SECTION – I Single Correct Answer Type There are five parts in this question. Four choices are given for each part and one of them is correct. Indicate you choice of the correct answer for each part in your answer-book by writing the letter (a), (b), (c) or (d) whichever is appropriate

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01 The length of a simple pendulum is about 100 cm know to an accuracy of 1 mm, It’s period of oscillation is 2 s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g? 0.2% 0.5% 0.1% 2% Problem

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02 Young ‘s modulus of the material of a wire is Y. on pulling the wire by a force F, the increase in it’s length is x. The potential energy of the stretched wire is: Fx Yx Fx 2 none of the above Problem

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Problem 03 A charge situated at a certain distance along the axes of an electric dipole experiences a force F. If the distance of the charge from the dipole is doubled, the force acting on it will become : 2F F/2 F/4 F/8

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Problem 04 Which of the following plots represents the variation of the electric filed with distance from the centre of a uniformly charged non-conducting sphere of radius R? a. b. c. d.

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Problem 05 A certain electrical conductor has a square cross-section , 2.0 mm on a side, and is 121 m long. The resistance between its ends is 0.072 . The resistivity of its material is equal to 2.4 x 10 -6 m 1.2 x 10 -6 m 1.2 x 10 -8 m 2.4 x 10 -8 m

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Problem 06 Figure shows three points A,B and C in a region of uniform electric field . The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good? V A =V B =V C V A = V B >V C V A =V B >V C V A =V B =V C Where V A ,V B and V C represent the electric potentials at points A,B and C respectively.

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Problem 07 The ( x,y,z )coordinates of two points A and B are given respectively as (o,3,-1) and (-2,6,4).The displacement vector from A to B may be given by: a. b. c. d.

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Problem 08 In the first second of its flight, rocket ejects of its mass with a velocity of 2400ms -1 . The acceleration of the rocket is: 19.6ms -2 30.2ms -2 40ms -2 49.8ms -2

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Problem 09 In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is f, then its acceleration in terms of the force F will be equal to: (F-f)/m F/m None of these

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Problem 10 The equivalent resistance between the points P and Q in the network shown in the figure is given by: 2.5 7.5 10 12.5

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Problem 11 the magnetic field amplitude of an electromagnetic wave is 2 x 10 -7 T. It’s electric field amplitude if the wave is traveling in free space is : 6Vm -1 60Vm -1 none of these

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Problem 12 A cart is moving horizontally along a straight line with constant speed 30m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80m. at what speed (relative to the cart )must the projectile be fired ?(Take g=10m/s 2 ): a. b. c. d. None of these

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Problem 13 A boy begins to walk eastward along a street infront of his house, and the graph in the following figure. His average speed for the whole time interval is equal to : 8 m/min. 6 m/min m/min 2 m/min

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Problem 14 What is the potential drop between points A and C in the following circuit ? Resistances 1 and 2 represent the internal resistances of the respective cells : 1.75 V 2.25 V V V

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Problem 15 The escape velocity of a projectile on the earth’s surface is 11.2 km s -1 . A body is projected out with thrice this speed. The speed of the body far away from the earth will be : 22.4 km s -1 31.7 km s -1 33.6 km s -1 none of the above

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Problem 16 A body moves along a circular path of radius 10m and the coefficient of friction is 0.5 What should be its angular velocity in rad /sec if it is not to slip form the surface ? (g = 9.8 ms -2 ) 5 10 0.1 0.7

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Problem 17 One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed, , the net force on the particle (directed towards the centre) is : T T- T + 0 T is the tension in the string .

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Problem 18 A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t proportional to : t 1/2 t t 3/2 t 2

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Problem 19 In the adjacent figure is shown a closed path P. A long straight conductor carrying a current I passes through O and perpendicular to the plane of the paper. Then which of the following hold good ? None of the above

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Problem 20 A long hollow copper tube carries a current I. Then which of the following will be true ? The magnetic field B will be zero at all points inside the tube The magnetic field B will be zero only at points on the axis of the tube The magnetic field B will be maximum at points on the axis of the tube The magnetic field will be zero at any points outside the tube

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Problem 21 The figure below shows the plot of versus P for oxygen gas at two different temperatures Read the following statements concerning the above curves : ( i ) the dotted line corresponds to the ‘ideal’ gas behaviour (ii) T 1 > T 2 (iii) The value of at the point where the curves meet on the y-axis is the same for all gases. Which of the above statements is true ? ( i ) only ( i ) and (ii) only all the above None of the above

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Problem 22 The following figure represents the temperature versus time plot for a given amount of a substance when heat energy is supplied to it at a fixed rate and at a constant pressure. Which part of the above plot represent a phase change ? a to b and e to f b to c and c to d d to e and e to f b to c and d to e

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Problem 23 A bar magnet has a coercivity 4 x 10 3 A. m -1 . It is desired to demagnetize it by inserting it inside a solenoid 12 cm long and having 60 turns. The current carried by the solenoid should be : 8 A 6 A 4.5 A 2 A

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Problem 24 In a series LCR circuit the frequency of a 10 V a.c voltage source is adjusted in such a fashion that the reactance of the inductor measures 15 and that of the capacitor 11 . If R = 3 , the potential difference across the series combination of L and C will be : 8 V 10 V 22 V 52 V

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Problem 25 A circuit draws 330 W from a 110 V, 60 Hz a.c . line. The power factor is 0.6 and the current lags the voltage. The capacitance of a series capacitor that will result in a power factor of unity is equal to : 31 54 151 201

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Problem 26 If the focal length of the lens is 20 cm, what is the distance of the image from the lens in the following figure ? 5.5 cm 7.5 cm 12.0 cm 20.0 cm

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Problem 27 An open U-tube contains mercury. When 11.2 cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial level ? 0.56 cm 1.35 cm 0.41 cm 2.32 cm

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Problem 28 The change in the entropy of a l mole of an ideal gas which went through an isothermal process from an initial state (P 1 , V 1 , T) to the final state (P 2 , V 2 , T) is equal to : Zero R ln T R ln R ln

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Problem 29 An unpolarized beam of light is incident on a glass surface at an angle of incidence equal to the polarizing angle of the glass. Read the following statements : ( i ) the reflected beam is completely polarized (ii) the reflected beam is partially polarized (iii) the angle between the reflected and the refracted beams is 90 0 . Which of the above statements is/are true ? ( i ) only (ii) only ( i ) and (iii) all the statements are correct

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Problem 30 The threshold frequency for certain metal is 3.3 x 10 14 Hz. If light of frequency 8.2 x 10 14 Hz is incident on the metal, the cut-off voltage of the photoelectric current will be : 4.9 V 3.0 V 2.0 V 1 V

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Problem 31 Frequencies higher than 10 MHz were found not being reflected by the ionosphere on a particular day at a place. The maximum electron density of the ionosphere on the day was near to : 1.5 x 10 10 m -3 1.24 x 10 12 m -3 3 x 10 12 m -3 None of the above

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Problem 32 The de-Broglie wavelength of an electron, -particle and a proton all having the same kinetic energy is respectively given as Then which of the following is not true ? a. b. c. d.

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Problem 33 What is the disintegration constant of radon if the number of its atoms diminishes by 18% in 24 hours ? 2.1 x 10 -3 s -1 2.1 x 10 -4 s -1 2.1 x 10 -5 s -1 2.1 x 10 -6 s -1

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Problem 34 Which of the following statements is true for an n–type semi-conductor ? The donor level lies closely below the bottom of the conduction band. The donor level lies closely above the top of the valence band The donor level lies at the halfway mark of the forbidden energy gap. None of the above

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Problem 35 Carbon, silicon and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by energy band gap respectively equal to ( Eg ) C , ( Eg ) Si and ( Eg ) Ge , Which of the following statements is true ? ( Eg ) C = ( Eg ) Si = ( Eg ) Ge ( Eg ) C > ( Eg ) Si > ( Eg ) Ge ( Eg ) C < ( Eg ) Ge > ( Eg ) Si ( Eg ) Si < ( Eg ) Ge > ( Eg ) C

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Problem 36 A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position ? 0.5 s 1.0 s 1.5 s 2.0 s

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Problem 37 The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase in the tension in order to raise the wave speed by 20% is : 44% 40% 20% 10%

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Problem 38 A straight rod of length L has one of its ends at the origin and the other at x = L. If the mass per unit length of the rod is given by Ax where A is constant, where is its mass centre ? L/3 L/2 2L/3 3L/4

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Problem 39 The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 4 m away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be : 0.5 m 1.0 m 1.5 m 2.0 m

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Problem 40 The total energy of a satellite moving with an orbital velocity around the earth is : a. b. - c. d.

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