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GATE 2019 : Physics (with Final Answer Keys)

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GATE 2019 General Aptitude (GA) Set-8 Q. 1 Q. 5 carry one mark each. Q.1 The fishermen, _______ the flood victims owed their lives, were rewarded by the government. (A) whom Q.2 (B) to which (C) to whom (D) that Some students were not involved in the strike. If the above statement is true, which of the following conclusions is/are logically necessary? 1. 2. 3. 4. Some who were involved in the strike were students. No student was involved in the strike. At least one student was involved in the strike. Some who were not involved in the strike were students. (A) 1 and 2 Q.3 (C) 4 (D) 2 and 3 The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is ______. (A) 17.1 Q.4 (B) 3 (B) 21.0 (C) 33.1 (D) 72.8 Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below: 1. No two odd or even numbers are next to each other. 2. The second number from the left is exactly half of the left-most number. 3. The middle number is exactly twice the right-most number. Which is the second number from the right? (A) 2 Q.5 (C) 7 (D) 10 Until Iran came along, India had never been ________________ in kabaddi. (A) defeated GA (B) 4 (B) defeating (C) defeat (D) defeatist 1/3 GATE 2019 General Aptitude (GA) Set-8 Q. 6 Q. 10 carry two marks each. Q.6 Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit interest rates. Which one of the following statements can be inferred from the given passage? (A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced (B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates (C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes (D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India Q.7 In a country of 1400 million population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country? (A) 10.50 Q.8 (B) 14.70 (C) 15.00 (D) 50.00 The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education the term gharana became acceptable. Gharana originally referred to hereditary musicians from a particular lineage, including disciples and grand disciples. Which one of the following pairings is NOT correct? (A) dhrupad, baani (B) gayaki, vocal (C) baaj, institution (D) gharana, lineage Q.9 Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is ______ AM. (A) 9 GA (B) 10 (C) 11 (D) 11.30 2/3 GATE 2019 General Aptitude (GA) Set-8 Q.10 I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community. Based on the paragraph above, the prestige of a head-hunter depended upon ___________ (A) the prestige of the kingdom (B) the prestige of the heads (C) the number of taxes he could levy (D) the number of heads he could gather END OF THE QUESTION PAPER GA 3/3 GATE 2019 PH Q. 1 Q. 25 carry one mark each. Q.1 The relative magnetic permeability of a type-I superconductor is (B) 1 (A) 0 Q.2 (D) Considering baryon number and lepton number conservation laws, which of the following processes is/are allowed? (i) (ii) + + + + + (A) both (i) and (ii) (B) only (i) (C) only (ii) (D) neither (i) nor (ii) Q.3 (C) + + For the following circuit, what is the magnitude of Vout if Vin = 1.5 V? 100 R R Vin +15V - Vout + -15V (A) 0.015 V (B) 0.15 V (C) 15 V (D) 150 V Q.4 For the differential equation its two independent solutions is (A) PH (B) + = (C) , where is a constant, the product of (D) + 1/15 GATE 2019 Q.5 PH Consider a one-dimensional gas of non-interacting particles of mass Hamiltonian for a single particle given by, = + The high temperature specific heat in units of (A) 1 (B) 1.5 (C) 2 (D) 2.5 Q.6 is the Boltzmann constant) is An electric field = is applied to a Hydrogen atom in = excited state. Ignoring spin, the = state is fourfold degenerate, which in the | , basis are given by | , , | , , | , and | , . If is the interaction Hamiltonian corresponding to the applied electric field, which of the following matrix elements is nonzero? (A) (B) (C) (D) Q.7 = + with the , , , , | | | | | , , | , | , | A large number of ideal bosons, each of mass m, are trapped in a three-dimensional . The bosonic system is kept at temperature which is much lower potential = than the Bose-Einstein condensation temperature . The chemical potential satisfies (A) Q.8 (B) > > (C) > > (D) = During a rotation, vectors along the axis of rotation remain unchanged. For the rotation matrix ( ), the unit vector along the axis of rotation is (A) ( + ) (B) PH ( + ) (C) ( ) (D) ( + ) 2/15 GATE 2019 Q.9 PH For a spin particle, let | and | denote its spin up and spin down states, respectively. | | +| | ) and | = | | | | ) are composite states If | = of two such particles, which of the following statements is true for their total spin S ? (A) S=1 for | , and | is not an eigenstate of the operator (B) | is not an eigenstate of the operator , and S=0 for | (C) S=0 for | , and S=1 for | (D) S=1 for | , and S=0 for | Q.10 Consider a transformation from one set of generalized coordinate and momentum another set , denoted by, = ; , to = where and are constants. The transformation is canonical if (A) (B) (C) (D) = = = = and = and = and = and = Q.11 In order to estimate the specific heat of phonons, the appropriate method to apply would be (A) Einstein model for acoustic phonons and Debye model for optical phonons (B) Einstein model for optical phonons and Debye model for acoustic phonons (C) Einstein model for both optical and acoustic phonons (D) Debye model for both optical and acoustic phonons Q.12 The pole of the function (A) a removable singularity (C) a simple pole = cot at = is (B) an essential singularity (D) a second order pole Q.13 A massive particle X in free space decays spontaneously into two photons. Which of the following statements is true for X? (A) X is charged (B) Spin of X must be greater than or equal to 2 (C) X is a boson (D) X must be a baryon PH 3/15 GATE 2019 PH Q.14 The electric field of an electromagnetic wave is given by = cos . The wave is (A) linearly polarized at an angle tan sin + from the x-axis (B) linearly polarized at an angle tan from the x-axis (C) elliptically polarized in clockwise direction when seen travelling towards the observer (D) elliptically polarized in counter-clockwise direction when seen travelling towards the observer Q.15 The nuclear spin and parity of (A) (B) (C) (D) + Ca in its ground state is + Q.16 An infinitely long thin cylindrical shell has its axis coinciding with the z-axis. It carries a surface charge density cos , where is the polar angle and is a constant. The magnitude of the electric field inside the cylinder is (A) 0 (B) (C) (D) Q.17 Consider a three-dimensional crystal of inert gas atoms. The total energy is given by = [ ], where = . , = . , and is the nearest neighbour distance between two atoms. The two constants, and , have the dimensions of energy and length, respectively. The equilibrium separation between two nearest neighbour atoms in units of (rounded off to two decimal places) is ___________ Q.18 The energy-wavevector ( - ) dispersion relation for a particle in two dimensions is = , where is a constant. If its density of states is proportional to then the value of is ______________ Q.19 A circular loop made of a thin wire has radius 2 cm and resistance 2 . It is placed perpendicular to a uniform magnetic field of magnitude | | = . Tesla. At time = the field starts decaying as = , where = . The total charge that passes through a cross section of the wire during the decay is Q. The value of Q in (rounded off to two decimal places) is________________ PH 4/15 GATE 2019 PH Q.20 The electric field of an electromagnetic wave in vacuum is given by = cos + . . The wave is reflected from the = surface. If the pressure exerted on the surface is , the value of (rounded off to one decimal place) is ___________ Q.21 The Hamiltonian for a quantum harmonic oscillator of mass where = + is the angular frequency. The expectation value of the oscillator in units of in three dimensions is in the first excited state of (rounded off to one decimal place) is __________ Q.22 The Hamiltonian for a particle of mass is = + where and are the generalized coordinate and momentum, respectively, is time and is a constant. For the initial condition, = and = at = , . The value of is _____________ Q.23 At temperature T Kelvin (K), the value of the Fermi function at an energy . eV above the Fermi energy is 0.01. Then T, to the nearest integer, is_____________ ( = . eV/K) Q.24 Let | = , | = represent two possible states of a two-level quantum system. is given by a density and | The state obtained by the incoherent superposition of | |. If = . and = . , the |+ | matrix that is defined as | matrix element (rounded off to one decimal place) is _________ Q.25 A conventional type-I superconductor has a critical temperature of . K at zero magnetic field and a critical magnetic field of 0.3 Tesla at K. The critical field in Tesla at K (rounded off to three decimal places) is ____________ PH 5/15 GATE 2019 PH Q. 26 Q. 55 carry two marks each. Q.26 Consider the following Boolean expression: + B [ + C A B+C ]+A B A It can be represented by a single three-input logic gate. Identify the gate. (A) AND (B) OR Q.27 The value of the integral (A) (B) Q.28 The wave function Here (A) + , where (C) > (D) NAND and > , is (D) of a particle is as shown below is a constant, and + (C) XOR > . The position uncertainty (B) + (C) of the particle is (D) Q.29 A solid cylinder of radius has total charge distributed uniformly over its volume. It is rotating about its axis with angular speed . The magnitude of the total magnetic moment of the cylinder is PH (A) (B) (C) (D) 6/15 GATE 2019 PH = | |. Its ground is proportional to Q.30 Consider the motion of a particle along the x-axis in a potential state energy is estimated using the uncertainty principle. Then (B) (A) (D) (C) Q.31 A 3-bit analog-to-digital converter is designed to digitize analog signals ranging from 0 V to 10 V. For this converter, the binary output corresponding to an input of 6 V is (A) 011 Q.32 (B) 101 (C) 100 (D) 010 The Hamiltonian operator for a two-level quantum system is the system at = (A) (C) ( + + cos[ is given by | / ) = then | (B) / ] (D) ( | cos[ =( ). If the state of | at a later time is / ) / ] Q.33 A particle of mass m moves in a lattice along the x-axis in a periodic potential = + with periodicity d. The corresponding Brillouin zone extends from to with these two k-points being equivalent. If a weak force F in the x-direction is applied to the particle, it starts a periodic motion with time period T. Using the equation of motion y al = for a particle moving in a band, where c y a is the crystal momentum of the particle, the period T is found to be ( is Planck constant) (A) PH (B) (C) (D) 7/15 GATE 2019 PH Q.34 Consider a potential barrier of the form: where is a constant. For particles of energy < incident on this barrier from the left, | which of the following schematic diagrams best represents the probability density | as a function of . (A) (B) (C) (D) Q.35 The spin-orbit interaction term of an electron moving in a central field is written as , where r is the radial distance of the electron from the origin. If an electron moves inside a uniformly charged sphere, then (A) (C) PH = constant (B) (D) 8/15 GATE 2019 PH Q.36 For the following circuit, the correct logic values for the entries X2 and Y2 in the truth table are C X A G Y B G 1 0 1 A 0 0 0 B 1 0 0 P 0 1 0 C 0 0 1 X 0 X2 0 Y 1 Y2 1 P (A) 1 and 0 (B) 0 and 0 (C) 0 and 1 (D) 1 and 1 h Q.37 In a set of successive polarizers, the polarizer makes an angle with the vertical. A vertically polarized light beam of intensity is incident on two such sets with = and = , where > . Let the intensity of light beams coming out be and , respectively. Which of the following statements is correct about the two outgoing beams? (A) > (B) < (C) > (D) < PH ; the polarization in each case is vertical ; the polarization in each case is vertical ; the polarization in each case is horizontal ; the polarization in each case is horizontal 9/15 GATE 2019 PH Q.38 A ball bouncing off a rigid floor is described by the potential energy function = = for for > 0 Which of the following schematic diagrams best represents the phase space plot of the ball? PH (A) (B) (C) (D) 10/15 GATE 2019 PH Q.39 An infinitely long wire parallel to the x-axis is kept at = and carries a current I in the positive x direction above a superconductor filling the region (see figure). The magnetic field inside the superconductor is zero so that the field just outside the superconductor is parallel to its surface. The magnetic field due to this configuration at a point , , > is (A) (B) (C) (D) + [ + ] + [ [ + + [ + + + + + + + + + + + + + + ] ] ] Q.40 The vector potential inside a long solenoid, with n turns per unit length and carrying , , = current , written in cylindrical coordinates is . If the term , , , the magnetic ( cos + sin ), where , , is added to field remains the same if (A) = (B) [ PH v = = Useful formulae: = (C) = + ( + = (D) ) + + ; ] 11/15 GATE 2019 PH Q.41 Low energy collision (s-wave scattering) of pion ( +) with deuteron (d) results in the production of two protons + + + . The relative orbital angular momentum (in units of ) of the resulting two-proton system for this reaction is (A) 0 (B) 1 Q.42 Consider the Hamiltonian (C) 2 , = + (D) 3 , where and are parameters with appropriate dimensions, and and are the generalized coordinate and momentum, respectively. The corresponding Lagrangian , is (A) (B) + (C) + (D) Q.43 For a given load resistance RL = 4.7 ohm, the power transfer efficiencies + = Ploa P o al of a dc voltage source and a dc current source with internal resistances R1 and R2, respectively, are equal. The product R1R2 in units of ohm2 (rounded off to one decimal place) is _____________ Q.44 The ground state electronic configuration of the rare-earth ion Nd + is [Pd] f s p . Assuming LS coupling, the Land -factor of this ion is . The effective magnetic moment in units of Bohr magneton (rounded off to two decimal places) is __________________ Q.45 A projectile of mass 1 kg is launched at an angle of 30 from the horizontal direction at = and takes time before hitting the ground. If its initial speed is 10 ms , the value of the action integral for the entire flight in the units of kg m s (rounded off to one decimal place) is _____________ [Take Q.46 Let = ms ] be a variable in the range = = < . Now consider a function for / otherwise. < / If its Fourier-series is written as = = , then the value of | | (rounded off to three decimal places) is _________________ PH 12/15 GATE 2019 PH Q.47 Two spaceships A and B, each of the same rest length , are moving in the same direction with speeds and , respectively, where is the speed of light. As measured by B, the time taken by A to completely overtake B [see figure below] in units of / (to the nearest integer) is _______________ Q.48 A radioactive element X has a half-life of 30 hours. It decays via alpha, beta and gamma emissions with the branching ratio for beta decay being 0.75. The partial half-life for beta decay in unit of hours is ________________ Q.49 In a thermally insulated container, 0.01 kg of ice at 273 K is mixed with 0.1 kg of water at 300 K. Neglecting the specific heat of the container, the change in the entropy of the system in J/K on attaining thermal equilibrium (rounded off to two decimal places) is ___________ (Specific heat of water is 4.2 kJ/kg-K and the latent heat of ice is 335 kJ/kg). PH 13/15 GATE 2019 PH Q.50 Consider a system of three charges as shown in the figure below: For = m; = degrees; = Coulomb, and = potential in volts (rounded off to three decimal places) at a point __________________ [ Use : = N ] , m, the electric dipole is Q.51 Consider two systems A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0, 1, 2 and 3 units with equal probability. The total energy of the combined system is 5 units. Assuming that the system A has energy 3 units and the system B has energy 2 units, the entropy of the combined system is ln . The value of is________________ Q.52 Electrons with spin in the -direction are passed through a Stern-Gerlach (SG) set up with the magnetic field at = o from . The fraction of electrons that will emerge with their spin parallel to the magnetic field in the SG set up (rounded off to two decimal places) is __________________ [ = , PH , = ] with . The fourth order contribution is . The value of (rounded off to three decimal places) Q.53 The Hamiltonian of a system is to the ground state energy of is _________ = = 14/15 GATE 2019 PH Q.54 Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth s frame. The time difference between the two events as seen by an observer in a spaceship moving with velocity 0.5c in the earth s frame along the line joining the earth to the Sun is , where c is the speed of light. Given that light travels from the Sun to the earth in 8.3 minutes in the earth s frame, the value of | | in minutes (rounded off to two decimal places) is ________________ (Take the earth s frame to be inertial and neglect the relative motion between the earth and the sun) Q.55 In a certain two-dimensional lattice, the energy dispersion of the electrons is ( ) = [cos + cos cos ] where = , ) denotes the wave vector, is the lattice constant and is a constant in units of eV. In this lattice the effective mass tensor of electrons calculated at the center of the Brillouin zone has the form = off to three decimal places) is ___________ . The value of (rounded END OF THE QUESTION PAPER PH 15/15 Q.No. Type Section Key/Range Marks 1 MCQ GA C 1 2 MCQ GA C 1 3 MCQ GA C 1 4 MCQ GA C 1 5 MCQ GA A 1 6 MCQ GA C 2 7 MCQ GA A 2 8 MCQ GA C 2 9 MCQ GA B 2 10 MCQ GA D 2 1 MCQ PH A 1 2 MCQ PH C 1 3 MCQ PH C 1 4 MCQ PH B 1 5 MCQ PH A 1 6 MCQ PH C 1 7 MCQ PH A 1 8 MCQ PH B 1 9 MCQ PH D 1 10 MCQ PH B 1 11 MCQ PH B 1 12 MCQ PH C 1 13 MCQ PH C 1 1/3 Q.No. Type Section Key/Range Marks 14 MCQ PH D 1 15 MCQ PH A 1 16 MCQ PH B 1 17 NAT PH 1.07 to 1.11 1 18 NAT PH 1 to 1 1 19 NAT PH 6.26 to 6.30 1 20 NAT PH 0.8 to 0.8 1 21 NAT PH 2.5 to 2.5 1 22 NAT PH 3 to 3 1 23 NAT PH 1260 to 1266 1 24 NAT PH 0.6 to 0.6 1 25 NAT PH 0.244 to 0.248 1 26 MCQ PH D 2 27 MCQ PH A 2 28 MCQ PH B 2 29 MCQ PH C 2 30 MCQ PH D 2 31 MCQ PH C 2 32 MCQ PH C 2 33 MCQ PH D 2 34 MCQ PH A 2 35 MCQ PH A 2 36 MCQ PH A 2 2/3 Q.No. Type Section Key/Range Marks 37 MCQ PH C 2 38 MCQ PH B 2 39 MCQ PH B 2 40 MCQ PH D 2 41 MCQ PH B 2 42 MCQ PH A 2 43 NAT PH 22.0 to 22.2 2 44 NAT PH 3.61 to 3.63 2 45 NAT PH 33.2 to 33.4 2 46 NAT PH 0.010 to 0.013 2 47 NAT PH 5 to 5 2 48 NAT PH 40 to 40 2 49 NAT PH 1.02 to 1.04 2 50 NAT PH 0.044 to 0.046 2 51 NAT PH 12 to 12 2 52 NAT PH 0.25 to 0.25 2 53 NAT PH 0.125 to 0.125 2 54 NAT PH 4.77 to 4.81 2 55 NAT PH 0.333 to 0.333 2 3/3

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