Regn. No. North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-09, Ph: ,

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1 1. Section-A contains Multiple Choice Questions (MCQ). Each question has 4 choices, (b), (c) and, for its answer, out of which ONLY ONE is correct. From Q.1 to Q.1 carries 1 Marks and Q.11 to Q. carries Marks each.. Section-B contains 1 Multiple Select Questions(MSQ). Each question has 4 choices, (b), (c) and for its answer, out of which ONE or MORE than ONE is/are correct. For each correct answer you will be awarded marks. 4. Section -C contains Numerical Answer Type (NAT) questions. From Q.41 to Q.5 carries 1 Mark each and Q.51 to Q.6 carries Marks each. For each NAT type question, the value of answer in between to 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/ marks will be deducted for each wrong answer. For all marks questions, / 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. Regn. No. -5, Mall Road, G.T.B. Nagar, Opp. G.T.B. Nagar Metro Station Gate No., Delhi-11 9 Delhi DOWNLOAD CAREER ENDEAVOUR APP: E : info@careerendeavour.in South Delhi : -A/11, Jia Sarai, w Near-IIT : ww w.careerendeavour.in Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

2 Section-A : Multiple Choice Questions (MCQ) Q.1 to Q.1 : Carry 1 Mark each. 1. A gas of molecules each having mass m is in thermal equilibrium at a temperature T. Let v and v y be the Cartesian components of velocity v of a molecule. The mean value of ( v v ) is y (b) k B T (c) k B T 1 k B T. The equation of tangent plane to the surface z 4y,1, is at the point 4 y z (b) 4 y z (c) 4 y z 17 4 y z iz If z iy and, then 1 implies that in the comple plane z i z lies on the real ais (b) z lies on the imaginary ais (c) z lies on the unit circle none of these 4. Two tuning fork are used to produce lissajous figure as shown below. y If the frequency of one fork used is Hz and other is 596 Hz, it is found that above lissajous figure changes its shape. The time interval after which it will repeats itself is.5 sec (b).5 sec (c) 1 sec.1 sec 5. A block of m slides on horizontal surface as shown in figure with initial velocity v. Coefficient of friction y between the surface and block is m v The block will stop at equal to v v (b) v v (c) g g g g 6. A sphere has uniform polarization P. If a spherical portion is cut from the sphere as shown in figure, field inside the cavity will be P P P (b) (c) 6 7. Assuming that the diodes are ideal in figure, the current in D 1 is 1 k 1 k 5V D 1 D V ma (b) 5 ma (c) ma ma South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

3 4. The binding energy per nucleon of deutron 1 H and helium nucleus He is 1.1 MeV and 7 MeV respectively. If two deutron nuclei react to form a single helium nucleus, then the energy released is 1.9 MeV (b) 6.9 MeV (c).6 MeV 19. MeV 9. A substance with face-centred cubic lattice has density 65 kg/m and molecular weight 6.. The lattice constant a is [Give Avogadro number (kg.mole) 1 ] Å (b) 4 Å (c) 6 Å 1 Å 1. What is the ratio of the power emitted by the two spherical stars (considering both as black body) at the same temperature if their radius are in the ratio : 1? 1 : 4 (b) 4 : 1 (c) : 1 1 : Q.11 to Q. : Carry Marks each. 11. Two finite, identical, solid bodies of constant heat capacity per body, C, are used as heat source to drive heat engine. Their initial temperature are T 1 and T respectively. If T f is the final temperature of the system, then which of the following is CORRECT? T1 T Tf T1 T (b) Tf T1 T (c) Tf T1 T T f 1. The equation of a state for a gas is N P V N N kbt, V where P, V, T, N and k B have standard means. If the value of critical pressure is units and critical volume is 4 units, the value of the critical temperature (in terms of the 1 N k B ) is / (b) /64 (c) 64/ / 1. If P and Q are square matrices. Q is used to diagonalise the matri P i.e. 1 Q PQ D P. If Trace P = 9 and det DP 1. Then the value of det e P is e 6 (b) e 6 (c) e 41 e Consider the fourier series of f where f Then the value of... is equal to The value of S (b) F ds, where y 4, z and z is (c) ˆ ˆ F yzi yj y kˆ and S is the surface of the solid bounded by (b) (c) 1 1 South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

4 k 16. A particle of mass m moves on a plane along orbit r Ae. If v be instantaneous speed of the particle then its angular momentum about origin is m v r m v r (b) m v r k (c) m v r 1 k 1 k A light beam of diameter 4mm, having frequency in range Hz, falls normally on grating. Number of lines ruled per meter of the grating that can be used to resolve first order spectrum of the incident light is 15 (b) 575 (c) An object of specific gravity is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is Hz. The object is immersed in water so that one half of its volume is submerged. The new fundamental frequency in Hz is 1/ 1/ w (b) 1 (c) 1 w 19. A uniform chain of length L is released from position shown in figure on smooth table. The chain will skip off the d table in time use ln a a L ln g L (b) ln ( ) g L 4 L (c) ln ln g g. A particle of mass m is projected with speed v at angle 6º with horizontal. Angular momentum of particle about the point of projection at the moment velocity makes an angle º with acceleration is mv g (b) mv g (c) 1. A capacitor of capacitance C is charged to potential difference V, and it is connected across an ideal inductor of inductance L. Energy stored in inductor at time t will be 1 CV sin t LC (b) 1 CV sin mv 4g mv g t LC (c) 1 t CV sin LC 1 CV cos. Region z is filled with uniform dielectric of dielectric constant r. There eists a uniform electric field E iˆ ˆj kˆ in z region. Potential difference between points (,, d ) and (,, d) is 1 d 1 r (b) d r (c) 1 d 1 r. An annular ring of inner and outer radii R 1 and R carries a current I flowing uniformly on it as shown in figure. Magnetic field at the centre of loop is I R R (c) I R R 1 1 (b) I R R 1 I R ln R R R 1 1 d r R R 1 t L/ LC L/ 4 South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

5 4. If 1 and are normalised eigenfunctions corresponding to the same eigenvalue and if d is real, then the normalised linear combination of 1 and which is orthogonal to 1 is * 5 1 dv d, where d 1 d 1 1 d 1 d (b) (c) 1 d 1 d 1 d 1 d 5. Consider a neutron which is confined to an infinite potential well of width a = fm. At line t = the neutron is assumed to be in the state 4, sin sin sin 7a a 7a a 7a a If an energy measurement is carried out on the system, then its average value is 6 (b) (c) ma ma ma 6. A particle bound in a one-dimensional potential have a wav function 5ik a a A e cos / a a 7 ma then the probability of finding the particle between = and a is (b) 1 1 (c) The transistor shunt regulator shown in the figure has a regulated output voltage of 1 V, when the input varies from V to V. The relevant parameters for the zener diode and the transistor are : VZ 9.5V, VBE.5V, 99 Neglect the current through R B. Then the maimum power dissipated in the zener diode (P Z) and the transistor (P ) are T I Z I C V in -V V Z R B V BE V out = 1V PZ 75mW, PT 7.9 W (b) PZ 5mW, PT.9 W (c) PZ 95mW, PT 9.9 W PZ 115mW, PT 11.9 W. The half-life period of a radio-active element X is same as the mean life time of another radioactive element Y. Initially they have same number of atoms. Then X and Y decays at same rate always (b) X will decay faster than Y (c) Y will decay faster than X X and Y have same decay rate initially South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

6 9. Assuming the potential seen by neutron in a nucleus to be schematically representd by a one-dimensional, infinite rigid walls potential of length 1 fm, then the minimum kinetic energy of the neutron is (Assume the neutron to be non-relativisitc i.e. E mnc and mnc MeV, c 197. MeV fm ).4 MeV (b).4 MeV (c) 1.5 MeV.4 MeV. Consider the following quantum mechanical operator ˆ i A ˆ pˆ The eigenfunction of the operator will be of the following form: eponentially decaying (b) eponentially growing (c) sinusoidally varying Gaussian Section-B : Multiple Select Questions (MSQ) 6 Q.1 to Q.4 : Carry Marks each. 1. Consider an ensemble in contact with a thermal reservoir at temperature T of microscopic quantum mechanical systems with two energy levels E and E. Which of the following is/are CORRECT? The average energy is E tanh ( E/ kbt ) (b) The average energy is E coth ( E/ kbt ) (c) The entropy at very high temperature is k B ln The entropy at very high temperature is ln k B. Two Carnot engines are connected in series with the source at K and the sink at K. If the heat goes into the system is double than the workdone by the second reservoir, which of the following is/are correct? (The diagram is given for the reference). T 1 = K Q 1 1 W 1 T Q Q W T Q = K 1 Q Q (b) Q Q (c) 1. Consider the two forces F iˆ yzj ˆ y kˆ and F ˆ ˆ yi j. Then 1 y 5 B(1,1) A ( 1, 1) F1 and F are both conservative (b) F 1 is conservative but not F (c) If F 1 acts on an object moving along the path, as shown in figure does no work If F acts on an object moving along the same path does J of work South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

7 dy d y y log y is defined and finite in the range y is defined and finite in the range 4. If y is the solution of the differential equation (b) (c) y is defined and finite in the range y blows up at = e with y 1 1, then 5. A liquid has refractive inde n = If a ray from a light source dipped inside liquid incident on the liquid air surface at an angle 55.º, then which of the following statement(s) is/are CORRECT? Air 7 n = 1.44 Refracted light is completely polarized (b) Reflected light is completely polarized (c) Refracted light is partially plane polarized Reflected light is partially polarized perpendicular to the plane 6. A thin rod of length l and mass m is released from position shown in figure on smooth horizontal surface. If collision is elastic then which of the following options is/are correct? After collision centre of rod rises to a height less than h. (b) Speed of centre of rod just after collision is gh (c) Angular momentum is conserved during collision about lower end of the rod but not about centre of rod. Impulsive force on the rod from surface due to collision is greater than mg. 7. In figure shown shaded region is a thin plate of mass density. Which of the following statements is/are correct? º h a Coordinate of COM is a, 15 (b) Mass of the plate is a 4 y a y = a (c) I a 5 a I y a 4 South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

8 . Consider a spinless particle of mass m confined in a rectangular bo of sides a,b,c with potential given as V, y, z a, y b, z c elsewhere then the correct statements is/are zero point energy of the particle is E m a b c (b) first ecited state wave function can be written as y z with degeneracy three. (c) first ecited state wave function can be written as y z with degeneracy three If a = b = c, then second ecited state is three fold degenerate with energy y z,, sin sin sin abc a b c y z,, sin sin sin abc a b c 9 E ma 9. A spaceship moves away from Earth with speed v and fires a shuttle craft in the forward direction at a speed v relative to the spaceship. The pilot of the shuttle craft launches a probe in the forward direction at speed v relative to the shuttle craft. The speed of the shuttle craft relative to the Earth v 1 (b) The speed of the probe relative to the Earth v 1 (c) The speed of the shuttle craft relative to the Earth v 1 The speed of the probe relative to the Earth v 1 4. A solid sphere of radius R has volume charge density and surface charge density the following statements is/are correct [take reference point at infinity] R Electgric field and potential at centre are zero and respectively (b) Electric field and potential at centre are both zero. (c) Electric field and potential are both zero outside the sphere. Electric field is zero but potential is constant outside sphere. R. Which of South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

9 9 Section-C : Numerical Answer Type (NAT) Q.41 to Q.5 : Carry 1 Mark each. 41. In a certain process, the temperature ( T ) and entropy ( S ) are related by ferms of the entropy for this process is ( S / n). The value of n is. 4. The system of equations, y z k y 4z z 1 has unique solution for k equal to. 4. The equation of stationary wave is given by y T S. If the heat capacity in 5cos sin 4t cm, y represents the displacement of a particle at the distance from the origin and at the time t. If it vibrate making four loop, length of the rope is (cm). 44. A thin hollow sphere rolls on a horizontal surface without slipping % of its kinetic energy is rotational then value of is. 45. A rocket of mass M blasts off at t in upward direction in pressure of uniform gravity a 1 and a are acceleration of rocket at initial moment and at the moment its mass becomes M /. If fuel is ejected at gm constant rate with velocity u with respect to rocket, then value of a1 / a is. u 46. An electric dipole of dipole moment p is placed along the ais of a uniformly charged ring of radius R and pq total charge Q. Force on the dipole is 4 R of is., if its distance from centre of ring is R, then value 47. An electromagnetic wave of intensity I is incident at 6º to normal of a fully reflecting surface. Pressure on the surface is ki/c, value of k is. 4. Propagation constant of an electromagnetic wave in a medium is k i. Ratio of wave length in medium to skin depth is. 49. High energy shows -rays are scattered from electrons initially at rest. Assume the photons are backscattered and their energies are much larger than the electrons rest mass energy, i.e. E m c, then the wavelength shift is 1 1 m. 5. Electrons emitted from a hot filament are accelarated through a voltage drop of 1 V. The wavelength of the electron is (in the units of A ) e South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

10 1 Q.51 to Q.6 : Carry Marks each. 51. If the boiling point of the water is 9 ºC at a hill, the decrease in the atmospheric pressure at the hill %. (To nearest integer). (Take latent heat of vaporization of water as 7 kj/kg and the change in the specific volume at the boiling point to be 1. m /kg). 5. If I 1/ di t dt then... d 5. If f 1, f ' 1 and f " then 1 f is equal to. 54. A line source of quasi-monochromatic light (= 5 nm) generates a fringe system on a screen m away when the source is just above and parallel to a polished glass plate. If the bright fringes have a peak-topeak separation of.667 mm, how high is the source above the plate? (mm). 55. From a semicircular plate of radius R and mass M a rectangular plate of maimum possible area is cut. Moment of inertia of rectangular plate about an ais through its centre and perpendicular to its plane is k mr, value of k is. 56. Two identical blocks of mass m are connected by a compressed spring of force constant k. The blocks are also connected by a thread which is burned at a certain moment. If the centre of mass of this system mg jumps to height k for initial compression 7 mg k, then value of is Consider a state 1, which is given in terms of three orthonormal 15 5 of an operator ˆB such that Bˆ n n 1 eigenstates 1, and value of ˆB for the state is 5. The output voltage for the circuit is V. 1k. Then the epectation n V = 1.5V in + k + V 59. A metallic conductor carries a current of 1. amp. Its area of cross-section is 1. cm. The specific resistance of the conductor is ohm-cm. The electric field inside the conductor is 1 4 Volt/m. 6. Assuming that the rest radius of earth is 6, 4 km and its orbital speed about the sun is.6c m/s, the amount of by which earth s diameter appear to be shortened to an observer on the sun, due to earth s orbital motion is km. South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

11 11 Space for rough work South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

12 1 IIT-JAM PHYSICA-PH TEST SERIES - 4 Date : FULL LENGTH TEST-1 ANSWER KEY Section-A : Multiple Choice Questions (MCQ) (b) (c). (c) 9. (b) 1. (b) 11. (b) 1. (c) 1. (c) 14. (b) 15. (b) (b) (b). (c) 1.. (c) (c) 6. (b) 7. (c). (c) 9.. Section-B : Multiple Select Questions (MSQ) 1.,(c)., (c). (b), (c), 4. (c), 5. (c), 6., (c), 7., (b), (c)., (b), (c), 9., 4. (a,c) Section-C : Numerical Answer Type (NAT) 41. () 4. () 4. (1) 44. (7.7-7.) 45. () 46. () 47. (.5) 4. ( ) 49. (.46) 5. (1.1 to 1.5) 51. (5) 5. (. to.5) 5. (.5) 54. (.75) 55. (.1 to.14) 56. () 57. (15) 5. (-6.7 to -6.4) 59. (1.5 to 1.9) 6. (56) South Delhi : -A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : , 6619 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,