## IIT JAM PHYSICS 2020

Previous Year Question Paper with Solution.

1. Which one of the following functions has a discontinuity in the second derivative at x = 0, where x is a real variable?

(a) f(x) = |x|^{3}

(b) f(x) = x|x|

(c) f(x) = cos(|x|)

(d) f(x) = |x|^{2}

Ans. (b)

Sol. The derivatives of the function

Assuming a function to be real.

Correct option is (b)

2. A collimated beam of laser light of wavelength 514 nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0, respectively, the percentage of light intensity reflected back is

(a) 0

(b) 4.0

(c) 3.6

(d) 4.2

Ans. (c)

Sol. Reflectance is defined as

Correct option is (c)

3. Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on:

(a) A sphere

(b) A plane

(c) A cylinder

(d) Two parallel planes

Ans. (b)

Sol. All points on the plane are at equal distance from charges, so potential will be zero.

Correct option is (b)

4. For a system undergoing a first order phase transition at a temperature T_{c}, which one of the following graphs best describes the variation of entropy (S) as a function of temperature (T)?

(a)

(b)

(c)

(d)

Ans. (d)

Sol. specific entropy. In first order Phase transition first order derivative of specific Gibbs free energy is discontinuous that is specific entropy.

Correct option is (d)

5. In a photoelectric effect experiment, a monochromatic light source emitting photons with energy greater than the work function of the metal under test is used. If the power of the light source is doubled, which one of the following statements is correct?

(a) The number of emitted photoelectrons remains the same.

(b) The stopping potential remains the same.

(c) The number of emitted photoelectrons decreases.

(d) The stopping potential doubles.

Ans. (b)

Sol. Stopping potential is not defined at power of light source

Correct option is (b)

6. The figure below shows a cubic unit cell with lattice constant a. The shaded crystallographic plane intersects the x-axis at 0.5a. The Miller indices of the shaded plane are

(a) (210)

(b)

(c) (110)

(d) (102)

Ans. (a)

Sol. (i) Intercepts along x, y, z-axis

(ii) Divide by lattice parameters

(iii) Take reciprocal, 2, 1, 0

The Miller indices is (2 1 0)

Correct option is (a)

7. For a particle moving in a central potential, which one of the following statements is correct?

(a) The motion is restricted to a plane due to the conservation of angular momentum.

(b) The motion is restricted to a plane due to the conservation of energy only.

(c) The motion is restricted to a plane due to the conservation of linear momentum.

(d) The motion is not restricted to a plane.

Ans. (a)

Sol. For central force problem angular momentum is conserved and which ensure that motion of particle is confined in plane

Correct option is (a)

8. Consider the motion of a quantum particle of mass m and energy E under the influence of a step potential of height V_{0}. If R denotes the reflection coefficient, which one of the following statements is true?

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Therefore, option (c) is correct

9.

(a) P

(b)

(c)

(d)

Ans. (b)

Sol.

Correct option is (b)

10. Three point charges each carrying a charge q are placed on the vertices of an equilateral triangle of side L. The electrostatic potential energy of the configuration is:

(a)

(b)

(c)

(d)

Ans. (c)

Sol. Work done in placing charges

Work on charge q indicated as (1) & (2)

Similarly at (3)

Correct option (c)

11. Which one of the following statements is correct?

(a)

(b)

(c)

(d)

Ans. (a)

Sol. Let's invoke De Moivre's theorem here. We have

Since n is a positive integer, the binomial theorem holds,

Hence, by expanding, we have

Since i^{2} = –1, i^{3} = –i, i^{4} = 1, i^{5} = i, ...., we have

By equating the real and imaginary parts, we obtain

Correct option is (a)

12.

(a)

(b) 0

(c)

(d) 1

Ans. (a)

Sol.

Correct option is (a)

13.

(a) 0

(b)

(c) e

(d) 1

Ans. (d)

Sol.

Correct option is (d)

14. A wheel is rotating at a frequency f_{0} Hz about a fixed vertical axis. The wheel stops in t_{0} seconds, with constant angular deceleration. The number of turns covered by the wheel before it comes to rest is given by:

(a) f_{0}t_{0}

(b) 2f_{0}t_{0}

(c) f_{0}t_{0}/2

(d)

Ans. (c)

Sol.

Correct option is (c)

15. Two objects of masses m and 2m are moving at speeds of v and v/2, respectively. After undergoing a completely inelastic collision, they move together with a speed of v/3. The angle between the initial velocity vectors of the two objects is

(a) 60º

(b) 120º

(c) 45º

(d) 90º

Ans. (b)

Sol. Change in momentum

For x direction,

Correct option is (b)

16. Two planets P_{1} and P_{2} having masses M_{1} and M_{2} revolve around the Sun in elliptical orbits, with time periods T_{1} and T_{2}, respectively. The minimum and maximum distances of planet P_{1} from the Sun are R and 3R, respectively, whereas for planet P_{2} these are 2R and 4R, respectively, where R is a constant. Assuming M_{1} and M_{2} are much smaller than the mass of the Sun, the magnitude of is

(a)

(b)

(c)

(d)

Ans. (c)

Sol. According to Keplar's third law

Correct option is (c)

17. The intensity of the primary maximum in a two-slit interference pattern is given by I_{2} and the intensity of the primary maximum in a three-slit interference pattern is given by I_{3}. Assuming the far-field approximation, same slit parameters and intensity of the incident light in both the cases, I_{2} and I_{3} are related as

(a)

(b)

(c)

(d)

Ans. (d)

Sol. Intensity of light is proportional to square of amplitude

For two slits, I_{2} = (a + a)^{2} = 4a^{2}

For three slits, I_{3} = (a + a + a)^{2} = 9a^{2}

^{ }

^{ }Correct option is (d)

18. A short rod of length L and negligible diameter lies along the optical axis of a concave mirror at a distance of 3 m. The focal length of the mirror is 1 m and L << 1 m. If L' is the length of image of the object in the mirror, then

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

19. A beam of unpolarized light of intensity I_{0} falls on a system of four identical linear polarizers placed in a line as shown in the figure. The transmission axes of any two successive polarizers make an angle of 30º with each other. If the transmitted light has intensity I, the ratio is

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

20. Consider an annular region in free space containing a uniform magnetic field in the z-direction, schematically represented by the shaded region in the figure. A particle having charge Q and mass M starts off from point P (a, 0, 0) in the +x-direction with constant speed v. if the radii of inner and outer circles are a and b, respectively, the minimum magnetic field required so that the particle returns to the inner circle is

(a)

(b)

(c)

(d)

Ans. (b)

Sol. In the right angle triangle shown in figure

(b – r)^{2} = a^{2} + r^{2}

^{ }

^{ }Radius of the circular path is

Correct option is (b)

21. A thin conducting square loop of side L is placed in the first quadrant of the xy-plane with one of the vertices at the origin. If a changing magnetic field is applied, where B_{0} is a constant, then the magnitude of the induced electromotive force in the loop is

(a) 4B_{0}L^{4}

(b) 3B_{0}L^{4}

(c) 2B_{0}L^{4}

(d) B_{0}L^{4}

Ans. (d)

Sol.

Correct option is (d)

22.

(a)

(b)

(c)

(d)

Ans. (c)

Sol.

Correct option is (c)

23.

(a)

(b)

(c)

(d)

Ans. (b)

Sol.

Correct option is (b)

24. The root mean square (rms) speeds of Hydrogen atoms at 500 K, V_{H}, and Helium atoms at 2000 K, V_{He}, are related as

(a) V_{H} > V_{He}

(b) V_{H} < V_{He}

(c) V_{H} = V_{He}

(d) V_{H} > V_{He}

Ans. (c)

Sol. Average root mean square velocity

Therefore V_{H} < V_{He}

Correct option is (c)

25.

Which one of the following is the probability of finding the particle outside the classically allowed region?

(The classically allowed region is where the total energy is greater than the potential energy)

(a)

(b)

(c) 0.5

(d) 0

Ans. (b)

Sol. Turning point is

Probability to find the particle in classical forbidden region

Correct option is (b)

26.

(a)

(b)

(c)

(d)

Ans. (d)

Sol.

Correct option is (d)

27. Consider a one-dimensional infinite potential well of width a. This system constains five non-interacting electrons, each of mass m, at temperature T = 0 K. The energy of the highest occupied state is

(a)

(b)

(c)

(d)

Ans. (d)

Sol. Ground state have two electrons so energy is 2E_{0}.

First excited state has two electrons, 2·(4E_{0}).

Correct option is (d)

28. Consider the crystal structure shown in the figure, where black and grey spheres represent atoms of two different elements and a denotes the lattice constant. The Bravais lattice for this structure is

(a) Simple cubic

(b) Face-centered cubic

(c) Body-centered cubic

(d) Triclinic

Ans. (b)

Sol. This is a structure of sodium-chloride whose lattice is Face Centred Cubic. Thus, the

Correct option is (b)

29. For an unbiased Silicon n-p-n transistor in thermal equilibrium, which one of the following electronic energy band diagrams is correct? (E_{c} = conduction band minimum, E_{v} = valence band maximum, E_{F} = Fermi level).

(a)

(b)

(c)

(d)

Ans. (b)

Sol. In equilibrium fermi-level on each side aligned.

Correct option is (b)

30. In the circuit shown in the figure, both Op-Amps are ideal. The output for the circuit V_{out} is

(a) 20V_{1} + 10V_{2}

(b) –20V_{1} + 10V_{2}

(c) 10V_{1} – 20V_{2}

(d) 20V_{1} – 10V_{2}

Ans. (d)

Sol.

Correct option is (d)

31. If P and Q are Hermitian matrices, which of the following is/are true?

(a) PQ + QP is always Hermitian

(b) i(PQ – QP) is always Hermitian

(c) PQ is always Hermitian

(d) PQ – QP is always Hermitian

Ans. (a, b)

Sol.

Correct options are (a, b)

32.

(a)

(b)

(c)

(d)

Ans. (a, b, d)

Sol. (a) Gauss's Divergence Theorem

Hence option (b) is correct.

(d) Stoke's Theorem

Correct options are (a, b and d)

33. A thin rod of uniform density and length m is undergoing small oscillations about a pivot point. The time period of oscillation (T_{m}) is minimum when the distance of the pivot point from the center-of-mass of the rod is x_{m}. Which of the following is/are correct?

(Assume acceleration due to gravity g = 10 m/s^{2})

(a) x_{m} = 1 m

(b)

(c)

(d)

Ans. (a, d)

Sol.

Hence option (a) and (d) are correct.

34.

(a)

(b)

(c)

(d)

Ans. (a, b)

Sol.

Using the principle of superposition

Correct options are (a, b)

35. An object executes simple harmonic motion along the x-direction with angular frequency and amplitudea. The speed of the object is 4 cm/s and 2 cm/s, when it is at distances 2 cm and 6 cm, respectively from the equilibrium position. Which of the following is/are correct?

(a)

(b)

(c)

(d)

Ans. (a, c)

Sol. Displacement equation for simple harmonic wave oscillation is

Divide (i) and (ii), we get

Correct options are (a, c)

36.

(a)

(b)

(c)

(d)

Ans. (b, d)

Sol. Correct options are (b and d)

37.

(a) The surface density of bound charges on the inner and outer surfaces are –k and +k, respectively. The volume density of bound charges inside the dielectric is zero.

(b) The surface density of bound charges is zero on both the inner and outer surfaces. The volume density of bound charges inside the dielectric is +k.

(c) The surface density of bound charges on the inner and outer surfaces are and , respectively. The volume density of bound charges inside the dielectric is zero.

(d) The surface density of bound charges is zero on both the inner and outer surfaces. The volume density of bound charges inside the dielectric is

Ans. (c)

Sol.

Correct option is (c)

38. One mole of an ideal gas having specific heat ratio of 1.6 is mixed with one mole of another ideal gas having specific heat ratio of 1.4. If C_{V} and C_{P} are the molar specific heat capacities of the gas mixture at constant volume and pressure, respectively, which of the following is/are correct? (R denotes the universal gas constant).

(a) C_{V} = 2.08 R

(b) C_{P} = 2.9 R

(c) C_{P} = 1.48 C_{V}

(d) C_{P} = 1.52 C_{V}

Ans. (a, c)

Sol.

Correct options are (a and c)

39. Two relativistic particles with opposite velocities collide head-on and come to rest by sticking with each other. Which of the following quantities is/are conserved in the collision?

(a) Total momentum

(b) Total energy

(c) Total kinetic energy

(d) Total rest mass

Ans. (a, b)

Sol. Correct options are (a and b)

40. Figure shows a circuit diagram comprising boolean logic gates and the corresponding timing diagrams show the digital signals at various points in the circuit. Which of the following is/are true?

(a) Points 3 and 7 are shorted.

(b) The NOT gate on the right is faulty.

(c) The AND gate is faulty and acts like a NOR gate.

(d) The AND gate is faulty and acts like an OR gate.

Ans. (d)

Sol. Correct option is (d)

41. The line integral of the vector function along the straight line from (0, 0) to (2, 4) is ____________

Ans. (12)

Sol.

Correct answer is (12)

42. Consider a thin bi-convex lens of relative refractive index n = 1.5. The radius of curvature of one surface of the lens is twice that of the other. The magnitude of larger radius of curvature in units of the focal length of the lens is __________ (Round off to 1 decimal place).

Ans. (1.5)

Sol.

Correct answer is (1.5)

43. Water flows in a horizontal pipe in a streamlined manner at an absolute pressure of 4 × 10^{5} Pa and speed of 6 m/s. If it exist the pipe at a pressure of 10^{5} Pa, the speed of water at the exit point is _______ m/s (Round off to 1 decimal place).

(The density of water is 1000 kg/m^{3})

Ans. (25.2)

Sol. Applying Bernoulli's equation

Correct answer is (25.2)

44. Consider a retarder with refractive indices n_{e} = 1.551 and n_{0} = 1.542 along the extraordinary and ordinary axes, respectively. The thickness of this retarder for which a left circularly polarized light of wavelength 600 nm will be converted into a right circularly polarized light is ______ µm.

(Round off to 2 decimal places)

Ans. (33.33)

Sol. For half wave plate.

Correct answer is (33.33)

45. Using a battery, a 10 pF capacitor is charged to 50 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is ____________ pF.

Ans. (15)

Sol. Case I: Capacitor is charged upto q = CV = 10 pF × 50V = 500 pC,

Case II: First Capacitor is connected in parallel to second and common voltage is 20 V.

Correct answer is (15)

46. Consider two spherical perfect blackbodies with radii R_{1} and R_{2} at temperatures T_{1} = 1000 K and T_{2} = 2000 K, respectively. They both emit radiation of power 1 kW. the ratio of their radii, R_{1}/R_{2} is given by ____________.

Ans. (4)

Sol. Power radiated in black body radiation is

Correct answer is (4)

47. In a Compton scattering experiment, the wavelength of incident X-rays is 0.500 Å. If the Compton wavelength is 0.024 Å, the value of the longest wavelength possible for the scattered X-ray is ________ Å. (Specify up to 3 decimal places)

Ans. (0.548)

Sol.

Correct answer is (0.548)

48. A solid with FCC crystal structure is probed using X-rays of wavelength 0.2 nm. For the crystallographic plane given by (2, 0, 0), a first order diffraction peak is observed for a Bragg angle of 21º. The unit cell size is __________ nm. (Round off to 2 decimal places)

Ans. (0.56)

Sol. From Bragg's equations

Correct answer is (0.56)

49. The figure shows a circuit containing two diodes D_{1} and D_{2} with threshold voltages V_{TH} of 0.7 V and 0.3 V, respectively. Considering the simplified diode model, which assumes diode I-V characteristic as shown in the plot on the right, the current through the resistor R is __________ µA.

Ans. (97)

Sol. Diodes D_{1}(Si) and D_{2}(Ge) are in parallel. So once switch is ON, D_{2}(Ge) will be ON and D_{1}(Si) will be OFF.

Correct answer is (97)

50. An ideal gas undergoes an isothermal expansion along a path AB, adiabatic expansion along BC, isobaric compression along CD, isothermal compression along DE, and adiabatic compression along EA, as shown in the figure. The work done by the gas along the process BC is 10 J. The change in the internal energy along process EA is 16 J. The absolute value of the change in the internal energy along the process CD is _________ J.

Ans. (6)

Sol. In a process

Correct answer is (6)

51.

Ans. (0.60)

Sol.

Solve (i) and (ii) we will get; c_{1} = 6, c_{2} = –4

Correct answer is (0.60)

52. A vehicle of mass 600 kg with an engine operating at constant power P accelerates from rest on a straight horizontal road. The vehicle covers a distance of 600 m in 1 minute. Neglecting all losses, the magnitude of P is _________ kW. (Round off to 2 decimal places)

Ans. (1.11 to 1.13)

Sol. Correct answer is (1.11 to 1.13)

53. The angular momentum of a particle relative to origin varies with time (t) as

The angle between and the torque acting on the particle becomes 45º after a time of _________ s.

Ans. (2)

Sol.

Correct answer is (2)

54.

Ans. (2)

Sol. Time difference (Separation) between two zero velocities

Correct answer is (2)

55. For the ac circuit shown in the figure, R = 100 and C = 10 pF, the phase difference between V_{in} and V_{out} is 90º at the input signal frequency of ________ kHz. (Round off to 2 decimal places)

Ans. (159.2)

Sol.

Correct answer is (159.2)

56.

Ans. (2.86)

Sol.

Correct answer is (2.86)

57. A body at a temperature T is brought into contact with a reservoir at temperature 2T. Thermal equilibrium is established at constant pressure. The heat capacity of the body at constant pressure is C_{p}. The total change in entropy of the body and the reservoir in units of C_{p} is _________.

(Round off to 2 decimal places)

Ans. (0.19 to 0.20)

Sol. Entropy of the system defined as

Correct answer is (0.19 to 0.20)

58. One mole of an ideal monatomic gas at pressure P, volume V and temperature T is expanded isothermally to volume 4V. There after, the gas is heated isochorically (at constant volume) till its pressure becomes P. If R is the universal gas constant, the total heat transfer in the process, in units of RT is ____________. (Round off to 2 decimal places)

Ans. (5.88 to 5.94)

Sol. Heat released in isothermal process is equal to workdone

C_{V} = 1.5 R (Monoatomic Gas)

Total dQ = RT(2ln 2 + 4.5) = 5.886

Correct answer is (5.88 to 5.94)

59. In the transistor circuit given in the figure, the emitter-base junction has a voltage drop of 0.7 V. A collector-emitter voltage of 14 V reverse biases the collector. Assuming the collector current to be the same as the emitter current, the value of R_{B} is ___________

Ans. (865)

Sol.

Apply KVL in input section

Correct answer is (865)

60. The radioactive nuclei ^{40}K decay to ^{40}Ar with a half-life of 1.25 × 10^{9} years. The ^{40}K/^{40}Ar isotopic ratio for a particular rock is found to be 50. The age of the rock is m × 10^{7} years. The value of m is ___________. (Round off to 2 decimal place)

Ans. (3.57)

Sol.

Correct answer is (3.57)