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GATE 2018 : Physics (with Final Answer Keys)

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GATE 2018 General Aptitude (GA) Set-4 Q. 1 Q. 5 carry one mark each. Q.1 When she fell down the _______, she received many _______ but little help. The words that best fill the blanks in the above sentence are (A) stairs, stares (C) stares, stairs Q.2 (B) stairs, stairs (D) stares, stares In spite of being warned repeatedly, he failed to correct his _________ behaviour. The word that best fills the blank in the above sentence is (A) rational Q.3 For , (D) good (B) , (C) , (D) , The area of an equilateral triangle is . What is the perimeter of the triangle? (A) 2 Q.5 (C) errant , sin and cos are both decreasing functions in the interval ________. (A) Q.4 (B) reasonable (B) 4 (C) 6 (D) 8 Arrange the following three-dimensional objects in the descending order of their volumes: (i) A cuboid with dimensions 10 cm, 8 cm and 6 cm (ii) A cube of side 8 cm (iii) A cylinder with base radius 7 cm and height 7 cm (iv) A sphere of radius 7 cm (A) (i), (ii), (iii), (iv) (B) (ii), (i), (iv), (iii) (C) (iii), (ii), (i), (iv) (D) (iv), (iii), (ii), (i) Q. 6 Q. 10 carry two marks each. Q.6 An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey? (A) 72 GA (B) 73 (C) 74 (D) 75 1/2 GATE 2018 General Aptitude (GA) Set-4 Q.7 A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed? (A) 20 Q.8 (B) 48 (D) 72 To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test? (A) 30,000 Q.9 (C) 60 If + (A) 1 (B) 2,70,000 = (C) 3,90,000 what is the value of + (B) 5 4 (D) 4,20,000 ? (C) 7 (D) 9 Q.10 In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another unrelated study, it was found that the revenue from cracker sales in India which remained fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. The solid line in the graph below refers to annual sale of crackers and the dashed line refers to the annual crow births in India. Choose the most appropriate inference from the above data. (A) There is a strong correlation between crow birth and cracker sales. (B) Cracker usage increases crow birth rate. (C) If cracker sale declines, crow birth will decline. (D) Increased birth rate of crows will cause an increase in the sale of crackers. END OF THE QUESTION PAPER GA 2/2 GATE 2018 Physics Q. 1 Q. 25 carry one mark each. Q.1 The eigenvalues of a Hermitian matrix are all (A) real (B) imaginary (C) of modulus one (D) real and positive Q.2 Q.3 Which one of the following represents the 3p radial wave function of hydrogen atom? (a0 is the Bohr radius) (A) (B) (C) (D) Given the following table, Group I P: Stern-Gerlach experiment Q: Zeeman effect R: Frank-Hertz experiment S: Davisson-Germer experiment Group II 1: Wave nature of particles 2: Quantization of energy of electrons in the atoms 3: Existence of electron spin 4: Space quantization of angular momentum which one of the following correctly matches the experiments from Group I to their inferences in Group II? (A) P-2, Q-3, R-4, S-1 (C) P-3, Q-4, R-2, S-1 Q.4 In spherical polar coordinates ( , , ), the unit vector at (A) PH (B) P-1, Q-3, R-2, S-4 (D) P-2, Q-1, R-4, S-3 (B) ( + ) (C) ( + ) , / , / (D) is ( ) 1/12 GATE 2018 Q.5 Q.6 Physics The scale factors corresponding to the covariant metric tensor coordinates are in spherical polar (A) , (D) , , sin , sin (B) , , sin (C) 1, 1, 1 In the context of small oscillations, which one of the following does NOT apply to the normal coordinates? (A) Each normal coordinate has an eigen-frequency associated with it (B) The normal coordinates are orthogonal to one another (C) The normal coordinates are all independent (D) The potential energy of the system is a sum of squares of the normal coordinates with constant coefficients Q.7 For the given unit cells of a two dimensional square lattice, which option lists all the primitive cells? (A) and (C) , , and Q.8 Among electric field ( ), magnetic field ( ), angular momentum ( ), and vector potential ( ), which is/are odd under parity (space inversion) operation? (A) only Q.9 (B) , and (D) , , , and (B) & (C) & only only (D) & only The expression for the second overtone frequency in the vibrational absorption spectra of a diatomic molecule in terms of the harmonic frequency and anharmonicity constant is (A) (B) 2 (C) (D) Q.10 Match the physical effects and order of magnitude of their energy scales given below, where = respectively. is fine structure constant; Group I P: Lamb shift Q: Fine structure R: Bohr energy S: Hyperfine structure (A) P-3, Q-1, R-2, S-4 (C) P-4, Q-2, R-1, S-3 PH and are electron and proton mass, Group II 1: ~ 2: ~ 3: ~ 4: ~ / (B) P-2, Q-3, R-1, S-4 (D) P-2, Q-4, R-1, S-3 2/12 GATE 2018 Physics Q.11 The logic expression (A) XOR (B) + + AND + can be simplified to (C) 0 (D) 1 Q.12 At low temperatures ( ), the specific heat of common metals is described by (with as constants) + (A) Q.13 (C) exp / (B) (D) and + In a 2-to-1 multiplexer as shown below, the output X = A0 if C = 0, and X = A1 if C = 1. C A0 X A1 Which one of the following is the correct implementation of this multiplexer? (A) (B) A0 A0 X C A1 (C) X C A1 (D) A0 A0 X C A1 X C A1 Q.14 The elementary particle is placed in the baryon decuplet, shown below, at (A) P PH (B) Q (C) R (D) S 3/12 GATE 2018 Physics Q.15 The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is ( is the Bohr radius) (A) (B) zero (C) (D) Q.16 The high temperature magnetic susceptibility of solids having ions with magnetic moments with as absolute temperature and as constant. The three can be described by + behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described, respectively, by (A) < , > , = (B) > , < , = (C) = , < , > (D) = , > , < Q.17 Which one of the following is an allowed electric dipole transition? (A) 1 S0 3 S1 Q.18 In the decay, (A) (B) 2 P3/2 2 D5/2 + + + (B) (C) + , what is ? (C) 2 D5/2 2 P1/2 (D) (D) 3 P0 5 D0 Q.19 A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places). Q.20 For an operational amplifier (ideal) circuit shown below, 4 k V1 V2 2 k 5 k +10 V + V0 RL -10 V if V1 = 1 V and V2 = 2 V, the value of V0 is ________V (up to one decimal place). Q.21 An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy from the wire is ________. density at distance to that at = PH 4/12 GATE 2018 Physics Q.22 A light beam of intensity is falling normally on a surface. The surface absorbs 20% of the , intensity and the rest is reflected. The radiation pressure on the surface is given by where X is ________ (up to one decimal place). Here is the speed of light. Q.23 The number of independent components of a general electromagnetic field tensor is ________. Q.24 If is the dimensionality of a free electron gas, the energy ( ) dependence of density of states is given by , where is ________. Q.25 For nucleus 164Er, a = + state is at 90 keV. Assuming 164Er to be a rigid rotor, the energy of its + state is ________ keV (up to one decimal place). PH 5/12 GATE 2018 Physics Q. 26 Q. 55 carry two marks each. Q.26 Given = and = + + , which one of the following makes ( , , ) a complete set for a three dimensional real linear vector space ? (A) = + + (C) = + + (B) = (D) = + + + Q.27 An interstellar object has speed at the point of its shortest distance larger mass . Given = / , the trajectory of the object is (A) circle (B) ellipse (C) parabola from a star of much (D) hyperbola Q.28 A particle moves in one dimension under a potential = | | with some non-zero total energy. Which one of the following best describes the particle trajectory in the phase space? (A) (B) (C) (D) Q.29 Consider an infinitely long solenoid with turns per unit length, radius and carrying a current = cos , where is a constant and is the angular frequency. The magnitude of electric field at the surface of the solenoid is sin (A) sin (C) cos (B) cos (D) Q.30 A constant and uniform magnetic field = pervades all space. Which one of the following is the correct choice for the vector potential in Coulomb gauge? (A) Q.31 If (B) + (C) is the Hamiltonian for a free particle with mass (A) / PH + (B) / (C) / (D) , the commutator [ , [ , ]] is (D) / 6/12 GATE 2018 Physics Q.32 A long straight wire, having radius and resistance per unit length , carries a current . The magnitude and direction of the Poynting vector on the surface of the wire is (A) (B) (C) (D) , perpendicular to axis of the wire and pointing inwards , perpendicular to axis of the wire and pointing outwards , perpendicular to axis of the wire and pointing inwards , perpendicular to axis of the wire and pointing outwards Q.33 Three particles are to be distributed in four non-degenerate energy levels. The possible number of ways of distribution: (i) for distinguishable particles, and (ii) for identical Bosons, respectively, is (A) (i) 24, (ii) 4 (B) (i) 24, (ii) 20 (C) (i) 64, (ii) 20 (D) (i) 64, (ii) 16 Q.34 The term symbol for the electronic ground state of oxygen atom is (A) (B) (C) (D) Q.35 The energy dispersion for electrons in one dimensional lattice with lattice parameter is cos , where and are constants. The effective mass of given by = the electron near the bottom of the band is (A) (B) (C) (D) Q.36 Amongst electrical resistivity , thermal conductivity ( ), specific heat ( ), Young s modulus (Y), and magnetic susceptibility , which quantities show a sharp change at the superconducting transition temperature? (A) , , , Y PH (B) , , (C) , , , (D) , Y, 7/12 GATE 2018 Physics Q.37 A quarter wave plate introduces a path difference of / between the two components of polarization parallel and perpendicular to the optic axis. An electromagnetic wave with = + is incident normally on a quarter wave plate which has its optic axis making an angle with the -axis as shown. The emergent electromagnetic wave would be (A) elliptically polarized (B) circularly polarized (C) linearly polarized with polarization as that of incident wave (D) linearly polarized but with polarization at to that of the incident wave Q.38 A p-doped semiconductor slab carries a current = mA in a magnetic field = . T as shown. One measures = . mV and = mV. The mobility of holes in the semiconductor is ________ m2V 1s 1 (up to two decimal places). PH 8/12 GATE 2018 Physics Q.39 An n-channel FET having Gate-Source switch-off voltage VGS(OFF) = 2 V is used to invert a 0 5 V square-wave signal as shown. The maximum allowed value of R would be ________ k (up to two decimal places). +5V 5 k Vout Vin R 5V 0V 5V 0V 100 1 k - 12 V Q.40 Inside a large nucleus, a nucleon with mass 939 MeVc 2 has Fermi momentum 1.40 fm 1 at absolute zero temperature. Its velocity is Xc, where the value of X is ________ (up to two decimal places). ( = MeV-fm) Q.41 4 MeV -rays emitted by the de-excitation of 19F are attributed, assuming spherical symmetry, to the transition of protons from 1d3/2 state to 1d5/2 state. If the contribution of spin-orbit term to the total energy is written as , the magnitude of is ________ MeV (up to one decimal place). Q.42 An particle is emitted by a Th nucleus. Assuming the potential to be purely Coulombic beyond the point of separation, the height of the Coulomb barrier is ________ MeV (up to two decimal places). ( = . MeV-fm, = . fm) Q.43 For the transformation (where PH = + cos , = is a constant) to be canonical, the value of sin is________. 9/12 GATE 2018 Physics Q.44 Given = and boundary conditions two decimal places). and + = , = , the value of . is ________ (up to Q.45 The absolute value of the integral over the circle | . | = + , in complex plane, is ________ (up to two decimal places). Q.46 A uniform circular disc of mass and radius is rotating with angular speed about an axis passing through its center and making an angle = with the axis of the disc. If the kinetic energy of the disc is , the value of is ________ (up to 2 decimal places). Q.47 The ground state energy of a particle of mass in an infinite potential well is changes to + , when there is a small potential bump of height = and width = / to two decimal places). PH , as shown in the figure. The value of . It is ________ (up 10/12 GATE 2018 Physics Q.48 An electromagnetic plane wave is propagating with an intensity = . Wm 2 in a medium with = and = . The amplitude of the electric field inside the medium is ________ Vm 1 (up to one decimal place). ( = . C2 N 1 m 2, = NA 2, = ms 1) Q.49 A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy state. Both states are non-degenerate. If the total energy of this ensemble is , its entropy will be ________ (up to one decimal place), where is the Boltzmann constant. Q.50 A two-state quantum system has energy eigenvalues corresponding to the normalized states | . At time = , the system is in quantum state [| + + | ]. The probability that the system will be in the same state at = / is ________ (up to two decimal places). Q.51 An air-conditioner maintains the room temperature at 27 oC while the outside temperature is 47 oC. The heat conducted through the walls of the room from outside to inside due to temperature difference is 7000 W. The minimum work done by the compressor of the airconditioner per unit time is ________ W. Q.52 Two solid spheres A and B have same emissivity. The radius of A is four times the radius of B, and temperature of A is twice the temperature of B. The ratio of the rate of heat radiated from A to that from B is ________. Q.53 The partition function of an ensemble at a temperature is = ( cosh ) , where , is the Boltzmann constant. The heat capacity of this ensemble at where the value of is ________ (up to two decimal places). = is Q.54 An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its 650 nm spectral line is 0.03 nm. The magnitude of the field is ________ Tesla (up to two decimal places). ( PH = . C, = . kg, = . ms 1) 11/12 GATE 2018 Physics Q.55 The quantum effects in an ideal gas become important below a certain temperature when de Broglie wavelength corresponding to the root mean square thermal speed becomes equal to the inter-atomic separation. For such a gas of atoms of mass kg and number density . m 3, = __________ K (up to one decimal place). ( = . J/K, = . J-s) END OF THE QUESTION PAPER PH 12/12 Q.No. Type Section Key/Range Marks 1 MCQ GA A 1 2 MCQ GA C 1 3 MCQ GA B 1 4 MCQ GA C 1 5 MCQ GA D 1 6 MCQ GA A 2 7 MCQ GA C 2 8 MCQ GA D 2 9 MCQ GA C 2 10 MCQ GA A 2 1 MCQ PH A 1 2 MCQ PH B 1 3 MCQ PH C 1 4 MCQ PH D 1 5 MCQ PH D 1 6 MCQ PH B 1 7 MCQ PH C 1 8 MCQ PH B 1 9 MCQ PH D 1 10 MCQ PH C 1 11 MCQ PH A 1 12 MCQ PH A 1 13 MCQ PH A 1 14 MCQ PH C 1 Q.No. Type Section Key/Range Marks 15 MCQ PH B 1 16 MCQ PH C 1 17 MCQ PH B 1 18 MCQ PH D 1 19 NAT PH 0.185 to 0.189 1 20 NAT PH 3.7 to 3.5 1 21 NAT PH 4 to 4 1 22 NAT PH 1.8 to 1.8 1 23 NAT PH 6 to 6 1 24 NAT PH 1 to 1 1 25 NAT PH 297.0 to 300.1 1 26 MCQ PH D 2 27 MCQ PH C 2 28 MCQ PH A 2 29 MCQ PH A 2 30 MCQ PH C 2 31 MCQ PH B 2 32 MCQ PH A 2 33 MCQ PH C 2 34 MCQ PH D 2 35 MCQ PH A 2 36 MCQ PH B 2 37 MCQ PH C 2 38 NAT PH 1.55 to 1.58 2 Q.No. Type Section Key/Range Marks 39 NAT PH 0.70 to 0.73 2 40 NAT PH 0.28 to 0.31 2 41 NAT PH 1.6 to 1.6 2 42 NAT PH 24.4 to 27.6 2 43 NAT PH 2 to 2 2 44 NAT PH 0.81 to 0.84 2 45 NAT PH 81.60 to 81.80 2 46 NAT PH 0.21 to 0.23 2 47 NAT PH 0.78 to 0.82 2 48 NAT PH 6.5 to 6.7 2 49 NAT PH 6.1 to 6.3 2 50 NAT PH 0.25 to 0.25 2 51 NAT PH 466 to 467 2 52 NAT PH 256 to 256 2 53 NAT PH 0.41 to 0.43 2 54 NAT PH 1.51 to 1.53 2 55 NAT PH 78 to 90 2

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