JAM 2024 Physics (PH) Exam Paper PDF

JAM 2024 PHYSICS (PH) Section A: Q.1 – Q.10 Carry ONE mark each. Q.1 The total number of Na and Cl ions per unit cell of the NaCl crystal is: (A) 2 (B) 4 (C) 8 (D) 16 Q.2 Th...

JAM 2024 PHYSICS (PH) Section A: Q.1 – Q.10 Carry ONE mark each. Q.1 The total number of Na and Cl ions per unit cell of the NaCl crystal is: (A) 2 (B) 4 (C) 8 (D) 16 Q.2 The sum of three binary numbers, 10110.10, 11010.01, and 10101.11, in decimal system is: (A) 70.75 (B) 70.25 (C) 70.50 (D) 69.50 PH 1/40 JAM 2024 PHYSICS (PH) Q.3 Which of the following matrices is Hermitian as well as unitary? (A) (0 −𝑖 ) 𝑖 0 (B) (0 𝑖 ) 𝑖 0 (C) (1 −𝑖 ) 𝑖 1 (D) ( 0 1+𝑖 ) 1−𝑖 0 PH 2/40 JAM 2024 PHYSICS (PH) Q.4 𝑟̂ The divergence of a 3-dimensional vector (𝑟̂ is the unit radial vector) is: 𝑟3 (A) 1 − 𝑟4 (B) Zero (C) 1 𝑟3 (D) 3 − 𝑟4 Q.5 The magnitudes of spin magnetic moments of electron, proton and neutron are e, p and n, respectively. Then, (A) e  p  n (B) e = p  n (C) e  p  n (D) e  p = n PH 3/40 JAM 2024 PHYSICS (PH) Q.6 A particle moving along the x-axis approaches 𝑥 = 0 from 𝑥 = − with a total energy E. It is subjected to a potential 𝑉(𝑥). For time 𝑡 → , the probability density P(x) of the particle is schematically shown in the figure. The correct option for the potential 𝑉(𝑥) is: (A) (B) (C) (D) PH 4/40 JAM 2024 PHYSICS (PH) Q.7 A plane electromagnetic wave is incident on an interface AB separating two media (refractive indices 𝑛1 = 1.5 and 𝑛2 = 2.0) at Brewster angle 𝜃𝐵 , as schematically shown in the figure. The angle 𝛼 (in degrees) between the reflected wave and the refracted wave is: D B n1 = 1.5 A  B n2 = 2.0 O C (A) 120 (B) 116 (C) 90 (D) 74 PH 5/40 JAM 2024 PHYSICS (PH) Q.8 If the electric field of an electromagnetic wave is given by, 𝐸⃗ = (4𝑥̂ + 3𝑦̂)𝑒 𝑖(𝜔𝑡+𝑎𝑥−600𝑦) , then the value of a is: (all values are in the SI units) (A) 450 (B) −450 (C) 800 (D) −800 PH 6/40 JAM 2024 PHYSICS (PH) Q.9 A vector field is expressed in the cylindrical coordinate system (s, , z) as, 𝐴 𝐵 𝐹 = 𝑠̂ + 𝑧̂. 𝑠 𝑠 If this field represents an electrostatic field, then the possible values of A and B, respectively, are: (A) 1 and 0 (B) 0 and 1 (C) −1 and 1 (D) 1 and −1 Q.10 Which of the following types of motion may be represented by the trajectory, 𝑦(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 ? (Here a, b, and c are constants; x, y are the position coordinates) (A) Projectile motion in a uniform gravitational field (B) Simple harmonic motion (C) Uniform circular motion (D) Motion on an inclined plane in a uniform gravitational field PH 7/40 JAM 2024 PHYSICS (PH) Section A: Q.11 – Q.30 Carry TWO marks each. Q.11 A crystal plane of a lattice intercepts the principal axes 𝑎1 , 𝑎2 , and 𝑎3 at 3𝑎1 , 4𝑎2, and 2𝑎3 , respectively. The Miller indices of the plane are: (A) (436) (B) (342) (C) (634) (D) (243) Q.12 The number of atoms in the basis of a primitive cell of hexagonal closed packed structure is: (A) 1 (B) 2 (C) 3 (D) 4 PH 8/40 JAM 2024 PHYSICS (PH) Q.13 Consider the following logic circuit. A Y B The output Y is LOW when: (A) A is HIGH and B is LOW (B) A is LOW and B is HIGH (C) Both A and B are LOW (D) Both A and B are HIGH PH 9/40 JAM 2024 PHYSICS (PH) Q.14 The value of the line integral for the vector, 𝑣 = 2𝑥̂ + 𝑦𝑧 2 𝑦̂ + (3𝑦 + 𝑧 2 )𝑧̂ along the closed path OABO (as shown in the figure) is: z B 1 O A y 1 x (Path AB is the arc of a circle of unit radius) (A) 1 (3𝜋 − 1) 4 (B) 1 3𝜋 − 4 (C) 3𝜋 −1 4 (D) 3𝜋 − 1 PH 10/40 JAM 2024 PHYSICS (PH) Q.15 In the x-y plane, a vector is given by −𝑦𝑥̂ + 𝑥𝑦̂ 𝐹 (𝑥, 𝑦) =. 𝑥 2 + 𝑦2 ⃗ × 𝐹, through a circular loop of radius 2, centered The magnitude of the flux of ∇ at the origin, is: (A) 𝜋 (B) 2𝜋 (C) 4𝜋 (D) 0 PH 11/40 JAM 2024 PHYSICS (PH) Q.16 The roots of the polynomial, 𝑓(𝑧) = 𝑧 4 − 8𝑧 3 + 27𝑧 2 − 38𝑧 + 26, are 𝑧1 , 𝑧2 , 𝑧3 , & 𝑧4 , where 𝑧 is a complex variable. Which of the following statements is correct? (A) 𝑧1 + 𝑧2 + 𝑧3 + 𝑧4 4 =− 𝑧1 𝑧2 𝑧3 𝑧4 19 (B) 𝑧1 + 𝑧2 + 𝑧3 + 𝑧4 4 = 𝑧1 𝑧2 𝑧3 𝑧4 13 (C) 𝑧1 𝑧2 𝑧3 𝑧4 26 =− 𝑧1 + 𝑧2 + 𝑧3 + 𝑧4 27 (D) 𝑧1 𝑧2 𝑧3 𝑧4 13 = 𝑧1 + 𝑧2 + 𝑧3 + 𝑧4 19 PH 12/40 JAM 2024 PHYSICS (PH) Q.17 The ultraviolet catastrophe in the classical (Rayleigh-Jeans) theory of cavity radiation is attributed to the assumption that (A) the standing waves of all allowed frequencies in the cavity have the same average energy (B) the density of the standing waves in the cavity is independent of the shape and size of the cavity (C) the allowed frequencies of the standing waves inside the cavity have no upper limit (D) the number of allowed frequencies for the standing waves in a frequency range to ( + d) is proportional to 2 Q.18 Given that the rest mass of electron is 0.511MeV/c2, the speed (in units of c) of an electron with kinetic energy 5.11MeV is closest to: (A) 0.996 (B) 0.993 (C) 0.990 (D) 0.998 PH 13/40 JAM 2024 PHYSICS (PH) Q.19 A one-dimensional infinite square-well potential is given by: Let 𝐸𝑒 (𝑥) and 𝑒 (𝑥) be the ground state energy and the corresponding wave function, respectively, if an electron (e) is trapped in that well. Similarly, let 𝐸µ (𝑥) and µ (𝑥) be the corresponding quantities, if a muon (µ) is trapped in the well. Choose the correct option: (A) (B) (C) (D) PH 14/40 JAM 2024 PHYSICS (PH) Q.20 In a Newton’s rings experiment (using light of free space wavelength 580nm), there is an air gap of height d between the glass plate and a plano-convex lens (see figure). The central fringe is observed to be bright. d The least possible value of d (in nm) is: (A) 145 (B) 290 (C) 580 (D) 72.5 PH 15/40 JAM 2024 PHYSICS (PH) Q.21 Linearly polarized light (free space wavelength 𝜆0 = 600nm) is incident normally on a retarding plate (𝑛𝑒 − 𝑛𝑜 = 0.05 at 𝜆0 = 600nm). The emergent light is observed to be linearly polarized, irrespective of the angle between the direction of polarization and the optic axis of the plate. The minimum thickness (in µm) of the plate is: (A) 6 (B) 3 (C) 2 (D) 1 Q.22 A 15.7mW laser beam has a diameter of 4mm. If the amplitude of the associated 𝐴 magnetic field is expressed as , the value of A is: √𝜀0 𝑐 3 (𝜀0 is the free space permittivity and 𝑐 is the speed of light) (A) 50 (B) 35.4 (C) 100 (D) 70.8 PH 16/40 JAM 2024 PHYSICS (PH) Q.23 The plane 𝑧 = 0 separates two linear dielectric media with relative permittivities 𝜀𝑟1 = 4 and 𝜀𝑟2 = 3, respectively. There is no free charge at the interface. If the electric field in the medium 1 is 𝐸⃗1 = 3𝑥̂ + 2𝑦̂ + 4𝑧̂ , then the displacement vector ⃗ 2 in medium 2 is: 𝐷 (𝜀0 is the permittivity of free space) (A) (3𝑥̂ + 4𝑦̂ + 6𝑧̂ )𝜀0 (B) (3𝑥̂ + 6𝑦̂ + 8𝑧̂ )𝜀0 (C) (9𝑥̂ + 6𝑦̂ + 16𝑧̂ )𝜀0 (D) (4𝑥̂ + 2𝑦̂ + 3𝑧̂ )𝜀0 PH 17/40 JAM 2024 PHYSICS (PH) Q.24 A tank, placed on the ground, is filled with water up to a height ℎ. A small hole is made at a height ℎ1 such that ℎ1 < ℎ. The water jet emerging from the hole strikes the ground at a horizontal distance D, as shown schematically in the figure. Which of the following statements is correct? (g is the acceleration due to gravity) (A) Velocity at ℎ1 is √2𝑔ℎ1 (B) 𝐷 = 2(ℎ − ℎ1 ) (C) D will be maximum when ℎ1 = 2 ℎ 3 (D) The maximum value of D is h PH 18/40 JAM 2024 PHYSICS (PH) Q.25 An incompressible fluid is flowing through a vertical pipe (height h and cross- sectional area 𝐴𝑜 ). A thin mesh, having n circular holes of area 𝐴ℎ , is fixed at the bottom end of the pipe. The speed of the fluid entering the top-end of the pipe is 𝑣𝑜. The volume flow rate from an individual hole of the mesh is given by: (g is the acceleration due to gravity) (A) 𝐴𝑜 √𝑣𝑜2 + 2𝑔ℎ 𝑛 (B) 𝐴𝑜 √𝑣𝑜2 + 𝑔ℎ 𝑛 (C) 𝑛(𝐴𝑜 − 𝐴ℎ )√𝑣𝑜2 + 2𝑔ℎ (D) 𝑛(𝐴𝑜 − 𝐴ℎ )√𝑣𝑜2 + 𝑔ℎ 𝑜 PH 19/40 JAM 2024 PHYSICS (PH) Q.26 A ball is dropped from a height ℎ to the ground. If the coefficient of restitution is 𝑒, the time required for the ball to stop bouncing is proportional to: (A) 2 + 𝑒 1−𝑒 (B) 1 + 𝑒 1−𝑒 (C) 1 − 𝑒 1+𝑒 (D) 2 − 𝑒 1+𝑒 Q.27 A cylinder-piston system contains N atoms of an ideal gas. If 𝑡𝑎𝑣𝑔 is the average time between successive collisions of a given atom with other atoms. If the temperature T of the gas is increased isobarically, then 𝑡𝑎𝑣𝑔 is proportional to : (A) √𝑇 (B) 1 √𝑇 (C) 𝑇 (D) 1 𝑇 PH 20/40 JAM 2024 PHYSICS (PH) Q.28 A gas consists of particles, each having three translational and three rotational degrees of freedom. The ratio of specific heats, Cp/Cv, is: (Cp and Cv are the specific heats at constant pressure and constant volume, respectively) (A) 5/3 (B) 7/5 (C) 4/3 (D) 3/2 Q.29 If two traveling waves, given by 𝑦1 = 𝐴0 sin(𝑘𝑥 − 𝜔𝑡) and 𝑦2 = 𝐴0 sin(𝑘𝑥 − 𝜔𝑡) are superposed, which of the following statements is correct? (A) For  =  = 1, the resultant wave is a standing wave (B) For  =  = −1, the resultant wave is a standing wave (C) For  =  = 2, the carrier frequency of the resultant wave is 3 𝜔 2 (D) For  =  = 2, the carrier frequency of the resultant wave is 3𝜔 PH 21/40 JAM 2024 PHYSICS (PH) Q.30 Suppose that there is a dispersive medium whose refractive index depends on the 𝑎 𝑏 wavelength as given by 𝑛(𝜆) = 𝑛0 + 2 − 4. The value of 𝜆 at which the group 𝜆 𝜆 and phase velocities would be the same, is: (A) 2𝑏 √ 𝑎 (B) 𝑏 √ 2𝑎 (C) 3𝑏 √ 𝑎 (D) 𝑏 √ 3𝑎 PH 22/40 JAM 2024 PHYSICS (PH) Section B: Q.31 – Q.40 Carry TWO marks each. Q.31 A pure Si crystal can be converted to an n-type crystal by doping with (A) P (B) As (C) Sb (D) In PH 23/40 JAM 2024 PHYSICS (PH) Q.32 In the following OP-AMP circuit, 𝑣𝑖𝑛 and 𝑣𝑜𝑢𝑡 represent the input and output signals, respectively. R2 n R1 R1 n n _ R2 n _ + 𝑣𝑜𝑢𝑡 + R3 ~ 𝑣𝑖𝑛 n R3 RL n n Choose the correct statement(s): (A) 𝑣𝑜𝑢𝑡 is out-of-phase with 𝑣𝑖𝑛 (B) Gain is unity when R1 = R2 (C) 𝑣𝑜𝑢𝑡 is in-phase with 𝑣𝑖𝑛 (D) 𝑣𝑜𝑢𝑡 is zero PH 24/40 JAM 2024 PHYSICS (PH) Q.33 A spring-mass system (spring constant 80N/m and damping coefficient 40N-s/m), initially at rest, is lying along the y-axis in the horizontal plane. One end of the spring is fixed and the mass (5kg) is attached at its other end. The mass is pulled along the y-axis by 0.5m from its equilibrium position and then released. Choose the correct statement(s). (Ignore mass of the spring) (A) Motion will be under damped (B) Trajectory of the mass will be 𝑦(𝑡) = 1 (1 + 𝑡)𝑒 −4𝑡 2 (C) Motion will be critically damped (D) Trajectory of the mass will be 𝑦(𝑡) = 1 (1 + 4𝑡)𝑒 −4𝑡 2 PH 25/40 JAM 2024 PHYSICS (PH) Q.34 Consider two different Compton scattering experiments, in which X-rays and γ- rays of wavelength () 1.024Å and 0.049Å, respectively, are scattered from stationary free electrons. The scattered wavelength (′) is measured as a function of the scattering angle ( ). If Compton shift is 𝛥 = ′ − , then which of the following statement(s) is/are true: ( h = 6.63  10-34J.s, me = 9.11  10-31kg, c = 3  108m/s ) (A) For γ-rays, ′ max ≈ 0.098Å (B) For X-rays, (Δ)max is observed at  = 180° (C) For X-rays, (Δ)max ≈ 1.049Å (D) For γ-rays, at  = 90° , ′ ≈ 0.049Å PH 26/40 JAM 2024 PHYSICS (PH) Q.35 A particle of mass m, having an energy E and angular momentum L, is in a parabolic trajectory around a planet of mass M. If the distance of the closest approach to the planet is rm, which of the following statement(s) is(are) true? (G is the Gravitational constant) (A) E > 0 (B) E = 0 (C) 𝐿 = √2𝐺𝑀𝑚2 𝑟𝑚 (D) 𝐿 = √2𝐺𝑀2 𝑚𝑟𝑚 PH 27/40 JAM 2024 PHYSICS (PH) Q.36 The inertial frame 𝑆 is moving away from the inertial frame S with a speed 𝑣 = 0.6𝑐 along the negative x-direction (see figure). The origins 𝑂’ and 𝑂 of the frames coincide at 𝑡 = 𝑡’ = 0. As observed in the frame 𝑆′, two events occur simultaneously at two points on the 𝑥′-axis with a separation of ∆𝑥 ′ = 5m. If, ∆𝑡 and ∆𝑥 are the magnitudes of the time interval and the space interval, respectively, between the events in S, then which of the following statements is(are) correct? (c = 3 × 108 m/s) (A) ∆𝑡 = 12.5ns (B) ∆𝑡 = 4.2ns (C) ∆𝑥 = 10.6m (D) ∆𝑥 = 6.25m PH 28/40 JAM 2024 PHYSICS (PH) Q.37 For the LCR AC-circuit (resonance frequency o) shown in the figure below, choose the correct statement(s). (A) o depends on the values of L, C, and R (B) At  = o, voltage VR and current I are in-phase (C) The amplitude of VR at  = o/2 is independent of R (D) The amplitude of VR at  = o is independent of L and C PH 29/40 JAM 2024 PHYSICS (PH) Q.38 The P-V diagram of an engine is shown in the figure below. The temperatures at points 1, 2, 3 and 4 are T1, T2, T3 and T4, respectively. 1 →2 and 3→4 are adiabatic processes, and 2→3 and 4→1 are isochoric processes. Identify the correct statement(s). [γ is the ratio of specific heats Cp (at constant P) and Cv (at constant V)] (A) 𝑇1 𝑇3 = 𝑇2 𝑇4 (B) 𝑃1 𝛾−1 𝛾 The efficiency of the engine is 1 − (𝑃 ) 2 (C) The change in entropy for the entire cycle is zero (D) 𝑇1 𝑇2 = 𝑇3 𝑇4 PH 30/40 JAM 2024 PHYSICS (PH) Q.39 A whistle S of sound frequency f is oscillating with angular frequency 𝜔 along the x-axis. Its instantaneous position and the velocity are given by 𝑥(𝑡) = 𝑎 sin(𝜔𝑡) and 𝑣(𝑡) = 𝑣0 cos (𝜔𝑡), respectively. An observer P is located on the y-axis at a distance L from the origin (see figure). Let 𝑣𝑃𝑆 (𝑡) be the component of 𝑣(𝑡) along the line joining the source and the observer. Choose the correct option(s): (Here 𝑎 and 𝑣0 are constants) (A) 1 𝑎𝑣0 𝑣𝑃𝑆 (𝑡) = sin (2𝜔𝑡) 2 √𝑎2 𝑠𝑖𝑛2 𝜔𝑡 + 𝐿2 (B) The observed frequency will be f when the source is at 𝑥 = 0 and 𝑥 = ±𝑎 (C) The observed frequency will be f when the source is at position 𝑥 = ± 𝑎 2 (D) 1 𝑎𝑣0 𝑣𝑃𝑆 (𝑡) = sin (2𝜔𝑡) 2 √𝑎2 + 𝐿2 PH 31/40 JAM 2024 PHYSICS (PH) Q.40 One mole of an ideal monoatomic gas, initially at temperature 𝑇𝑜 is expanded from an initial volume 𝑉𝑜 to 2.5𝑉𝑜. Which of the following statements is(are) correct? (R is the ideal gas constant) (A) When the process is isothermal, the work done is 𝑅𝑇𝑜 ln 2 (B) When the process is isothermal, the change in internal energy is zero (C) When the process is isobaric, the work done is 3 𝑅𝑇𝑜 2 (D) When the process is isobaric, the change in internal energy is 9 𝑅𝑇𝑜 2 Section C: Q.41 – Q.50 Carry ONE mark each. Q.41 Consider a p-n junction diode which has 1023 acceptor-atoms/m3 in the p-side and 1022 donor-atoms/m3 in the n-side. If the depletion width in the p-side is 0.16µm, then the value of depletion width in the n-side will be ______µm. (Rounded off to one decimal place) PH 32/40 JAM 2024 PHYSICS (PH) Q.42 The co-ordinate system (x,y,z) is transformed to the system (u,v,w), as given by: 𝑢 = 2𝑥 + 3𝑦 − 𝑧 𝑣 = 𝑥 − 4𝑦 + 𝑧 𝑤 =𝑥+𝑦 The Jacobian of the above transformation is ____________. Q.43 Two sides of a triangle OAB are given by: ⃗⃗⃗⃗⃗ 𝑂𝐴 = 𝑥̂ + 2𝑦̂ + 𝑧̂ ⃗⃗⃗⃗⃗ = 2𝑥̂ − 𝑦̂ + 3𝑧̂ 𝑂𝐵 The area of the triangle is _________. (Rounded off to one decimal place) PH 33/40 JAM 2024 PHYSICS (PH) Q.44 A particle of mass 1kg, initially at rest, starts sliding down from the top of a frictionless inclined plane of angle 𝜋/6 (as schematically shown in the figure). The magnitude of the torque on the particle about the point O after a time 2seconds is ___________N-m. (Rounded off to nearest integer) h 𝜋ൗ 6 O (Take g = 10m/s2) Q.45 The moment of inertia of a solid hemisphere (mass 𝑀 and radius 𝑅) about the axis 2 passing through the hemisphere and parallel to its flat surface is 𝑀𝑅 2. The 5 distance of the axis from the center of mass of the hemisphere (in units of 𝑅) is________. (Rounded off to two decimal places) Q.46 A collimated light beam of intensity 𝐼0 is incident normally on an air-dielectric (refractive index 2.0) interface. The intensity of the reflected light is _______𝐼0. (Rounded off to two decimal places) PH 34/40 JAM 2024 PHYSICS (PH) Q.47 A charge of −9C is placed at the center of a concentric spherical shell made of a linear dielectric material (relative permittivity 9) and having inner and outer radii of 0.1m and 0.2m, respectively. The total charge induced on its inner surface is ______C. (Rounded off to two decimal place) Q.48 A Zener diode (rating 10V, 2W) and a normal diode (turn-on voltage 0.7V) are connected in a circuit as shown in the figure. The voltage drop 𝑉𝐿 across the 2k resistance is __________V. (Rounded off to one decimal place) Q.49 The Fermi energy of a system is 5.5eV. At 500K, the energy of a level for which the probability of occupancy is 0.2, is ________eV. (Rounded off to two decimal places) (Boltzmann constant 𝑘𝐵 = 8.62  10−5 eV/K) PH 35/40 JAM 2024 PHYSICS (PH) Q.50 One mole of an ideal monoatomic gas is heated in a closed container, first from 273K to 303K, and then from 303K to 373K. The net change in the entropy is ______R. (Rounded off to two decimal places) (R is the ideal gas constant) Section C: Q.51 – Q.60 Carry TWO marks each. Q.51 For a simple cubic crystal, the smallest inter-planar spacing d that can be determined from its second order of diffraction using monochromatic X-rays of wavelength 1.32Å is _________Å. (Round off to two decimal places) PH 36/40 JAM 2024 PHYSICS (PH) Q.52 A transistor ( =100, 𝑉𝐵𝐸 = 0.7𝑉) is connected as shown in the circuit below. VCC = 15 V 20 k IC 10 k 5 k 2 k The current IC will be _________ mA. (Rounded off to two decimal places) Q.53 In the Taylor expansion of function, 𝐹(𝑥) = 𝑒 𝑥 sin 𝑥, around 𝑥 = 0, the coefficient of 𝑥 5 is ______________. (Rounded off to three decimal places) PH 37/40 JAM 2024 PHYSICS (PH) Q.54 A stationary nitrogen ( 147𝑁) nucleus is bombarded with  - particle ( 42𝐻𝑒) and the following nuclear reaction takes place: If the kinetic energies of 42𝐻𝑒 and 11𝐻 are 5.314MeV and 4.012MeV, respectively, then the kinetic energy of 178𝑂 is ______MeV. (Rounded off to one decimal place) (Masses are given in units of 𝑢 = 931.5MeV/c2) Q.55 A satellite of mass 10kg, in a circular orbit around a planet, is having a speed 𝑣=200m/s. The total energy of the satellite is _______kJ. (Rounded off to nearest integer) Q.56 When a system of multiple long narrow slits (width 2µm and period 4µm) is illuminated with a laser of wavelength 600nm. There are 40 minima between the two consecutive principal maxima observed in its diffraction pattern. Then maximum resolving power of the system is _______. PH 38/40 JAM 2024 PHYSICS (PH) Q.57 Consider a thick biconvex lens (thickness t = 4cm and refractive index n = 1.5) whose magnitudes of the radii of curvature R1 and R2, of the first and second surfaces are 30cm and 20cm, respectively. Surface 2 is silvered to act as a mirror. A point object is placed at point A on the axis (OA = 60cm) as shown in the figure. If its image is formed at point Q, the distance d between O and Q is ______cm. (Rounded off to two decimal places) Q.58 An unstable particle created at a point P moves with a constant speed of 0.998c until it decays at a point Q. If the lifetime of the particle in its rest frame is 632ns, the distance between points P and Q is ______m. (Rounded off to the nearest integer) (c = 3 × 108 m/s) PH 39/40 JAM 2024 PHYSICS (PH) Q.59 Two positive charges Q and 2Q are kept at points A and B, separated by a distance 2d, as shown in the figure. MCL is a semicircle of radius 2d centered at the origin 𝐿 O. If Q = 2C and d = 10cm, the value of the line integral ∫𝑀 𝐸⃗. ⃗⃗⃗ 𝑑𝑙 (where 𝐸⃗ represents electric field) along the path MCL will be _________V. Q.60 A time dependent magnetic field inside a long solenoid of radius 0.05m is given ⃗ (𝑡) = 𝐵0 sin 𝜔𝑡 𝑧̂. If 𝜔=100rad/s and 𝐵0= 0.98Weber/m2, then the amplitude by 𝐵 of the induced electric field at a distance of 0.07m from the axis of the solenoid is ______V/m. (Rounded off to two decimal places) PH 40/40