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IIT JAM 2019 : Physics

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JAM 2019 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 1/13 JAM 2019 PHYSICS - PH SECTION A MULTIPLE CHOICE QUESTIONS (MCQ) Q. 1 Q.10 carry one mark each. Q.1 The function f ( x) (A) x = 0 Q.2 (D) x = 3i (B) II and IV (C) I and IV (D) I and III (B) (C) (D) Which one of the following crystallographic planes represent (101) Miller indices of a cubic unit cell? (A) PH (C) x = 9i In the thermal neutron induced fission of 235U, the distribution of relative number of the observed fission fragments (Yield) versus mass number (A) is given by (A) Q.4 (B) x = 9 A classical particle has total energy E. The plot of potential energy (U) as a function of distance (r) from the centre of force located at r = 0 is shown in the figure. Which of the regions are forbidden for the particle? (A) I and II Q.3 8x is continuous everywhere except at x 9 2 (B) (C) (D) 2/13 JAM 2019 Q.5 PHYSICS - PH The Fermi-Dirac distribution function [ ( )] is ( is the Boltzmann constant, is the temperature and is the Fermi energy) (A) ( ) = e Q.6 (B) 1 ( ) = 1 (C) 1 e ( ) = 1 +1 e +1 (B) Solenoidal but not irrotational (D) Neither solenoidal nor irrotational (B) Pressure (C) Temperature (D) Volume Isothermal compressibility is given by (A) Q.9 1 ( ) = In a heat engine based on the Carnot cycle, heat is added to the working substance at constant (A) Entropy Q.8 e If (x,y,z) is a scalar function which satisfies the Laplace equation, then the gradient of is (A) Solenoidal and irrotational (C) Irrotational but not solenoidal Q.7 (D) 1 1 V V P T (B) 1 P P V T (C) 1 V V P T (D) 1 P P V T For using a transistor as an amplifier, choose the correct option regarding the resistances of base-emitter (RBE) and base-collector (RBC) junctions (A) Both RBE and RBC are very low (C) Very high RBE and very low RBC (B) Very low RBE and very high RBC (D) Both RBE and RBC are very high Q.10 A unit vector perpendicular to the plane containing A i j 2k and B 2i j k is (A) (C) 1 ( i 3 j 4k ) 26 1 ( i 5 j 3k ) 35 1 ( i 3 j 3k ) 19 1 ( i 5 j 3k ) (D) 35 (B) Q. 11 Q. 30 carry two marks each. Q.11 A thin lens of refractive index 3/2 is kept inside a liquid of refractive index 4/3. If the focal length of the lens in air is 10 cm, then its focal length inside the liquid is (A) 10 cm PH (B) 30 cm (C) 40 cm (D) 50 cm 3/13 JAM 2019 Q.12 PHYSICS - PH 3 i 0 The eigenvalues of i 3 0 are 0 0 6 (A) 2, 4 and 6 (B) 2i, 4i and 6 (C) 2i, 4 and 8 (D) 0, 4 and 8 Q.13 For a quantum particle confined inside a cubic box of side L, the ground state energy is given by E0. The energy of the first excited state is (A) 2E0 (B) 2 E0 (C) 3E0 (D) 6E0 Q.14 A small spherical ball having charge q and mass m, is tied to a thin massless nonconducting string of length l. The other end of the string is fixed to an infinitely extended thin non-conducting sheet with uniform surface charge density . Under equilibrium, the string makes an angle 45 with the sheet as shown in the figure. Then is given by (g is the acceleration due to gravity and 0 is the permittivity of free space) (A) PH mg 0 q (B) 2 mg 0 q (C) 2 mg 0 q (D) mg 0 q 2 4/13 JAM 2019 PHYSICS - PH Q.15 Consider the normal incidence of a plane electromagnetic wave with electric field given by E E0 exp i(k1 z t ) x over an interface at z = 0 separating two media [wave velocities v1 and v2 (v2 > v1) and wave vectors k1 and k2, respectively] as shown in figure. The magnetic field vector of the reflected wave is ( is the angular frequency) E0 exp i(k1 z t ) y v1 E0 exp i( k1 z t ) y (C) v1 E0 exp i( k1 z t ) y v1 E0 exp i(k1 z t ) y (D) v1 (A) (B) Q.16 The output of following logic circuit can be simplified to X Y Z (A) X + YZ (B) Y + XZ (C) XYZ (D) X + Y + Z Q.17 A red star having radius at a temperature and a white star having radius at a temperature , radiate the same total power. If these stars radiate as perfect black bodies, then (A) > and > (B) < and > (C) > and < (D) < and < Q.18 The mass per unit length of a rod (length 2 m) varies as = 3x kg/m. The moment of inertia (in kg m2) of the rod about a perpendicular-axis passing through the tip of the rod (at x = 0) is (A) 10 PH (B) 12 (C) 14 (D) 16 5/13 JAM 2019 PHYSICS - PH Q.19 For a forward biased p-n junction diode, which one of the following energy-band diagrams is correct? ( F is the Fermi energy) (A) (B) (C) (D) Q.20 The amount of work done to increase the speed of an electron from c/3 to 2c/3 is (c = 3 108 m/s and rest mass of electron is 0.511 MeV) (A) 56.50 keV (B) 143.58 keV (C) 168.20 keV (D) 511.00 keV Q.21 The location of Cs+ and Cl ions inside the unit cell of CsCl crystal is shown in the figure. The Bravais lattice of CsCl is (A) simple cubic (C) face centered cubic (B) body centered orthorhombic (D) base centered orthorhombic Q.22 A -ray photon emitted from a 137Cs source collides with an electron at rest. If the Compton shift of the photon is 3.25 10 13 m, then the scattering angle is closest to (Planck s constant h = 6.626 10 34 J s, electron mass me = 9.109 10 31 kg and velocity of light in free space c = 3 108 m/s) (A) 45o PH (B) 60o (C) 30o (D) 90o 6/13 JAM 2019 PHYSICS - PH Q.23 During free expansion of an ideal gas under adiabatic condition, the internal energy of the gas (A) Decreases (C) Increases (B) Initially decreases and then increases (D) Remains constant Q.24 In the given phase diagram for a pure substance, regions I, II, III, IV, respectively represent (A) Vapor, Gas, Solid, Liquid (C) Gas, Liquid, Vapor, Solid (B) Gas, Vapor, Liquid, Solid (D) Vapor, Gas, Liquid, Solid Q.25 Light of wavelength (in free space) propagates through a dispersive medium with refractive index n( )=1.5 + 0.6 . The group velocity of a wave travelling inside this medium in units of 108 m/s is (A) 1.5 (B) 2.0 (C) 3.0 (D) 4.0 Q.26 The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 m) illuminated by a laser beam (wavelength 0.630 m) will be (A) 4 (B) 7 (C) 12 (D) 15 Q.27 During the charging of a capacitor C in a series RC circuit, the typical variations in the magnitude of the charge q(t) deposited on one of the capacitor plates, and the current i(t) in the circuit, respectively are best represented by (A) Fig. I and Fig. II (C) Fig. III and Fig. II PH (B) Fig. I and Fig. IV (D) Fig. III and Fig. IV 7/13 JAM 2019 PHYSICS - PH Q.28 Which one of the following is an impossible magnetic field B ? (A) B 3x2 z 2 x 2xz 3 z z3 (B) B 2 xy x yz 2 y 2 yz z 3 z2 (C) B xz 4 y x yx3 y x3 z z 2 2 (D) B 6 xz x 3 yz y Q.29 If the motion of a particle is described by x = 5 cos(8 t), y = 5 sin(8 t) and z = 5t, then the trajectory of the particle is (A) Circular (B) Elliptical (C) Helical (D) Spiral Q.30 A ball of mass m is falling freely under gravity through a viscous medium in which the drag force is proportional to the instantaneous velocity v of the ball. Neglecting the buoyancy force of the medium, which one of the following figures best describes the variation of v as a function of time t? (A) (B) (C) (D) SECTION - B MULTIPLE SELECT QUESTIONS (MSQ) Q. 31 Q. 40 carry two marks each. Q.31 The relation between the nuclear radius (R) and the mass number (A), given by R = 1.2 A1/3 fm, implies that (A) The central density of nuclei is independent of A (B) The volume energy per nucleon is a constant (C) The attractive part of the nuclear force has a long range (D) The nuclear force is charge dependent Q.32 Consider an object moving with a velocity in a frame which rotates with a constant angular velocity . The Coriolis force experienced by the object is (A) along (B) along (C) perpendicular to both and (D) always directed towards the axis of rotation PH 8/13 JAM 2019 PHYSICS - PH Q.33 The gradient of a scalar field S(x,y,z) has the following characteristic(s). (A) (B) (C) (D) Line integral of a gradient is path-independent Closed line integral of a gradient is zero Gradient of S is a measure of the maximum rate of change in the field S Gradient of S is a scalar quantity Q.34 A thermodynamic system is described by the P, V, T coordinates. Choose the valid expression(s) for the system. P V P (A) V T T P T V V T V (C) T P P V P T P V P (B) V T T P T V V T V (D) T P P V P T Q.35 Which of the following statement(s) is/are true? (A) Newton s laws of motion and Maxwell s equations are both invariant under Lorentz transformations. (B) Newton s laws of motion and Maxwell s equations are both invariant under Galilean transformations. (C) Newton s laws of motion are invariant under Galilean transformations and Maxwell s equations are invariant under Lorentz transformations. (D) Newton s laws of motion are invariant under Lorentz transformations and Maxwell s equations are invariant under Galilean transformations. Q.36 For an underdamped harmonic oscillator with velocity v(t), (A) Rate of energy dissipation varies linearly with v(t) (B) Rate of energy dissipation varies as square of v(t) (C) The reduction in the oscillator frequency, compared to the undamped case, is independent of v(t) (D) For weak damping, the amplitude decays exponentially to zero Q.37 Out of the following statements, choose the correct option(s) about a perfect conductor. (A) The conductor has an equipotential surface (B) Net charge, if any, resides only on the surface of conductor (C) Electric field cannot exist inside the conductor (D) Just outside the conductor, the electric field is always perpendicular to its surface Q.38 In the X-ray diffraction pattern recorded for a simple cubic solid (lattice parameter a = 1 ) using X rays of wavelength 1 , the first order diffraction peak(s) would appear for the (A) (100) planes (C) (210) planes PH (B) (112) planes (D) (220) planes 9/13 JAM 2019 Q.39 PHYSICS - PH Consider a classical particle subjected to an attractive inverse-square force field. The total energy of the particle is E and the eccentricity is . The particle will follow a parabolic orbit if (A) E > 0 and = 1 (C) E = 0 and = 1 (B) E < 0 and < 1 (D) E < 0 and = 1 Q.40 An atomic nucleus X with half-life TX decays to a nucleus Y, which has half-life TY. The condition(s) for secular equilibrium is(are) (A) TX TY (B) TX < TY (C) TX TY (D) TX TY SECTION C NUMERICAL ANSWER TYPE (NAT) Q. 41 Q. 50 carry one mark each. Q.41 In a typical human body, the amount of radioactive 40K is 3.24 10 5 percent of its mass. The activity due to 40K in a human body of mass 70 kg is ________ kBq. (Round off to 2 decimal places) (Half-life of 40K = 3.942 1016 s, Avogadro s number NA = 6.022 1023 mol 1) Q.42 Sodium (Na) exhibits body-centered-cubic (BCC) crystal structure with atomic radius 0.186 nm. The lattice parameter of Na unit cell is ________ nm. (Round off to 2 decimal places) Q.43 Light of wavelength 680 nm is incident normally on a diffraction grating having 4000 lines/cm. The diffraction angle (in degrees) corresponding to the third-order maximum is ________. (Round off to 2 decimal places) Q.44 Two gases having molecular diameters D1 and D2, and mean free paths 1 and 2, respectively, are trapped separately in identical containers. If D2 = 2D1, then 1/ 2 = ________. (Assume there is no change in other thermodynamic parameters) Q.45 An object of 2 cm height is placed at a distance of 30 cm in front of a concave mirror with radius of curvature 40 cm. The height of the image is ________ cm. PH 10/13 JAM 2019 PHYSICS - PH Q.46 The flux of the function F ( y 2 ) x (3xy z 2 ) y (4 yz) z passing through the surface ABCD along n is ________. (Round off to 2 decimal places) Q.47 The electrostatic energy (in units of 1 4 0 charge 5 C and radius 4 m is ________. (Round off to 3 decimal places) J) of a uniformly charged spherical shell of total Q.48 An infinitely long very thin straight wire carries uniform line charge density 8 10 2 C/m. The magnitude of electric displacement vector at a point located 20 mm away from the axis of the wire is ______ C/m2. Q.49 The 7th bright fringe in the Young s double slit experiment using a light of wavelength 550 nm shifts to the central maxima after covering the two slits with two sheets of different refractive indices n1 and n2 but having same thickness 6 m. The value of |n1 n2| is ________. (Round off to 2 decimal places) Q.50 For the input voltage Vi = (200 mV) sin (400t), the amplitude of the output voltage (V0) of the given OPAMP circuit is ________ V. (Round off to 2 decimal places) 35 k 35 k 35 k 10 k R1 Rf + Rf 10 k R2 + Rf 10 k R3 + V0 Vi PH 11/13 JAM 2019 PHYSICS - PH Q. 51 Q. 60 carry two marks each. Q.51 The value of emitter current in the given circuit is ________ A. (Round off to 1 decimal place) +VCC = 10 V 4 k 2 M B 0.3 V C =100 E 2 k Q.52 2 3 i The value of + CE z dz 2 , along the line 3y x , where z x iy is ________. 0 (Round off to 1 decimal place) Q.53 If the wavelength of K 2 X-ray line of an element is 1.544 , then the atomic number (Z) of the element is ________. (Rydberg constant R = 1.097 107m 1 and velocity of light c = 3 108 m/s) Q.54 A proton is confined within a nucleus of size 10 13 cm. The uncertainty in its velocity is ________ 108 m/s. (Round off to 2 decimal places) (Planck s constant h = 6.626 10 34 J s and proton mass mp = 1.672 10 27 kg) Q.55 PH 2 sin x for 0 < x < L and 0 elsewhere, L L the probability of finding the particle between x = 0 and x =L/2 is _______. (Round off to 1 decimal place) Given the wave function of a particle ( x) 12/13 JAM 2019 PHYSICS - PH Q.56 The Zener current IZ for the given circuit is ________ mA. R= 10 k IZ RL = 20 k VR VZ = 20 V Vin = 40 V + VL Q.57 If the diameter of the Earth is increased by 4% without changing the mass, then the length of the day is ________hours. (Take the length of the day before the increment as 24 hours. Assume the Earth to be a sphere with uniform density.) (Round off to 2 decimal places) Q.58 A di-atomic gas undergoes adiabatic expansion against the piston of a cylinder. As a result, the temperature of the gas drops from 1150 K to 400 K. The number of moles of the gas required to obtain 2300 J of work from the expansion is ________. (The gas constant R = 8.314 J mol 1K 1.) (Round off to 2 decimal places) Q.59 The decimal equivalent of the binary number 110.101 is ________. Q.60 A surface current K 100 x A/m flows on the surface z = 0, which separates two media with magnetic permeabilities 1 and 2 as shown in the figure. If the magnetic field in the region 1 is B1 = 4 x 6 y 2 z mT, then the magnitude of the normal component of B2 will be ________ mT. END OF THE QUESTION PAPER PH 13/13

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