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IIT JAM 2021 : Physics (with Answer Keys)

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JAM 2021 PHYSICS - PH Paper Specific Instructions 1. The examination is of 3 hours duration. There are a total of 60 questions carrying 100 marks. The entire paper is divided into three sections, A, B and C. All sections are compulsory. Questions in each section are of different types. 2. Section A contains a total of 30 Multiple Choice Questions (MCQ). Each MCQ type question has four choices out of which only one choice is the correct answer. Questions Q.1 Q.30 belong to this section and carry a total of 50 marks. Q.1 Q.10 carry 1 mark each and Questions Q.11 Q.30 carry 2 marks each. 3. Section B contains a total of 10 Multiple Select Questions (MSQ). Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices. The candidate gets full credit if he/she selects all the correct answers only and no wrong answers. Questions Q.31 Q.40 belong to this section and carry 2 marks each with a total of 20 marks. 4. Section C contains a total of 20 Numerical Answer Type (NAT) questions. For these NAT type questions, the answer is a real number which needs to be entered using the virtual keyboard on the monitor. No choices will be shown for these type of questions. Questions Q.41 Q.60 belong to this section and carry a total of 30 marks. Q.41 Q.50 carry 1 mark each and Questions Q.51 Q.60 carry 2 marks each. 5. In all sections, questions not attempted will result in zero mark. In Section A (MCQ), wrong answer will result in NEGATIVE marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer. For all 2 marks questions, 2/3 marks will be deducted for each wrong answer. In Section B (MSQ), there is NO NEGATIVE and NO PARTIAL marking provisions. There is NO NEGATIVE marking in Section C (NAT) as well. 6. Only Virtual Scientific Calculator is allowed. Charts, graph sheets, tables, cellular phone or other electronic gadgets are NOT allowed in the examination hall. 7. The Scribble Pad will be provided for rough work. PH 1/20 JAM 2021 PHYSICS - PH SECTION A MULTIPLE CHOICE QUESTIONS (MCQ) Q. 1 Q.10 carry one mark each. Q.1 The function (A) Q.2 Q.3 is Taylor expanded about PH (C) e (D) Zero (A) and and (B) (C) and (D) and 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 and is , then An object of density of the liquid is (B) (C) (D) 300 is floating in a liquid with 75% of its volume submerged. The density (B) (C) (D) 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 3 108 m/s, the value of n is (A) 1.01 Q.6 e is be a 2 2 matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues are (A) Q.5 (B) = . The coefficient of Let (A) Q.4 cos (B) 1.04 (C) 1.06 (D) 1.10 For a semiconductor material, the conventional flat band energy diagram is shown in the figure. The variables Y, X, respectively, are (A) Energy, Momentum (B) Energy, Distance (C) Distance, Energy (D) Momentum, Energy 2/20 JAM 2021 Q.7 PHYSICS - PH For the given circuit, VD is the threshold voltage of the diode. The graph that best depicts the variation of Vo with Vi is (A) (B) (D) (C) Q.8 Arrange the following telescopes, where D is the telescope diameter and is the wavelength, in order of decreasing resolving power: I. D = 100 m, = cm II. D = 2 m, = nm III. D = 1 m, = nm IV. D = 2 m, = mm (A) III, II, IV, I (B) II, III, I, IV (C) IV, III, II, I (D) III, II, I, IV PH 3/20 JAM 2021 Q.9 PHYSICS - PH 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) Q.10 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) Q. 11 Q. 30 carry two marks each. Q.11 Let Let , denote the coordinates in a rectangular Cartesian coordinate system , denote the coordinates in another coordinate system , defined by = + = + The area element in , is (A) (B) (C) (D) . Q.12 Three events, = , = , = , = and = , = occur, as observed in an inertial frame . Frame is moving with a speed along the positive -direction with respect to . In , let , , be the respective times at which , , and occurred. Then, (A) (B) (C) (D) < = < < < = < < Q.13 The solution (A) an ellipse PH of the differential equation (B) a circle + = , (C) a parabola = , is described by (D) a straight line 4/20 JAM 2021 PHYSICS - PH Q.14 In the figure below, point A is the object and point B is the image formed by the lens. Let , and denote the optical path lengths of the three rays , and , respectively. Identify the correct statement. = (A) (B) > < = > = (C) (D) = < Q.15 A particle, initially at the origin in an inertial frame , has a constant velocity . Frame is rotating about the -axis with angular velocity (anticlockwise). The coordinate axes of S coincide with those of at = . The velocity of the particle ( , ) in the frame, at = is (A) , (B) , (C) , (D) , Q.16 For the given circuit, the output Y is (A) 0 PH (B) 1 (C) A (D) A 5/20 JAM 2021 PHYSICS - PH Q.17 The total charge contained within the cube (see figure), in which the electric field is given + , where is the permittivity of free space, is by = (A) (B) (C) (D) Zero Q.18 Four charges are placed very close to each other, as shown. The separation between the two charges on the y-axis is . 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 from the origin , is (A) (B) (C) (D) PH ( ) ( ) ( ) 6/20 JAM 2021 PHYSICS - PH Q.19 At = , number of a radioactive nuclei start decaying into with a decay constant . The daughter nuclei decay into nuclei with a decay constant . Then, the number of nuclei at small time (to the leading order) is (A) (B) + (C) (D) Q.20 The electric field of an electromagnetic wave has the form = . At t=0, a test particle of charge is at z = 0, and has velocity = . , where c is the speed of light. The total instantaneous force on the particle is (A) (B) + (C) ( ) (D) Zero Q.21 The rms velocity of molecules of oxygen gas is given by at some temperature . The molecules of another gas have the same rms velocity at temperature . The second gas is (A) Hydrogen (B) Helium (C) Nitrogen (D) Neon Q.22 A system undergoes a thermodynamic transformation from state S1 to state S2 via two different paths 1 and 2. The heat absorbed and work done along path 1 are 50 J and 30 J, respectively. If the heat absorbed along path 2 is 30 J, the work done along path 2 is (A) Zero (B) 10 J (C) 20 J (D) 30 J Q.23 The condition for maxima in the interference of two waves integer, by + and + is given in terms of the wavelength and , an (A) ( ) + ( ) = (B) ( + ) + ( ) = (C) ( ) ( ) = (D) ( ) + ( ) = PH + 7/20 JAM 2021 PHYSICS - PH Q.24 A semiconductor pn junction at thermal equilibrium has the space charge density profile as shown in the figure. The figure that best depicts the variation of the electric field E with x is (W denotes the width of the depletion layer) (A) (C) PH (B) (D) 8/20 JAM 2021 PHYSICS - PH Q.25 A mass is connected to a massless spring of spring constant , which is fixed to a wall. Another mass , having kinetic energy , 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) Q.26 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) (B) (C) (D) Q.27 The expression for the magnetic field that induces the electric field = ( + + )cos ) is (A) (B) (C) (D) PH + sin + + sin + + sin + sin 9/20 JAM 2021 PHYSICS - PH Q.28 In the Fourier series expansion of two functions + , the Fourier coefficients the interval cos and sin , respectively) satisfy (A) = and for and for (B) (C) = (D) and and = for for ; ; = and ; and ; Q.29 A thin circular disc lying in the and = and = and = + and ( and = + in are coefficients of for for for for -plane has a surface mass density , given by ={ > where is the distance from its center. Its moment of inertia about the z-axis, passing through its center is (A) (B) (C) (D) Q.30 The radial component of acceleration in plane polar coordinates is given by (A) (B) (C) (D) PH + + 10/20 JAM 2021 PHYSICS - PH SECTION - B MULTIPLE SELECT QUESTIONS (MSQ) Q. 31 Q. 40 carry two marks each. Q.31 A gaseous system, enclosed in an adiabatic container, is in equilibrium at pressure and volume . Work is done on the system in a quasi-static manner due to which the pressure and volume change to and , respectively, in the final equilibrium state. At every instant, the pressure and volume obey the condition = , where = and is a constant. If the work done is zero, then identify the correct statement(s). (A) (B) (C) (D) = = + = = Q.32 An isolated ideal gas is kept at a pressure and volume . The gas undergoes free expansion and attains a pressure and volume . Identify the correct statement(s). = (A) This is an adiabatic process (B) (C) = = (D) This is an isobaric process PH 11/20 JAM 2021 PHYSICS - PH Q.33 A beam of light traveling horizontally consists of an unpolarized component with intensity I0 and a polarized component with intensity Ip. The plane of polarization is oriented at an angle with respect to the vertical. The figure shows the total intensity Itotal 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 statement(s). (A) = 125 (B) Ip = 5 W/m2 (C) I0 = 17.5 W/m2 (D) I0 = 10 W/m2 ; Ip = 20 W/m2 Q.34 Consider the following differential equation that describes the oscillations of a physical system: + + If and are held fixed, and is increased, then, = (A) the frequency of oscillations increases (B) the oscillations decay faster (C) the frequency of oscillations decreases (D) the oscillations decay slower PH 12/20 JAM 2021 PHYSICS - PH Q.35 For the given circuit, identify the correct statement(s). (A) Io = 1 mA (B) Vo = 3 V (C) If RL is doubled, Io will change to 0.5 mA (D) If RL is doubled, Vo will change to 6 V Q.36 A Carnot engine operates between two temperatures, = K and = K. Each cycle of the engine lasts for . seconds during which the power delivered is J/second. Let be the corresponding heat absorbed by the engine and be the heat lost. Identify the correct statement(s). (A) (B) = J (C) The change in entropy of the engine and the hot bath in a cycle is (D) The change in entropy of the engine in . seconds is zero PH J/K 13/20 JAM 2021 PHYSICS - PH Q.37 A time independent conservative force has the form, = = is . The allowed form(s) of , is(are) (A) (B) (C) (D) + + + = + , . Its magnitude at + cos Q.38 The figure shows the cross-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 moves 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 3 108 m/s). (A) The refractive index of the gas is 1.05 (B) The time taken for the light beam to travel from the laser to the rim of the tank when < . m is 8.9 ns (C) The time taken for the light beam to travel from the laser to the rim of the tank when > . m is 9.7 ns (D) The critical angle for the water-gas interface is 56.77 PH 14/20 JAM 2021 PHYSICS - PH Q.39 Identify the correct statement(s) regarding nuclei (A) The uncertainty in the momentum of a proton in a nucleus is roughly times the uncertainty in the momentum of the electron in the ground state of Hydrogen atom (B) The volume of a nucleus grows linearly with the number of nucleons in it (C) The energy of rays due to de-excitation of a nucleus can be of the order of MeV (D) 56 Fe is the most stable nucleus Q.40 A particle of mass m is in an infinite square well potential of length L. It is in a superposed state of the first two energy eigenstates, as given by Identify the correct statement(s). h is Planck s constant. (A) = (B) = (C) = = = + = . (D) = SECTION C NUMERICAL ANSWER TYPE (NAT) Q. 41 Q. 50 carry one mark each. Q.41 PH One of the roots of the equation, product of the other five roots is _________. = is given by = . The value of the 15/20 JAM 2021 PHYSICS - PH Q.42 The following Zener diode voltage regulator circuit is used to obtain 20 V regulated output at load resistance RL from a 35 V dc power supply. Zener diodes are rated at 5W and 10V. The value of the resistance R is ________ . Q.43 A small conducting square loop of side is placed inside a concentric large conducting square loop of side . The value of mutual inductance of the system is expressed as The value of n is ______ (Round off to two decimal places). . Q.44 Consider N1 number of ideal gas particles enclosed in a volume V1. If the volume is changed to V2 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). Q.45 A particle is moving with a velocity . (c is the speed of light) in an inertial frame S1. Frame S2 is moving with a velocity . with respect to S1. Let E1 and E2 be the respective energies of the particle in the two frames. Then, places). is _______ (Round off to two decimal Q.46 At some temperature T, two metals A and B, have Fermi energies and , respectively. The free electron density of A is times that of B. The ratio is ________. Q.47 A crystal has monoclinic structure, with lattice parameters, a = 5.14 , b = 5.20 , c = 5.30 and angle = 99 . It undergoes a phase transition to tetragonal structure with lattice parameters, a = 5.09 and c = 5.27 . The fractional change in the volume | | of the crystal due to this transition is ________ (Round off to two decimal places). PH 16/20 JAM 2021 PHYSICS - PH Q.48 A laser beam shines along a block of transparent material of length 2.5 m. Part of the beam goes to the detector D1 while the other part travels through the block and then hits the detector D2. The time delay between the arrivals of the two light beams is inferred to be 6.25 ns. The speed of light c = 3 108 m/s. The refractive index of the block is _______ (Round off to two decimal places). Q.49 An ideal blackbody at temperature , emits radiation of energy density . The corresponding value for a material at temperature is . Its emissivity is ________ (Round off to three decimal places). Q.50 A particle with positive charge C and mass . kg is thrown upwards from the ground at an angle with the horizontal with a speed of m/s. The projectile moves through a horizontal electric field of V/m, which is in the same direction as the horizontal m . component of the initial velocity of the particle. The acceleration due to gravity is s The range is ________ m. (Round off to three decimal places). PH 17/20 JAM 2021 PHYSICS - PH Q. 51 Q. 60 carry two marks each. Q.51 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 of the lens) at which the ray crosses the optical axis is ___________ cm (Round off to two decimal places). Q.52 Twenty non-interacting spin particles are trapped in a three-dimensional simple harmonic oscillator potential of frequency . The ground state energy of the system, in units of , is ________. Q.53 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). Q.54 For the Boolean expression = combinations for which the output = PH + + is _________. + , the number of 18/20 JAM 2021 PHYSICS - PH Q.55 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). Q.56 A current is uniformly distributed across a long straight nonmagnetic wire ( = of circular cross-section with radius . Two points P and Q are at distances and , respectively, from the axis of the wire. The ratio of the magnetic fields at points P and Q is _________. Q.57 A particle of mass is moving with a velocity , and collides elastically with a particle , of mass . is initially at rest. After collision, moves with a velocity . If is the final speed of , then = . The value of is ________. Q.58 In an X-ray diffraction experiment with Cu crystals having lattice parameter 3.61 , 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 ________. PH 19/20 JAM 2021 PHYSICS - PH Q.59 A parallel plate capacitor having plate area of 50 cm2 and separation of 0.1 mm is completely filled with a dielectric (dielectric constant K = 10). The capacitor is connected to a k resistance and an alternating voltage = sin , as shown in the figure. The switch S is initially open and then closed at t = 0. The ratio of the displacement current in the capacitor, to the current in the resistance, at time t = seconds is _______ (Round off to three decimal places). Q.60 The wavelength of characteristic K X-ray photons from Mo (atomic number 42) is _______ . (Round off to one decimal place). (speed of light is m/s; Rydberg constant = . /m END OF THE QUESTION PAPER PH 20/20 Answer Key of JAM-2021 Physics (PH) Paper Note: Question numbers pertain to the question paper published on the JAM 2021 website Q. No. Answer Q. No. Answer 1 B 31 A 2 A 32 A,B 3 D 33 D 4 A 34 A 5 A 35 A,B,D 6 B 36 A,C,D 7 A 37 A,C 8 D 38 B,C,D 9 C 39 A,B,C or A,B,C,D 10 C 40 A,B,C 11 A 41 -8 12 A 42 30 13 A 43 2.80 to 2.85 14 A 44 0.5 15 A 45 1.64 to 1.68 16 D 46 16 17 A 47 0.02 to 0.03 18 A 48 1.73 to 1.77 19 A 49 0.060 to 0.065 20 A 50 2.510 to 2.515 21 A 51 15.81 to 16.01 22 B 52 60 23 A 53 470.56 to 470.62 24 A 54 4 25 A 55 18.5 to 19 26 A 56 3 27 A 57 1 28 B 58 2 29 B 59 0.005 to 0.010 30 B 60 0.6 to 0.8

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