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AIEEE-2003 www.aieeepage.com P 1 of 45 Section I - Physics & Chemistry 1. The physical quantities not having same dimensions are (1) speed and (mo eo ) ? 1 / 2 (2) torque and work (3) momentum and Planck?s constant (4) stress and Young?s modulus sol (3) Momentum [p] = [MLT?1] and Plank?s constant [h] = [ML2T?1] 2. Three forces start acting simultaneously on a particle moving with velocity, v. These forces are represented in magnitude and direction by the three sides of a triangle ABC (as shown). The particle will now move with velocity (1) v, remaining unchanged (2) less than v (3) greater than v (4) | v | in the direction of the largest force BC sol (1) Net force on the particle is zero so the vr remains unchanged 3. The coordinates of a moving particle at any time ?t? are given by x = at3 and y = bt3 . The speed of the particle at time ?t? is given by (1) (a2 + b2 ) 2) 3t (a2 + b2 ) (3) 3t 2 (a2 + b2 ) (4) t 2 (a2 + b2 ) sol (3) r = x2 + y2 Þ r2 = (a2 +b2 ) t6 Þ 2r (dr / dt) = (a2 +b2 ) . 6t5 Þ (dr / dt) = 3t2 (a2 + b2 ) . 4. A car, moving with a speed of 50 km / hr, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km / hr, the minimum stopping distance is (1) 6 m (2) 12 m (3) 18 m (4) 24 m sol (4) 0 = (250 / 18)2 + 2a . 6; S = u2 / 2a = 24. AIEEE 2003 HINTS & SOLUTIONS AIEEE-2003 www.aieeepage.com P 2 of 45 5. A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m /s. at an angle of 30° with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground ? (1) 8.66 m (2) 5.20 m (3) 4.33 m (4) 2.60 m sol (1) calculate the range of ball R = q = ´ = = 5 3 10 2 sin 2 (10)2 sin(2 30) g v 8.66 m 6. The displacement of a particle varies according to the relation x = 4 (cos pt+ sin pt ). The amplitude of the particle is (1) 8 (2) ? 4 (3) 4 (4) 4 2 sol (4) x = 4 2 (cos pt . sin 45º + sin pt . cos 45º) = 4 2 sin ( pt + 45º) 7. Consider the following two statements : A. Linear momentum of a system of particles is zero. B. Kinetic energy of a system of particles is zero. Then (1) A implies B and B implies A (2) A does not imply B and B does not imply A (3) A implies B but B does not imply A (4) A does not imply B but B implies A sol (4) Momentum being a vector quantity where K.E. being a scalar and a +ve quantity 8. A horizontal force of 10 N necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is (1) 2 N (2) 20 N (3) 50 N (4) 100 N sol (1) f = m R = mg = 0.2 × 10 = 2 N 9. A marble block of mass 2 kg lying on ice when given a velocity of 6 m / s is stopped by friction in 10 s. Then the coefficient of friction is (1) 0.01 (2) 0.02 (3) 0.03 (4) 0.04 sol (2) The Correct answer is 0.06 10N AIEEE-2003 www.aieeepage.com P 3 of 45 10. A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is (1) Both the scales read M / 2 kg each (2) Both the scales read M kg each (3) The scale of the lower one reads M kg and of the upper one zero (4) The reading of the two scales can be anything but the sum of the reading will be M kg sol (2) The mass is hanging from the lower spring. Since the springs are light, tension is constant throughout the springs. 11. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is (1) PM / (M + m) (2) Pm / (M + m)10 N (3) Pm / (M ? m) (4) P sol (1) P? = Ma; P = (m + M)a Þ P? = PM / (m + M) 12. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m / s2, the reading of the spring balance will be (1) 49 N (2) 24 N (3) 74 N (4) 15 N sol (2) When the lift is stationary R= mg Þ 49 = m´9.8Þ m = 5kg When the lift is moving downward with an acceleration R = m (9.8 - a) Þ R = 5 (9.8-5) = 24N 13. When a U238 nucleus originally at rest, decays by emitting an alpha particle having a speed ?u?, the recoil speed of the residual nucleus is (1) ? 4u / 238 (2) 4u / 238 (3) ? 4u / 234 (4) 4u / 234 sol (4) Initial momentum of the system = Mass ´ velocity of nucleus = 238 ´ 0 = 0 Final momentum of the system = Momentum of a particle + Momentum of residual nucleus = 4u + 34v By equating 4u + 234v = 0 Þ . 234 4u v = r But speed = . 234 4u 14. A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ?t? is proportional to (1) t½ (2) t¾ (3) t3 / 2 (4) t¼ sol (3) P = const. (d / dt)(½ mv2) = const. AIEEE-2003 www.aieeepage.com P 4 of 45 15. A rocket with a lift-off mass 3.5 × 104 kg is blasted upwards with an initial acceleration of 10 m / s2. Then the initial thrust of the blast is (1) 1.75 × 105 N (2) 3.5 × 105 N (3) 7.0 × 105 N (4) 14.0 × 105 N sol (3) F? mg = ma F = m (g + a) F = 7 × 105 16. Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is (1) 1.5 R (2) 2.5 R (3) 4.5 R (4) 7.5 R sol (4) am = 5a5m. since the force on both the masses will be equal 17. A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is (1) L / 2 (2) L / 4 (3) 2L (4) 4L sol (2) w E = LwLa E 3 1 so if its angular frequency is doubled and its kinetic energy is haved then new angular momentum will become 4 L times. 18. Let F be the force acting on a particle having position vector r, and T be the torque of this force about the origin. Then (1) r . T = 0 and F . T = 0 (2) r . T = 0 and F . T 1 0 (3) r . T ¹ 0 and F . T = 0 (4) r . T ¹ 0 and F . T 1 0 sol (1) since T = F × r, T is ^ r to F & r 19. A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t / 4. Then the relation between the moment of inertia IX and IY is (1) IY = 64 IX (2) IY = 32 IX (3) IY = 16 IX (4) IY = IX sol (1) Moment of inertia of circular disc I R T I R4t 2 1 = r p 4 Þ µ (where r = density, R= Radius, t = thickness) IY I X t t R I R 64 4 1 (4)4 1 2 4 1 2 = Þ ÷ ø ö ç è æ Þ ÷ ÷ ø ö ç çè æ ÷ ÷ø ö ç çè æ = x Y I AIEEE-2003 www.aieeepage.com P 5 of 45 20. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become (1) 20 hours (2) 10 hours (3) 80 hours (4) 40 hours sol (4) (4) 8 8 5 40 1 1 3/ 2 1 3/ 2 2 2 1 2 / 3 = ´ = ´ = = ÷ ø ö ç è µ Þ = æ T T R R T R T T hours . 21. The escape velocity for a body projected vertically upwards from the surface of earth is 11 km / s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be (1) 11/ 2 km / s (2) 11 2 km / s (3) 22 km / s (4) 11 km / s sol (4) Escape velocity does not depends on angle of projection R GM ve 2 = 22. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes5T/ 3.Then the ratio of m / M is (1) 5 / 3 (2) 3 / 5 (3) 25 / 9 (4) 16 / 9 sol (4) T µ M / k Þ (5T / 3) = 2 p {(M + m)/k} = 16 / 9. 23. A spring of spring constant 5 × 103 N / m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is (1) 6.25 N - m (2) 12.50 N - m (3) 18.75 N - m (4) 25.00 N - m sol (3) Work done = K x - x = 5´10 (10 - 5 )´10- = 18.75 N -m 2 1 ( ) 2 1 2 3 2 2 4 1 2 2 24. A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is (1) 0.1 J (2) 0.2 J (3) 10 J (4) 20 J sol (1) E = ½ F . (dl) = ½ × 200 × 10?3 = 0.1 J AIEEE-2003 www.aieeepage.com P 6 of 45 25. A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement x. Which of the following statements is true ? (1) P.E. is maximum when x = 0 (2) K.E. is maximum when x = 0 (3) T.E. is zero when x = 0 (4) K.E. is maximum when x is maximum. sol (2) Kinetic Energy is maximum at mean position KE = ( ) 2 1 m w2 a2 - x2 2 max 2 1 KE = mw2a (when x = a i.e., mean position) 26. The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is (1) 10% (2) 11% (3) 21% (4) 42% sol (1) T µ l Þ T? / T = (1.21 l / l) Þ T? = 1.1 T Þ % increased in T = 10%. 27. Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2,respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitudes of A and B is (1) k1 / k2 (2) (k1 / k2 ) (3) k2 / k1 (4) (k2 / k1 ) sol (4) B B s A A A B A B A m K a m K (Vmax ) = (Vmax ) Þ a wA = a wB Þ a = [mA = mB given] 1 2 1 2 k k a a a k a k B A A = B Þ = 28. A metal wire of linear mass density of 9.8 g / m is stretched with a tension of 10 kg-wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is (1) 25 Hz (2) 50 Hz (3) 100 Hz (4) 200 Hz sol (2) In condition of resonance frequency of A.C. will be equal to natural frequency of wire Hz T l n 50 2 100 9.8 10 10 9.8 2 1 1 2 1 3 = = ´ ´ ´ = m = - AIEEE-2003 www.aieeepage.com P 7 of 45 29. The displacement y of a wave travelling in the x-direction is given by y = 10?4 sin (600 t ? 2x + (p / 3)) metres, where x is expressed in metres and t in seconds. The speed of the wave-motion, in ms? 1, is (1) 200 (2) 300 (3) 600 (4) 1200 sol (2) y = a sin (wt - kx + f) in above equation wave velocity k v = w So by comparing this with given equation w = 600, k = 2 so v = 300 m/s 30. A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was (1) 256 + 5 Hz (2) 256 + 2 Hz (3) 256 ? 2 Hz (4) 256 ? 5 Hz sol (4) 256 ~ fp = 5 Þ fp = (256 ? 5) or (256 + 5); since f µ T, fp increases to f ?p;since 256 ~ f ?p = 2, fp = (256 ? 5). 31. A Carnot engine takes 3 × 106 cal. of heat from a reservoir at 627° C, and gives it to a sink at 27° C. The work done by the engine is (1) zero (2) 4.2 × 106 J (3) 8.4 × 106 J (4) 16.8 × 106 J sol (3) 6 cal 6 2 2 1 2 1 2 10 900 3 10 300 Þ = ´ = Þ = Q Q Q Q T T Work done = Q Q 6 6 6 cal 6 J 6 J 1 - 2 = 3´10 -10 = 2´10 = 2´ 4.2´10 = 8.4´10 32. ?Heat cannot by itself flow from a body at lower temperature to a body at higher temperature? is a statement or consequence of (1) first law of thermodynamics (2) second law of thermodynamics (3) conservation of momentum (4) conservation of mass sol (2) 33. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ration Cp / Cv for the gas is (1) 3 / 2 (2) 4 / 3 (3) 2 (4) 5 / 8 sol (1) Adiabatic law P1-gT g = constant P µT g/g-1 given that 2 = Þ g = 3 g -1 Pa T3 g 3 AIEEE-2003 www.aieeepage.com P 8 of 45 34. Which of the following parameters does not characterize the thermodynamic state of matter? (1) Volume (2) Temperature (3) Pressure (4) Work. sol 4 P, V & T are thermodynamic variables which characterize the thermodynamic state of matter. 35. According to Newton?s law of cooling, the rate of cooling of a body is proportional to (Dq)n, where Dq is the difference of the temperature of the body and the surroundings, and n is equal to (1) one (2) two (3) three (4) four. sol (1) Rate of cooling µ Dq, n = 1 36. The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by (1) Wien?s law (2) Rayleigh Jeans law (3) Planck?s law of radiation (4) Stefan?s law of radiation. sol (3) Infra-red lies in longer wavelength side and Planck?s law is applicable both for short and long waves. 37. To get three images of a single object, one should have two plane mirrors at an angle of (1) 30° (2) 60° (3) 90° (4) 120° sol (3) By using - Þq = 90° q = Þ ÷ ø ö ç è æ - q = 1 360 1 3 360 n 38. Consider telecommunication through optical fibers. Which of the following statements is not true? (1) Optical fibers may have homogeneous core with a suitable cladding (2) Optical fibers can be of graded refractive index (3) Optical fibers are subject to electromagnetic interference from outside (4) Optical fibers have extremely low transmission loss. sol (2) If optical fibers are subjected to electromagnetic interference from outside then due to interference, the transmission of a particular signal could never have been possible 39. The image formed by an objective of a compound microscope is (1) virtual and enlarged (2) virtual and diminished (3) real and diminished (4) real and enlarged sol (4) since uo > fo, image (vo) is real and enlarged. AIEEE-2003 www.aieeepage.com P 9 of 45 40. To demonstrate the phenomenon of interference, we require two sources which emit radiation (1) of the same frequency and having a definite phase relationship (2) of nearly the same frequency (3) of the same frequency (4) of different wavelengths sol 1 For interference, the sources should be coherent 41. Dimensions of (1 / moeo ), where symbols have their usual meaning, are (1) [LT ?1] (2) [L? 1 T] (3) [L? 2T2] (4) [L? 2T ?2] sol (4) C = 1 / (moeo) , [1 / (moeo ) ] = [C2] = [L2T?2] 42. Three charges ?q1, + q2 and ?q3 are placed as shown in the figure. The x-component of the force on ?q1 is proportional to (1) (q2 / b2) ? (q3 / a2) sin q (2) (q2 / b2) ? (q3 / a2) cos q (3) (q2 / b2) + (q3 / a2) sin q (4) (q2 / b2) + (q3 / a2) cos q sol (3) force on ?q1 due to q2 µ (q2 / b2) along +ve X-direction and that due to q3 µ (q3 / a2) along the direction making an angle of q with ?ve Y-axis & (90° ? q ) with +ve Xaxis Fnet µ {(q2 / b2) + (q3 / a2) sin q } 43. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell.The electrostatic potential at a point P a distance R / 2 from the centre of the shell is (1) ((q + Q) / (4 peo )) (2 / R) (2) 2Q / 4peo R (3) (2Q / 4peo R) ? (2q / 4peo R) (4) (2Q / 4peo R) + (q / 4peo R) sol (4) Net potential at P R q R Q V R q R Q V 0 0 0 pe0 + pe Þ = pe + ÷ø ö ç è pe æ = 4 4 2 . 4 1 2 4 1 -q 3 a b -q1 +q2 x q AIEEE-2003 www.aieeepage.com P 10 of 45 44. If the electric flux entering and leaving an enclosed surface respectively is f1 and f2 , the electric charge inside the surface will be (1) o (f1 + f2 )e (2) o (f2 - f1)e (3) o (f1 + f2 ) / e (4) o (f2 - f1) / e sol (2) Electric flux entering the surface (f1) taken negative while flux leaving the surface (f2 ) taken positive and according to Gauss Law T 0 2 1 0 0 Þ = = f ´ e Þ = f - f ´e e f = ( ) ( ) 1 Total Qenclosed Qenclosed Qenclosed otal Qenclosed 45. The work done in placing a charge of 8 × 10?18 coulomb on a condenser of capacity 100 micro-farad is (1) 32 ×10? 32 joule (2) 16 ×10? 32 joule (3) 3.1 ×10? 26 joule (4) 4 ×10? 10 joule. sol (1) By using W J C Q W 32 6 2 18 2 32 10 2 100 0 (8 10 ) 2 - - - = ´ ´ ´ = Þ = ´ 46. A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor (1) increases (2) decreases (3) Remains unchanged (4) Becomes infinite. sol (3) By using ' . d t A C - e = 0 It t » neglibible, then d A C e0 '= 47. A 3volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current, I , in the circuit will be (1) 1 / 3A (2) 1A (3) 1.5A (4) 2A sol (3) c Req. = (3 × 6) / (3 + 6) = 2 W , i = (3 / 2) = 1.5 A 48. An ammeter reads upto 1 ampere. Its internal resistance is 0.81 ohm. To increase the range to 10 A the value of the required shunt is (1) 0.09 W (2) 0.03W (3) 0.3W (4) 0.9W sol (1) ig G = (i ? ig) . SÞ 1 × 0.81 = (10 ? 1) S Þ S = 0.09 W AIEEE-2003 www.aieeepage.com P 11 of 45 49. The length of a wire of a potentiometer is 100 cm, and the e.m.f of its stand ard cell is E volt. It is employed to measure the e.m.f. of a battery whose internal resistance is 0.5W . If the balance point is obtained at l = 30 cm.from the positive end, the e.m.f. of the battery is (1) 30 E / 100 (2) 30 E / 100. |
