Q. 1 Q. 5 carry one mark each.

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1 G 6 General ptitude - G Set- Q. Q. carry one mar each. Q. he volume of a sphere of diameter unit is than the volume of a cube of side unit. () least () less lesser low Q. he unruly crowd demanded that the accused be without trial. () hanged () hanging hanering hung Q. Choose the statement(s) where the underlined word is used correctly: (i) (ii) (iii) prone is a dried plum. He was lying prone on the floor. People who eat a lot of fat are prone to heart disease. () (i) and (iii) only () (iii) only (i) and (ii) only (ii) and (iii) only Q.4 Fact: If it rains then the field is wet. Read the following statements: (i) It rains (ii) he field is not wet (iii) he field is wet (iv) It did not rain Which one of the options given below is NO logically possible based on the given fact? () If (iii) then (iv). () If (i) then (iii). If (i) then (ii). If (ii) then (iv). Q. window is made up of a square portion and an equilateral triangle portion above it. he base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m the area of the window in m is. ().4 ()

2 G 6 General ptitude - G Set- Q. 6 Q. carry two mars each. Q.6 Students taing an exam are divided into two groups P and Q such that each group has the same number of students. he performance of each of the students in a test was evaluated out of mars. It was observed that the mean of group P was while that of group Q was 8. he standard deviation of group P was while that of group Q was. ssuming that the mars were distributed on a normal distribution which of the following statements will have the highest probability of being RU? () No student in group Q scored less mars than any student in group P. () No student in group P scored less mars than any student in group Q. Most students of group Q scored mars in a narrower range than students in group P. he median of the mars of group P is. Q.7 smart city integrates all modes of transport uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city something which critics argue will lead to a surveillance state. Which of the following can be logically inferred from the above paragraph? (i) (ii) (iii) (iv) ll smart cities encourage the formation of surveillance states. Surveillance is an integral part of a smart city. Sustainability and surveillance go hand in hand in a smart city. here is a perception that smart cities promote surveillance. () (i) and (iv) only (iv) only () (ii) and (iii) only (i) only Q.8 Find the missing sequence in the letter series. FH LNP. () SUW () UVW VZ WZ Q.9 he binary operation is defined as a b = ab+(a+b) where a and b are any two real numbers. he value of the identity element of this operation defined as the number x such that a x = a for any a is. () ()

3 G 6 General ptitude - G Set- Q. Which of the following curves represents the function = ln( ( ) ) for <? Here represents the abscissa and represents the ordinate. () () ND OF H QUSION PPR

4 G 6 Physics Q. Q. carry one mar each. Q. Consider the linear differential equation dy xy. If y at x then the value of y at x= is dx given by () e () e e e Q. Which of the following magnetic vector potentials gives rise to a uniform magnetic field ˆ? () z ˆ () xˆ j y iˆ x ˆ j y iˆ x ˆj Q. he molecule 7 O is () Raman active but not NMR (nuclear magnetic resonance) active. () Infrared active and Raman active but not NMR active. Raman active and NMR active. Only NMR active. Q.4 here are four electrons in the d shell of an isolated atom. he total magnetic moment of the atom in units of ohr magneton is. Q. Which of the following transitions is NO allowed in the case of an atom according to the electric dipole radiation selection rule? () s-s () p-s p-s d-p Q.6 In the SU() quar model the triplet of mesons () Isospin = Strangeness = () Isospin = Strangeness = Isospin = Strangeness = + Isospin = Strangeness = - Q.7 he magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current I is m. If this loop is changed to a circular shape with the same current I passing has through it the magnetic dipole moment becomes pm. he value of p is. Q.8 he total power emitted by a spherical blac body of radius R at a temperature is P. Let P be the total power emitted by another spherical blac body of radius R ept at temperature. he ratio P P is. (Give your answer upto two decimal places) PH

5 G 6 Physics Q.9 he entropy S of a system of N spins which may align either in the upward or in the downward direction is given by S N p ln p ( p) ln( p). Here is the oltzmann constant. he probability of alignment in the upward direction is p. he value of p at which the entropy is maximum is. (Give your answer upto one decimal place) Q. For a system at constant temperature and volume which of the following statements is correct at equilibrium? () he Helmholtz free energy attains a local minimum. () he Helmholtz free energy attains a local maximum. he Gibbs free energy attains a local minimum. he Gibbs free energy attains a local maximum. Q. N atoms of an ideal gas are enclosed in a container of volume V. he volume of the container is changed to 4V while eeping the total energy constant. he change in the entropy of the gas in units of N ln is where is the oltzmann constant. Q. Which of the following is an analytic function of z everywhere in the complex plane? () z * () z z z Q. In a oung s double slit experiment using light the apparatus has two slits of unequal widths. When only slit- is open the maximum observed intensity on the screen is 4I. When only slit- is open the maximum observed intensity is I. When both the slits are open an interference pattern appears on the screen. he ratio of the intensity of the principal maximum to that of the nearest minimum is. Q.4 Consider a metal which obeys the Sommerfeld model exactly. If F is the Fermi energy of the metal at = K and R H is its Hall coefficient which of the following statements is correct? () H F R () H F R R H F F. R H is independent of Q. one-dimensional linear chain of atoms contains two types of atoms of masses m and m (where m > m ) arranged alternately. he distance between successive atoms is the same. ssume that the harmonic approximation is valid. t the first rillouin zone boundary which of the following statements is correct? () he atoms of mass m are at rest in the optical mode while they vibrate in the acoustical mode. ( he atoms of mass m are at rest in the optical mode while they vibrate in the acoustical mode. oth types of atoms vibrate with equal amplitudes in the optical as well as in the acoustical modes. oth types of atoms vibrate but with unequal non-zero amplitudes in the optical as well as in the acoustical modes. Q.6 Which of the following operators is Hermitian? d () dx d () dx d d i dx dx PH

6 G 6 Physics Q.7 he inetic energy of a particle of rest mass m is equal to its rest mass energy. Its momentum in units of c where c is the speed of light in vacuum is. (Give your answer upto two m decimal places) Q.8 he number density of electrons in the conduction band of a semiconductor at a given temperature 9 is m. Upon lightly doping this semiconductor with donor impurities the number density of conduction electrons at the same temperature becomes 4 m. he ratio of majority to minority charge carrier concentration is. Q.9 wo blocs are connected by a spring of spring constant. One bloc has mass m and the other bloc has mass m. If the ratio m = 4 s the angular frequency of vibration ω of the two bloc spring system in is. (Give your answer upto two decimal places) s Q. particle moving under the influence of a central force F( r) r (where r is the position vector of the particle and is a positive constant) has non-zero angular momentum. Which of the following curves is a possible orbit for this particle? () straight line segment passing through the origin. () n ellipse with its center at the origin. n ellipse with one of the foci at the origin. parabola with its vertex at the origin. Q. 4 Consider the reaction Mn + () γ 4 e Cr 4 +. he particle is () n π e Q. he scattering of particles by a potential can be analyzed by orn approximation. In particular if the scattered wave is replaced by an appropriate plane wave the corresponding orn approximation is nown as the first orn approximation. Such an approximation is valid for () large incident energies and wea scattering potentials. () large incident energies and strong scattering potentials. small incident energies and wea scattering potentials. small incident energies and strong scattering potentials. Q. Consider an elastic scattering of particles in l states. If the corresponding phase shift is 9 and the magnitude of the incident wave vector is equal to cross section in units of fm is. fm - then the total scattering Q.4 hydrogen atom is in its ground state. In the presence of a uniform electric field z ˆ the n leading order change in its energy is proportional to( ). he value of the exponent n is. PH

7 G 6 Physics Q. solid material is found to have a temperature independent magnetic susceptibility C. Which of the following statements is correct? () If C is positive the material is a diamagnet. () If C is positive the material is a ferromagnet. If C is negative the material could be a type I superconductor. If C is positive the material could be a type I superconductor. Q. 6 Q. carry two mars each. Q.6 n infinite conducting slab ept in a horizontal plane carries a uniform charge density. nother infinite slab of thicness t made of a linear dielectric material of dielectric constant is ept above the conducting slab. he bound charge density on the upper surface of the dielectric slab is () ( ) () ( ) Q.7 he number of spectroscopic terms resulting from the L S coupling of a p electron and a d electron is. Q.8 Which of the following statements is NO correct? () deuteron can be disintegrated by irradiating it with gamma rays of energy 4 MeV. () deuteron has no excited states. deuteron has no electric quadrupole moment. he S state of deuteron cannot be formed. Q.9 If s and s are the spin operators of the two electrons of a He atom the value of s s ground state is for the () () 4 4 Q. two-dimensional square rigid box of side L contains six non-interacting electrons at = K. he mass of the electron is m. he ground state energy of the system of electrons in units of is ml. Q. n alpha particle is accelerated in a cyclotron. It leaves the cyclotron with a inetic energy of 6 MeV. he potential difference between the D electrodes is ilovolts. he number of revolutions the alpha particle maes in its spiral path before it leaves the cyclotron is. Q. Let V be the i component of a vector field V which has zero divergence. If x the expression for ε ε V is equal to () j Vi () j Vi V j i V j i PH 4

8 G 6 Physics Q. he direction of f for a scalar field f(x y z) = x xy + z at the point P( ) is ˆj ˆ ˆj ˆ ˆj ˆ ˆj ˆ () () Q.4 and is equal to x y z are the Pauli matrices. he expression x y y x () i () z i z i z i z Q. particle of mass m =. g is initially at rest at origin. It starts moving with a uniform acceleration ˆ a i ms at t =. he action S of the particle in units of J-s at t = s is. (Give your answer upto two decimal places) Q.6 periodic function f(x) of period π is defined in the interval ( π < x < π) as: π < x < f(x) = < x < π he appropriate Fourier series expansion for f(x) is () f ( x) 4 [sin x (sin x) (sin x)...] () f ( x) 4 [sin x (sin x) (sin x)...] f ( x) 4 [cos x (cos x) (cos x)...] f ( x) 4 [cos x (cos x) (cos x)...] Q.7 toms which can be assumed to be hard spheres of radius R are arranged in an fcc lattice with lattice constant a such that each atom touches its nearest neighbours. ae the center of one of the atoms as the origin. nother atom of radius r (assumed to be hard sphere) is to be accommodated at a position ( a ) without distorting the lattice. he maximum value of rr is. (Give your answer upto two decimal places) Q.8 In an inertial frame of reference S an observer finds two events occurring at the same time at coordinates x and x d. different inertial frame S moves with velocity v with respect to S along the positive x-axis. n observer in S also notices these two events and finds them to occur at times t and t and at positions x and x respectively. If t t t x x x and v c which of the following statements is true? () t x d () t x d t vd c x d t vd c x d PH

9 G 6 Physics Q.9 he energy vs. wave vector approximated as ( a) ( a ) relationship near the bottom of a band for a solid can be 4 where the lattice constant a =. Å. he values of and 9 are 6. J and. J respectively. t the bottom of the conduction band the ratio of the effective mass of the electron to the mass of free electron is. (Give your answer upto two decimal places) (ae =.x -4 J-s mass of free electron= 9.x - g) Q.4 he electric field component of a plane electromagnetic wave travelling in vacuum is given by ( z t) cos( z t) iˆ. he Poynting vector for the wave is () c cos ( z t) j () c cos ( z t) c cos ( z c cos ( z t) ˆj t) ˆ ˆ ˆ Q.4 Consider a system having three energy levels with energies and with respective degeneracies of and. Four bosons of spin zero have to be accommodated in these levels such that the total energy of the system is. he number of ways in which it can be done is. Q.4 he Lagrangian of a system is given by sin mgl cos where m l and g are constants. L ml Which of the following is conserved? () sin () sin sin sin Q.4 Protons and α-particles of equal initial momenta are scattered off a gold foil in a Rutherford scattering experiment. he scattering cross sections for proton on gold and α-particle on gold are and respectively. he ratio p is. p PH 6

10 G 6 Physics PH 7 Q.44 For the digital circuit given below the output is () C () C) ( C) ( C) ( Q.4 he Fermi energies of two metals and are ev and 7 ev and their Debye temperatures are 7 K and 4 K respectively. he molar specific heats of these metals at constant volume at low temperatures can be written as C V and C V where γ and are constants. ssuming that the thermal effective mass of the electrons in the two metals are same which of the following is correct? () 8 7 () Q.46 two-level system has energies zero and. he level with zero energy is non-degenerate while the level with energy is triply degenerate. he mean energy of a classical particle in this system at a temperature is () e e () e e e e e e C

11 G 6 Physics Q.47 particle of rest mass M is moving along the positive x-direction. It decays into two photons and as shown in the figure. he energy of is GeV and the energy of is.8 GeV. he value of M (in units of GeVc ) is. (Give your answer upto two decimal places) Q.48 If x and p are the x components of the position and the momentum operators of a particle respectively the commutator [ x p ] is () i ( xp px) () i ( xp px) i ( xp px) i ( xp px) Q.49 he x-y plane is the boundary between free space and a magnetic material with relative permeability r. he magnetic field in the free space is iˆ x zˆ. he magnetic field in the magnetic material is () i ˆ x zˆ () iˆ x ˆ r z iˆ x zˆ iˆ r x zˆ r Q. Let l m be the simultaneous eigenstates of x y z L and L z. Here L is the angular momentum operator with Cartesian components ( L L L ) l is the angular momentum quantum number and m is the azimuthal quantum number. he value of ( L il ) () () Q. For the parity operator P which of the following statements is NO true? x y is () P = P () P P P I P = P

12 G 6 Physics Q. For the transistor shown in the figure assume V =.7 V and βdc =. If Vin = V Vout (in Volts) is. (Give your answer upto one decimal place) Q. he state of a system is given by where state Q.4 and form an orthonormal set. he probability of finding the system in the is. (Give your answer upto two decimal places) ccording to the nuclear shell model the respective ground state spin-parity values of 7 8 O nuclei are () () 8 O and

13 G 6 Physics Q. particle of mass m and energy moving in the positive x direction is incident on a step potential at x = as indicated in the figure. he height of the potential is V where V >. t x x where x the probability of finding the electron is e times the probability of finding m( V it at x =. If ) the value of x is V x = x = x () () 4 ND OF H QUSION PPR PH

PHYSICAL SCIENCES MODEL QUESTION PAPER PART A PART B

PHYSICAL SCIENCES MODEL QUESTION PAPER PART A PART B PHYSICAL SCIENCES This Test Booklet will contain 65 ( Part `A + Part `B+5 Part C ) Multiple Choice Questions (MCQs). Candidates will be required to answer 5 in part A, in Part B and questions in Part C