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JAM 2022, , Q.5, , PHYSICS - PH, , The resultant of the binary subtraction 1110101 − 0011110 is, , (A) 1001111, , (B) 1010111, , (C) 1010011, , (D) 1010001, , Q.6, , Consider a particle trapped in a three-dimensional potential well such that, 𝑈(𝑥, 𝑦, 𝑧) = 0 for 0 ≤ 𝑥 ≤ 𝑎, 0 ≤ 𝑦 ≤ 𝑎, 0 ≤ 𝑧 ≤ 𝑎 and 𝑈(𝑥, 𝑦, 𝑧) = ∞, everywhere else. The degeneracy of the 5th excited state is, , (A) 1, , (B) 3, , (C) 6, , (D) 9, , PH, , 4/36

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JAM 2022, , Q.8, , PHYSICS - PH, , Consider a two-dimensional force field, ⃗⃗⃗ (𝑥, 𝑦) = (5𝑥 2 + 𝑎𝑦 2 + 𝑏𝑥𝑦) 𝑥̂ + (4𝑥 2 + 4𝑥𝑦 + 𝑦 2 ) 𝑦., 𝐹, ̂, If the force field is conservative, then the values of 𝑎 and 𝑏 are, , (A) 𝑎 = 2 and 𝑏 = 4, , (B) 𝑎 = 2 and 𝑏 = 8, , (C) 𝑎 = 4 and 𝑏 = 2, , (D) 𝑎 = 8 and 𝑏 = 2, , Q.9, , Consider an electrostatic field 𝐸⃗ in a region of space. Identify the INCORRECT, statement., , (A) The work done in moving a charge in a closed path inside the region is zero, , (B) The curl of 𝐸⃗ is zero, , (C) The field can be expressed as the gradient of a scalar potential, , (D) The potential difference between any two points in the region is always zero, , PH, , 6/36

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JAM 2022, , Q.10, , PHYSICS - PH, , Which one of the following figures correctly depicts the intensity distribution for, Fraunhofer diffraction due to a single slit? Here, 𝒙 denotes the distance from the, centre of the central fringe and 𝑰 denotes the intensity., , (A), , (B), , (C), , (D), , PH, , 7/36

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JAM 2022, , Q.22, , PHYSICS - PH, , ⃗ = 𝐵0 𝑧,, A uniform magnetic field 𝐵, ̂ where 𝐵0 > 0 exists as shown in the figure., A charged particle of mass m and charge q (q > 0) is released at the origin, in the, yz-plane, with a velocity 𝑣, ⃗⃗⃗ directed at an angle 𝜃 = 45∘ with respect to the, positive 𝑧-axis. Ignoring gravity, which one of the following is TRUE., , (A) The initial acceleration 𝑎 =, , (B) The initial acceleration 𝑎 =, , 𝑞𝑣𝐵0, √2 𝑚, , 𝑥̂, , 𝑞𝑣𝐵0, √2 𝑚, , 𝑦̂, , (C) The particle moves in a circular path, , (D) The particle continues in a straight line with constant speed, , PH, , 16/36

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JAM 2022, , Q.23, , PHYSICS - PH, , For an ideal intrinsic semiconductor, the Fermi energy at 0 𝐾, , (A) lies at the top of the valence band, , (B) lies at the bottom of the conduction band, , (C) lies at the center of the bandgap, , (D) lies midway between center of the bandgap and bottom of the conduction band, , PH, , 17/36

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JAM 2022, , Q.29, , PHYSICS - PH, , The dispersion relation for certain type of waves is given by 𝜔 = √𝑘 2 + 𝑎2 ,, where 𝑘 is the wave vector and 𝑎 is a constant. Which one of the following, sketches represents 𝑣𝑔 , the group velocity?, , (A), , (B), , (C), , (D), , PH, , 22/36

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JAM 2022, , Q.30, , PHYSICS - PH, , Consider a binary number with 𝑚 digits, where 𝑚 is an even number. This binary, number has alternating 1’s and 0’s, with digit 1 in the highest place value. The, decimal equivalent of this binary number is, , (A) 2𝑚 − 1, , (B) (2𝑚 − 1), 3, (C) (2𝑚+1 − 1), 3, (D) 2 𝑚, (2 − 1), 3, , PH, , 23/36

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JAM 2022, , PHYSICS - PH, , Section B: Q.31 – Q.40 Carry TWO marks each., , 0, 𝑎, , Q.31, , Consider the 2 × 2 matrix 𝑀 = (, , 𝑎, ), where 𝑎, 𝑏 > 0. Then,, 𝑏, , (A) 𝑀 is a real symmetric matrix, , (B) One of the eigenvalues of 𝑀 is greater than 𝑏, , (C) One of the eigenvalues of 𝑀 is negative, , (D) Product of eigenvalues of 𝑀 is 𝑏, , In the Compton scattering of electrons, by photons incident with wavelength λ,, , Q.32, , (A), , ∆𝜆, 𝜆, , (B), , ∆𝜆, 𝜆, , is independent of λ, , increases with decreasing λ, , (C) there is no change in photon’s wavelength for all angles of deflection of the, photon, , (D), , ∆𝜆, 𝜆, , PH, , increases with increasing angle of deflection of the photon, , 24/36

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JAM 2022, , Q.33, , PHYSICS - PH, , The figure shows a section of the phase boundary separating the vapour (1) and, liquid (2) states of water in the P − 𝑇 plane. Here, 𝐶 is the critical point. 𝜇1 , 𝑣1, and 𝑠1 are the chemical potential, specific volume and specific entropy of the, vapour phase respectively, while 𝜇2 , 𝑣2 and 𝑠2 respectively denote the same for, the liquid phase. Then, , (A) 𝜇1 = 𝜇2 along AB, , (B) 𝑣1 = 𝑣2 along AB, , (C) 𝑠1 = 𝑠2 along AB, , (D) 𝑣1 = 𝑣2 at the point C, , PH, , 25/36

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JAM 2022, , PHYSICS - PH, , A particle is executing simple harmonic motion with time period 𝑇. Let 𝑥, 𝑣 and, , Q.34, , 𝑎 denote the displacement, velocity and acceleration of the particle, respectively,, at time t. Then,, , (A), , 𝑎𝑇, 𝑥, , does not change with time, , (B) (𝑎𝑇 + 2𝜋𝑣) does not change with time, , (C) 𝑥 and 𝑣 are related by an equation of a straight line, , (D) 𝑣 and 𝑎 are related by an equation of an ellipse, , Q.35, , A linearly polarized light beam travels from origin to point A (1,0,0). At the point, A, the light is reflected by a mirror towards point B (1, −1, 0). A second mirror, located at point B then reflects the light towards point C (1, −1, 1). Let, 𝑛̂(𝑥, 𝑦, 𝑧) represent the direction of polarization of light at (𝑥, 𝑦, 𝑧)., , (A) If 𝑛̂(0, 0, 0) = 𝑦̂, then 𝑛̂(1, −1, 1) = 𝑥̂, , (B) If 𝑛̂(0, 0, 0) = 𝑧̂ , then 𝑛̂(1, −1, 1) = 𝑦̂, , (C) If 𝑛̂(0, 0, 0) = 𝑦̂, then 𝑛̂(1, −1, 1) = 𝑦̂, , (D) If 𝑛̂(0, 0, 0) = 𝑧̂ , then 𝑛̂(1, −1, 1) = 𝑥̂, , PH, , 26/36

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JAM 2022, , Q.40, , PHYSICS - PH, , For an 𝑛-type silicon, an extrinsic semiconductor, the natural logarithm of, normalized conductivity (𝜎 ) is plotted as a function of inverse temperature., Temperature interval-I corresponds to the intrinsic regime, interval-II, corresponds to saturation regime and interval-III corresponds to the freeze-out, regime, respectively. Then, , (A) the magnitude of the slope of the curve in the temperature interval-I is, proportional to the bandgap, 𝐸𝑔, , (B) the magnitude of the slope of the curve in the temperature interval-III is, proportional to the ionization energy of the donor, 𝐸𝑑, , (C) in the temperature interval-II, the carrier density in the conduction band is equal, to the density of donors, , (D) in the temperature interval-III, all the donor levels are ionized, , PH, , 29/36

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JAM 2022, , PHYSICS - PH, , Section C: Q.41 – Q.50 Carry ONE mark each., Q.41, , The integral ∬(𝑥 2 + 𝑦 2 )𝑑𝑥𝑑𝑦 over the area of a disk of radius 2 in the 𝑥𝑦, plane is ___𝜋., , Q.42, , For the given operational amplifier circuit 𝑅1 = 120 Ω, 𝑅2 = 1.5 kΩ and, 𝑉𝑠 = 0.6 V, then the output current 𝐼0 is ___________ mA., , PH, , 30/36

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JAM 2022, , Q.43, , PHYSICS - PH, , For an ideal gas, AB and CD are two isothermals at temperatures 𝑇1 and 𝑇2 (𝑇1 >, 𝑇2 ), respectively. AD and BC represent two adiabatic paths as shown in figure., Let 𝑉𝐴 , 𝑉𝐵 , 𝑉𝐶 and 𝑉𝐷 be the volumes of the gas at A, B, C and D respectively. If, 𝑉𝐶, 𝑉𝐵, , Q.44, , = 2 , then, , 𝑉𝐷, 𝑉𝐴, , = __________., , A satellite is revolving around the Earth in a closed orbit. The height of the, satellite above Earth’s surface at perigee and apogee are 2500 km and 4500 km,, respectively. Consider the radius of the Earth to be 6500 km. The eccentricity of, the satellite’s orbit is ____ (Round off to 1 decimal place)., , Q.45, , Three masses 𝑚1 = 1, 𝑚2 = 2 and 𝑚3 = 3 are located on the 𝑥-axis such that, their center of mass is at 𝑥 = 1 . Another mass 𝑚4 = 4 is placed at 𝑥0 and the, new center of mass is at 𝑥 = 3. The value of 𝑥0 is _____., , PH, , 31/36

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JAM 2022, , Q.46, , PHYSICS - PH, , A normal human eye can distinguish two objects separated by 0.35 𝑚 when, viewed from a distance of 1.0 𝑘𝑚. The angular resolution of eye is, ________seconds (Round off to the nearest integer)., , Q.47, , A rod with a proper length of 3 m moves along 𝑥-axis, making an angle of 300, 𝑐, , with respect to the 𝑥-axis. If its speed is 2 m/s, where c is the speed of light, the, change in length due to Lorentz contraction is ____m (Round off to 2 decimal, places)., [Use 𝑐 = 3 × 108 𝑚/𝑠], , Q.48, , Consider the Bohr model of hydrogen atom. The speed of an electron in the, second orbit (𝑛 = 2) is ______× 106 𝑚/𝑠 (Round off to 2 decimal places)., [Use ℎ = 6.63 × 10−34 𝐽𝑠, 𝑒 = 1.6 × 10−19 𝐶, 𝜖0 = 8.85 × 10−12 𝐶 2 𝑚2 /𝑁], , Q.49, , Consider a unit circle 𝐶 in the 𝑥𝑦 plane with center at the origin. The line integral, of the vector field, 𝐹 (𝑥, 𝑦, 𝑧) = −2𝑦𝑥̂ − 3𝑧𝑦̂ + 𝑥𝑧̂ , taken anticlockwise over 𝐶, is _____ 𝜋., , PH, , 32/36

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JAM 2022, , Q.50, , PHYSICS - PH, , Consider a p-n junction at 𝑇 = 300 𝐾. The saturation current density at reverse, bias is −20 𝜇𝐴/𝑐𝑚2. For this device, a current density of magnitude, 10 𝜇𝐴/𝑐𝑚2 is realized with a forward bias voltage, 𝑉𝐹 . The same magnitude of, current density can also be realized with a reverse bias voltage, 𝑉𝑅 . The value of, |𝑉𝐹 /𝑉𝑅 | is _______ (Round off to 2 decimal places)., , PH, , 33/36

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JAM 2022, , PHYSICS - PH, , Section C: Q.51 – Q.60 Carry TWO marks each., , Q.51, , Consider the second order ordinary differential equation, 𝑦 ′′ + 4𝑦 ′ + 5𝑦 = 0. If, 𝑦(0) = 0 and 𝑦′(0) = 1, then the value of 𝑦(𝜋/2) is __________ (Round off, to 3 decimal places)., , Q.52, , A box contains a mixture of two different ideal monoatomic gases, 1 and 2, in, equilibrium at temperature 𝑇. Both gases are present in equal proportions. The, atomic mass for gas 1 is 𝑚, while the same for gas 2 is 2𝑚 . If the rms speed of, 𝑘𝐵 𝑇, , a gas molecule selected at random is 𝑣𝑟𝑚𝑠 = 𝑥√, , 𝑚, , , then 𝑥 is __________, , (Round off to 2 decimal places)., , Q.53, , A hot body with constant heat capacity 800 𝐽/𝐾 at temperature 925 𝐾 is dropped, gently into a vessel containing 1 𝑘𝑔 of water at temperature 300 𝐾 and the, combined system is allowed to reach equilibrium. The change in the total entropy, Δ𝑆 is _________ 𝐽/𝐾 (Round off to 1 decimal place)., [Take the specific heat capacity of water to be 4200 𝐽/𝑘𝑔 𝐾. Neglect any loss of, heat to the vessel and air and change in the volume of water.], , PH, , 34/36

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JAM 2022, , Q.57, , PHYSICS - PH, , A pipe of 1 𝑚 length is closed at one end. The air column in the pipe resonates at, its fundamental frequency of 400 𝐻𝑧. The number of nodes in the sound wave, formed in the pipe is _____., [Speed of sound = 320 𝑚/𝑠], , Q.58, , The critical angle of a crystal is 30∘ . Its Brewster angle is ______ degrees (Round, off to the nearest integer)., , Q.59, , In an LCR series circuit, a non-inductive resistor of 150 Ω, a coil of 0.2 𝐻, inductance and negligible resistance, and a 30 µ𝐹 capacitor are connected across, an ac power source of 220 𝑉, 50 Hz. The power loss across the resistor is ____W, (Round off to 2 decimal places)., , Q.60, , A charge q is uniformly distributed over the volume of a dielectric sphere of, radius a. If the dielectric constant 𝜖𝑟 = 2, then the ratio of the electrostatic energy, stored inside the sphere to that stored outside is_______ (Round off to 1 decimal, place)., , END OF THE QUESTION PAPER, , PH, , 36/36