent material of length 2.5 m. Part of the beam goes to the detector D_{1} while the other part travels through the block and then hits the detector D_{2}. The time delay between the arrivals of the two light beam is inferred to be 6.25 ns. The speed of light c = 3 × 10^{8} m/s. The refractive index of the block is ______ (Round off to two decimal places).

Ans. (1.75)

Sol.

For the medium

Correct answer is (1.75)

51. The wavelength of characteristic X – ray photons from Mo (atomic number 42) is ____ Å. (Round off to one decimal place).

(speed of light is 3 × 10^{8} m/s; Rydberg constant R = 1.09 × 10^{7} / m)

Ans. (0.7)

Sol. For charecteristic X-ray

we have

n_{i} = 2

n_{f} = 1

For M_{0}, z = 42

or = 1415.6 × 10^{7}

^{}

^{}

Correct answer is (0.7)

52. A thin film of alcohol is spread over a surface. When light from a tunable source is incident normally, the intensity of reflected light at the detector is maximum for = 640 nm and minimum for = 512 nm. Taking the refractive index of alcohol to be 1.36 for both the given wavelengths, the minimum thickness of the film would be ______ nm (Round off to two decimal places).

Ans. (470.56)

Sol.

t_{2} = 470.56

Correct answer is (470.56)

53.

Ans. (1)

Sol.

Total linear momentum is conserved along x and y-axis

Along x-axis

Along y-axis

Squaring and adding equ. (1) and (2)

Total kinetic energy is conserved just before and after collision.

Just before collision just after collision

substracting equation (3) and (4)

k = 1

Correct answer is (1)

54.

Ans. (60)

Sol.

Correct answer is (60)

55. Consider a hemispherical glass lens (refractive index is 1.5) having radius of curvature R = 12 cm for the curved surface. An incoming ray, parallel to the optical axis, is incident on the curved surface at a height h = 1 cm above the optical axis, as shown in the figure. The distance d (from the flat surface to the lens) at which the ray crosses the optical axis is_____ cm (Round off to two decimal places).

Ans. (16)

Sol.

Correct answer is (16)

56.

Ans. (0.038)

Sol.

V = I_{R} R

Q = CV

Correct answer is (0.038)

57.

Ans. (4)

Sol.

58.

Ans. (3)

Sol.

59. In an X – ray diffraction experiment with Cu crystals having lattice parameter 3.61 Å, X – rays of wavelength of 0.090 nm are incident on the family of planes {1 1 0}. The highest order present in the diffraction pattern is_______.

Ans. (5)

Sol.

Correct answer is (5)

60. An RC circuit is connected to two dc power supplies, as shown in the figure. With switch S open, the capacitor is fully charged. S is then closed at time t = 0. The voltage across the capacitor at t = 2.4 milliseconds is _______ V (Round off to one decimal place).

Ans. (18.824)

Sol. Initially capapcitor will be charged upto 20 V with polarity shown in figure.

When Switch S is closed, then at t = 2.4 milliseconds

So net voltage capacitor is = (20 – 1.176) Volts = 18.824 Volts