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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES HCU-2015 Q1. The unit vector parallel to the resultant of the vectors r1 2iˆ 4 ˆj 5kˆ and r2 iˆ 2 ˆj 3kˆ is given by 1 1 1 (a) iˆ ˆj kˆ 3 6 2 (c) Q2. (b) 2ˆ 3 ˆ 6 ˆ i j k 7 7 7 (d) 3iˆ 6 ˆj 2kˆ The solution to the differential equation t3 A 3 t4 At B (c) x 12 where A and B are constants. (a) x Q3. Q4. 3ˆ 6 ˆ 2 ˆ i j k 7 7 7 d 2x t 2 is given by 2 dt t3 At B 3 t3 t2 (d) x A 3 2 (b) x If T sin x sin y sin z, 2T is given by (a) 0 (b) 2 sin x sin y sin z (c) 3 sin x sin y sin z (d) 3 sin x sin y sin z a force F A x 2i yj is irrotational. The potential energy function associated with it is given by Q5. x2 y2 (a) U A 2 3 x y2 (b) U A 3 2 x2 y (c) U A 3 2 x y3 (d) U A 3 2 A bead moves outward with constant speed u along the spoke of a wheel. It starts from the centre at t . The angular position of the spoke is given by wt, where is a constant. The acceleration of the bead is given by (a) ut 2 rˆ uˆ (b) urˆ u tˆ (c) u t 2 rˆ utˆ (d) ut 2 rˆ 2uˆ Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q6. A solid cylinder and a hollow cylinder are placed at the same height at the top of a long incline and released at the same time. (a) Both the cylinders reach the bottom together. (b) Solid cylinder reaches the bottom first. (c) Hollow cylinder reaches the bottom first (d) Any one of them can reach the bottom first. Q7. A large vertical drum spins so fast that a ball inside it, is pinned to the wall. What is the minimum steady angular velocity which prevents the ball from falling to the bottom of the drum? (The radius of the drum is R , the mass of the ball is M and is the co-efficient of friction.) (a) 2 Q8. Mg R (b) 2 g R (c) 2 g MR (d) 2 g R The equation of traveling wave is given as: y 10 cos x t . What is the speed 20s 5cm of the wave? (a) 1cm / s Q9. (b) 0.5 cm / s (c) 0.25cm / s (d) 0.1cm / s Two sound sources oscillate in phase with a frequency of 100 Hz . At a point 5m from one source and 5.85 m from the other the amplitude of the sound from each source separately is A . What is the phase difference of the two waves at that point (Assume that the speed of sound is 343m / s .) (a) 99o Q10. (b) 45o (d) 89o (c) 60o It is given that surface tension of water is 0.072N / m and its density 103 kg / m3 . What is the height to which water will rise in a tube of diameter 0.2 m m? (a) 14.7 cm Q11. (b) 34.2 cm (c) 29.4 cm (d) 1.27cm An air bubble of diameter 2 mm rises steadily through a solution of density 1750kg / m3 at the rate of 0.35cm / sec . If the density of air is negligible, what is the coefficient of viscosity of the solution’? (a) 1 poise (b) 11 poise (c) 20 poise Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] (d) 4 poise Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 2 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q12. Q13. Internal energy of an idea gas changes when (a) temperature changes. (b) volume changes. (c) entropy changes (d) pressure changes A gas expands adiabatically and reversibly to a temperature TA . If the same expansion happens adiabatically, but irreversibly, the final temperature is T . Then Q14. (a) T TA (b) T TA (c) T TA (d) T can take any value independent of TA A cylinder fitted with a piston contains an ideal gas at 500 Kilo Pascals and occupies a volume of 0.2m 3 . The gas expands isothermally to a pressure of’100 Kilo Pascals. The work done by the gas is (a) 160.9 KJ Q15. (b) 1609.0 KJ (d) 5 104 KJ (c) 16.09 KJ The sun delivers about 1000W / cm 2 of electromagnetic flux to the earth’s surface. Assume 7% conversion efficiency of the solar panel of dimensions 8m 20 m . If the radiation is incident normally the solar power converted for use is (a) 11.42 104 W Q16. (b) 11.35 104 W (c) 1.56 104 W (d) 1.12 104 W The angle of refraction for a light beam incident on a heavy flint glass n 1.65 at the po1arizing angle is given by (a) 31.22o Q17. (b) 30.25o (c) 28.20o (d) 33.41o A radio pulse from a doppler radar reflects off an aircraft in mid-flight. If the frequency of the reflected radio pulse is less than the original one, then which of the following statements is true? (a) The aircraft is not moving. (b)The aircraft is moving away from the radar (c) The aircraft is moving towards the radar. (d) Something is wrong with the radar Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 3 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q18. The total charge within a sphere of radius r in a charge cloud is given by: r2 q 2 a 2 r ar e e a . The electric field at the surface of the above sphere is given by r ar q a e e (a) 4 0 a 2 2 r ar e e a 2 r ar q a e e (d) 4 0 q 2 The electric field in the x y plane is given by E iˆ8x ˆj 4 y . Then the equation for the q (c) 0 a 2 Q19. q (b) 0 a 2 r a2 r e e 2a lines of force is given by (a) xy 2 constant (b) x 2 y constant (c) x 2 y constant Q20. (d) xy constant B Consider Maxwell’s equation: E . If is the scalar potential and A is the t vector potential, then E can be written as A (a) A (b) t (c) Q21. A t A (d) t What is the current I 1 , flowing in the circuit shown in the following figure? 10 k 10 k (a) Infinite 15k 20 k (b) 1 m A 30V (c) 0.5 m A 10 k 60 k 10 k (d) zero Q22. A 50 Hz sinusoidal signal is applied to the input of a full-wave rectifier The frequency of the output signal is (a) 100Hz (b) 50 Hz (c) 70.7 Hz Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] (d) 0 Hz Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 4 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q23. In a Bipolar Junction Transistor (BJT), the base-width is kept thinner than Emitter and Collector width. This is to Q24. (a) reduce the base current (b) increase the base current (c) increase the base current (d) decrease the collector current If 1 and 2 are two independent solutions of the time-independent Schrödinger equation, which of the following is also a solution of the same Schrodinger equation? (a) 1 2 Q25. (b) 1 2 (d) 1 2 (c) 1 2 1/ 2 If H 1 and H 2 are Hamiltonians of two non-interacting systems with wave functions 1 and 2 and energies E1 and E 2 respectively, the total wave function and energy E of the composite system are given by Q26. (a) 1 2 , E E1 E2 (b) 1 2 , E E1 E2 (c) 1 2 , E E1 E2 (d) 1 2 , E E1 E2 1 0 What value of will make the matrix 0 0 2 (a) Q27. (b) 1 0 orthogonal? (c) 1 (d) 2 1 2 The value of the integral of the function f x, y x 2 y 2 integrated along a straight line from 1, 0 to (0,1) as shown in the figure is (a) (c) 2 3 1 2 Y (b) 2 3 (d) 1 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] 0,1 1, 0 X Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 5 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q28. a b c If abc P and A c a b , where A is an orthogonal matrix, then the value of b c a a b c is (a) 2 Q29. (b) P (d) 1 (c) 2 P The general solution to the differential equation d 2 y 2dy 2 y 0 , is dx dx2 (a) e x A cos x iB sin x (b) e ix A cos x iB sin x (c) e ix A cos x iB sin x (d) e x A cos x iB sin x where A and B are arbitrary constants. Q30. In the complex z plane, the equation z 2 z 1 represents 2 3 (b) a circle of radius (c) a circle of radius 3 2 (d) a straight line through 0,0 and 1,1 . Q31. 1 , 2 (a) a circle of radius The power series 1 n n 2 x n converges for n 1 (a) 1 x 1 Q32. (b) 1 x 1 (c) 1 x 1 (d) 1 x On changing variable from x to t where t log x , the differential equation x2 d2y dy et y 0 , becomes 2 dt dt (a) e 2t (c) d2y dy e t y 0 2 dt dt d2y dy y 0 2 dt dt (b) d2y dy y 0 2 dt dt (d) d2y dy 1 y 0 2 dt dt Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 6 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q33. A uniform drum of radius 0.5 m , mass 40 kgs rolls (without slipping) down an incline of angle 5o If the drum starts from rest from a height of 29.4 metres, the speed of its centre of mass will be (a) 39.2 m / s Q34. (b) 19.6 m / s (c) 32.6 m / s (d) 25.5 m / s A mass M is moving along a closed rectangular path of length l along the Y y direction and a along the x direction (as shown in the figure) under the influence x2 of the force F b 0 1 2 ˆj . The work done is given a O (a) zero (b) b 0 l (c) b 0 a (d) b0 al B l by Q35. a A C X A force field F 3x y z iˆ x y z 2 ˆj 3x 2 y 4z kˆN is acting on a particle of mass m . The particle moves in a circular path of radius 5m with a constant speed of 5m / s in the x y plane. The cent of the orbit is the origin. The change in the kinetic energy as a particle completes one rotation is given by (a) 25 J Q36. (b) 25 J (c) 50 J (d) 50 J A particle moves along a trajectory whose displacement is given by r t cost iˆ sint ˆj tkˆ with 1 The path of the particle is a (a) parabola, with direction of motion to the right of the origin. (b) parabola, with direction of motion to the left of the origin (c) hyperbola with direction of motion to the right ‘of the origin. (d) hyperbola, with direction of motion to the left of the origin. Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 7 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q37. The centre of mass of a solid hemisphere (as shown in Z figure) of unit radius is given by Q38. 3 (a) 0, 0, 8 3 (b) 0, , 0 8 3 (c) 1, , 1 8 (d) 0, 0, 1 2 3 Unit radius X Solid Hemisphere A particle of mass m starts at rest from the top of a smooth fixed hemisphere of radius a . The angle at which the particle leaves the hemisphere is equal to 1 (a) cos1 3 Q39. (b) 2 The Lagrangian of Atwood’s machine (shown in the figure, where m2 m1 ) is given by (a) 1 1 m1 x12 m2 x x2 m1 gx1 m2 gx 2 2 2 1 1 (b) m1 x12 m2 x 1x m1 gx1 m2 g 2 2 2 (c) (d) Q40. 2 (d) sin 1 3 2 (c) cos1 3 R X1 1 m1 m2 x12 m1 m2 gx1 2 X2 m1 1 m1 m2 x12 m1 m2 gx1 2 m2 Consider a rope of mass per unit length length a , suspended just above a table as shown in figure. If the rope is released from rest at the top, the force on the table when a length x of the rope has dropped to the table is X (a) xg (b) 2 xg a (c) 3xg (d) 4 xg T able top Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 8 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q41. An object of unit mass orbits in a central potential given by U r . Its orbit is r a exp b with b 0 . The relationship between the angular momentum and the total energy E is given by L2 2 b 1 U r 2 L (c) E b 1 U r r (a) E Q42. L2 2 b 1 U r 2r 2 a 2 L2 (d) E 2 b 1 U r r (b) E A wave is propagating in a string of tension T and mass per unit 1ength . The traveling wave can be described as yx, t A sin kx t . What is the kinetic energy in one wavelength of the traveling wave (a) (c) Q43. 2TA 2 2 (b) TA2 2 2 (d) TA2 2 TA2 2 4 Consider the figure as shown. A and B have equal masses m and all the springs have the same spring constant k . What are the normal frequencies for the system, if the oscillations are assumed to be small? k A X1 Q44. k k B X2 (a) k 2k , m m (b) k k , 2m m (c) k 3k , m m (d) k k , 1 m m A violin string is held under tension T . What will be fractional change in the frequency of its fundamental mode of vibration if the tension is increased by the amount T ? (a) T T2 (b) T T (c) T T Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] (d) T 2T Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 9 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q45. One can estimate the resonant frequencies of the human ear canal of length 2.2 cm , that are in the range of human hearing. How many resonant frequencies lie in this range? Speed of sound is given as 343m / s . (a) 3 Q46. (b) 4 (c) 5 (d) 6 One end of a 100cm long wire (without load) is fixed and a mass of 2kg is attached to the other end. The mass is kept moving with uniform speed in a horizontal circle of radius 60cm . What is the strain of the wire it the radius of the wire is 0.032cm and Young’s modulus is 2 1011 / dynes/cm2 ? (a) 0.032 102 Q47. (b) 32 102 (c) 0.32 102 (d) 3.2 102 What will be density of lead under a pressure of 20,000N / cm2 ? (Density of lead 11.5gm / cm3 and bulk modulus of lead 0.80 1010 N / m 2 ) Q48. (a) 11.69 gm/ cc (b) 14.19gm/ cc (c) 13.89gm/ cc (d) 15.98 gm/ cc The excess of pressure inside a spherical soap bubble of radius 1cm is balanced by that due to a column of oil of specific gravity 0.9 gm / cm3 and height 1.36 m m. What is the surface tension T ? Q49. (a) T 3.06 103 N / m (b) T 323.0 102 N / m (c) T 3.06 102 N / m (d) T 3.06 104 N / m A big drop is formed by coalescing 1000 small droplets of water. By how many times will the surface energy decrease? (a) 100 Q50. (b) 10 (c) 5 (d) 30 A plate of area 100cm2 arid thickness 2 mm is placed on the upper surface of some castor oil. If the coefficient of viscosity is 15.5 poise, what. is the horizontal force necessary to move the plate with a velocity 3cm / sec ? (a) 10.2 N (b) 0.13 N (c) 2.3 N Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] (d) 0.23 N Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 10 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q51. The velocity of water in a river is 10km / hr near the surface. If the river is 5m what is the shearing stress between the horizontal layers of water? (The coefficient of viscosity of water 102 poise.) (b) 105 N / m 2 (a) 103 N / m 2 Q52. (d) 101 N / m 2 (c) 10N / m 2 The figures shown represent two engines in T S phase plane. Let a arid b the efficiencies of the engines (i) and (ii), respectively. Then T T T2 T2 T1 T1 S1 (a) b a Q53. (b) a b i S2 S (c) a b S S2 S1 ii (d) a b The relation between pressure and volume of an ideal gas in a reversible process is given by P aV b, where a 31 255 Pascal/met er 3 , b Pascals . The volume at which the 56 7 temperature attains maximum is (a) 32.9m 3 Q54. (b) 329.7 m 3 (d) 20.7 m3 (c) 0.329m 3 Clausius-Clapeyron equation for liquid-gas transition is given by: d 1 . If d T v g vl v g vl and vg RT , the expression for saturated vapour pressure is given by (a) constant e 1 RT (b) constant e (d) constant (c) 0 Q55. -1 RT For a nonmagnetic insulator, the specific heat is proportional to (a) T (b) T 2 (c) T 3 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] (d) e k BT Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 11 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q56. Consider the superposition of two sinusoidal waves given by: y1 4 sin 3x 2t cm and y2 4 sin3x 2t cm . The maximum displacement of the resultant motion at x 2.3 cm is (a) 8.65cm Q57. (b) 1.61cm (c) 4.63cm (d) 7.60cm A total of 25 fringes move across the field of view when one of the mirrors of’ the Michelson interferrometer is moved by a distance d . If the interferromneter is illuminated by a laser of wavelength 632.8 nm , the distance by which the mirror is moved is (b) 38.6m (a) 79.1 m Q58. (d) 158.2 m (c) 57.3 A parallel light beam of diameter d is incident on a convex lens of focal length f . The emerging beam from this lens passes again through another lens of focal length 2 f , kept at a distance 3 f from first lens. The diameter of the output beam is Q59. (a) d (b) 2 d (c) not related with d (d) 1 d 2 Consider a uniformly charged disc of radius a and surface charge density . Consider a point P on the axis of the disc at a distance z from the disc. The potential at P is given by (a) (c) 1 0 z (b) 2 a 2 z2 z 0 2 z2 a2 z2 (d) 0 Q60. a 2 a 2 z2 a 0 A charge q is distributed uniformly over the surface of a thin circular insulating of radius a . The potential at the rim of the disc is given by (a) (c) q a 0 2 q a 0 2 (b) q 4 0 a (d) q 4 a 2 0 2 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 12 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q61. Current I is passing through a conical shaped copper I wire of resistivity as shown in the figure. If L is a b the length of the wire, b is the front radius and a is the back radius of the wire, what is the resistance of L the wire? (a) Q62. L ab (b) L (c) a b L (d) ab 2 L ab ab A very long wire carrying charge q per unit length is held parallel to an infinite conducting plane at a distance from it. What is the force of attraction per unit length? (a) q 4 0 (b) q2 4 0 (c) q2 2 0 (d) q2 2 0 r Q63. The potential in a medium is given by r q e . The charge density for r 0 is 4 0 r given by r q gl e (a) 0 Q64. r 2 r r q q q (c) e e e (d) 2 2 4 0 4 0 r 4 r What is the magnetic field B produced at point P (center of the arcs) due to the current (b) I in the close loop as shown in figure? 0 I (a) B 4 1 1 ˆ k R1 R2 0 I (b) B 4 1 1 ˆ k R1 R2 0 I 1 1 ˆ (c) B k 4 R2 R1 0 I 1 1 ˆ (d) B k 4 R2 R1 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] I I R2 R1 P Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 13 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q65. In the circuit given below, the diode can be considered as ideal. The peak secondary voltage and the D.C. load voltage respectively are then given by 10.1 (a) 31.1V and 9.9 V (b) 22V and 9.9 V 10 (c) 22V and 7.0 V (d) 31.1V and 7.0 V Q66. What is the effective resistance between points A and B ? (a) Rab 10 20 (b) Rab 11 10 (c) Rab 15 10 (d) Rab 12 Q67. 20 20 20 10 10 What are the values of R4 and L4 , if the a.c. bridge shown in figure is balanced? 600 (a) R4 720 and L4 12 mH 100 R1 120m H R2 L1 (b) R4 3000 and L4 24 mH R4 R3 L4 (c) R4 120 and L4 600mH 500 (d) R4 3000 and L4 600mH Q68. What is the operating point VCE , I C for the transistor circuit shown in figure? (Assume I C I E and VBE 0.7V ) RC 700 (a) 5V , 2m A VCC 15V (b) 7.5V , 1.5 mA V BB 5V (c) 7.5V , 1mA RE 4.3 k (d) 10V , 1 m A Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 14 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q69. A particle of mass 1.40105 kg has a relativistic momentum of magnitude 3.151013 kg m / s . How fast is the particle traveling? (a) 2.68108 m/ s Q70. (b) 1.8108 m / s (c) 3.31016 m / s (d) 3108 m / s A proton of rest mass 1.681027 kg is traveling at 2.5108 m / s . What is kinetic energy of the proton? (a) 1.181010 J Q71. (b) 0.181010 J (c) 2.181027 J (d) 1.321027 J A spaceship passes you at a speed of 0.85c . You measure its length to be 48.2 m . What is its length at rest? (a) 80 m Q72. (b) 100m (d) 81m Which of the following functions is the eigen-function of the operator, i (a) expikx Q73. (c) 91.5 m (c) sin kx (b) coskx d ? dx (d) coskx sinkx In a one dimensional problem, the normalized wave function for the ground state is given by Ne x , where N is the normalization constant. What is the value of N ? 2 (a) Q74. 2 (c) (d) Commutator of two Hermitian operators has to be (a) Hermitian Q75. 2 (b) (b) anti-Hermitian (c) unitary (d) orthogonal A sample of radioactive isotopes contains two different nuclides, labeled A and B . Initially, the sample composition is 1 : 1 . The half-life of A is 3 hours and that of B is 6 hours. What is the expected ratio (a) 1 6 (b) 1 4 A after 18 hours? B (c) 1 8 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: [email protected] (d) 1 2 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 15

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