# Super 30 Entrance Exam – Online Practice Test

1. Fermi is a unit of...

2. The horizontal component of a force of 10 N inclined at 30° to the vertical is...

3. The acceleration due to gravity on Mars is 3.7 m/s² . Compared with her mass and weight on the earth, an astronaut on Mars has...

4. To keep a vehicle moving at the speed v requires a force F. The power needed is...

5. When the velocity of a moving object is doubled...

6. The intermolecular potential is dependent on...

7. A cable stretches by amount 'a' under a certain load. If it is replaced by a cable of the same material but half as long and half the diameter, the same load will stretch it by...

8. A certain person's heart beats 1.2 times per second and pumps 1.0 x10-4 m³ of blood per beat against an average pressure of 14 kPa. The power output of the heart is...

9. At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 20 °C

10. For monatomic gases, Cp/Cv is equal to...

11. Of the following the one that is a vector is...

12. Diamagnetic materials are substances that...

13. When a ferromagnet is inserted in a current-carrying loop, the magnetic field...

14. A light ray passes through a prism with an angle of incidence θ, an angle of deviation δ and an angle of emergence ε. Minimum deviation occurs when...

15. The image a camera forms on the film is...

16. If for the planets in solar system, r is the radius of the orbit and T is the periodic time, then the ratio r³ /T² is...

17. A boy swings from a rope 4.9 m long. His approximate period of oscillation is...

18. The primary effect when the source is moving is a change in...

19. The distance between a node and the immediate next antinode is...

20. A thin ring has mass M and radius R. Its moment of inertia about the axis passing through its center and perpendicular to its plane is...

21. Two satellites have periods P1 and P2, respectively. Their heights above the surface of the earth are h1 and h2,respectively. If h1 > h2, then...

22. A projectile is thrown in the direction making an angle θ with the horizontal. The projectile attains maximum height for θ equal to...

23. A Carnot engine operates between 800K and 200K. If it absorbs 8 kJ of heat in each cycle, the work done by it per cycle is...

24. In a uniform segment of a circuit the current is proportional to the...

25. To charge a secondary cell, what is needed is...

26. Two parallel wires carry current in the same direction,...

27. If the maximum value of the induced e.m.f. is Vm and maximum r.m.s. current is √ 2 ampere for an a.c. circuit with resistance R, then the value of Vm in volt is equal to...

28. The wavelength of light plays no role in...

29. The value of the stopping potential depends on...

30. The only atom which has no neutron in the nucleus is...

31. A Student measured the length of a rod and wrote it as 3.50cm. Which instrument did he use to measure it

32. An object moving with a speed of 6.25 m/sec, is decelerated at a rate given by (dy/dt) = -2.5√v . Where ‘v’ is the instantaneous speed. The time taken by the object to come to rest, would be

33. The energy stored in the electric field produced by a metal sphere is ‘4.5 joule’. The charge on the sphere is  '4μc' its radius will be  [(1/4πε0)=9×109    N - m2c-2]

34. A block of mass 10kg moving in X-direction with a constant speed of  10 msec-1, is subjected to a retarding force F = (x/10) (Joule/meter) during its travel from x=10m to x=20m its final kenetic energy will be (in Joule)

35. A radiation of energy ‘E’ falls normally on a perfectly reflecting surface. The momentum  transferred to the surface is (C is the Velocity of light )

36. Two bodies ‘A and B’ of masses 5 kg and 10 kg in contact with each other rest on a table against a rigid partition. Coefficient of friction between the bodies and the table is 0.2. A force of 200N is applied horizontally at ‘A’ action reaction force between A and B is (g = 10 m/sec2) 37. A thin circular loop of radius ‘R’ rotates about its vertical diameter with an angular frequency ‘ ’. A small bead on the wire loop remains at its lowermost point for ω ≤ √(g/R) . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √(2g/R) (Neglect the friction)

38. A rocket of initial mass  'm0' moving with velocity ‘v’ discharges a jet of gases of mean density ‘ρ’ and effective area ‘A’ the minimum value of ‘v’ of fuel gas, which enables the rocket to rise vertically above is nearly

39. Two equal masses ‘A and B’ moving along the same straight line with velocities 3i m/sec  and '-5i m/sec respectively collide elastically. Their velocities after the collision will be respectively

40. A cart of mass ‘M’ is tied by one end of a massless rope of length ‘10m’. The other end of the rope is in the hands of a man of mass ‘M’. The entire system is on a smooth horizontal surface. The man is at ‘x=o’ and the cart at ‘x=10m’ of the man pulls the cart by the rope , the man and the cart will meet at the point

41. Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the solid sphere about its diameter axis. After ‘t’ sec their angular velocities are . Choose the correct answer (initial angular speed of each is 'ω0'

42. A solid sphere of mass ’M’ ; radius ‘R’ and having moment of inertia about an axis passing through the centre of mass is ‘I’. It recast into a disc of thickness ‘t’. Whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains ‘I’ then radius of the disc will be

43. The radius of the planet is ‘R’ A satellite revolves around it in a circle of radius ‘r’ with an angular velocity ‘ω’. The acceleration due to the gravity onthe planet surface is

44. Out of the following functions representing motion of a particle which represents ‘SHM’

a) Y = sinωt - cosωt

b) Y = Sin3 ωt

c) Y = 5 cos[(3π/4) - 3ωt]

d) Y = 1 + ωt + ω2t2

45. Four identical hollow cylindrical columns of mild steel support a big structure of mass 88000 kg. The inner and outer radii of each column are 30cm and 40cm respectively. Assuming load distribution is uniform. The compressional strain of each column is (Y = 2×1011  N/m2 )

46. Gas at a pressure ‘P0’ is contained in a vessel. If the masses of all the molecules are halved and their r.m.s speeds are doubled, the resulting pressure will be equal to

47. Two metal spheres are falling through a liquid of density  2 × 103 kg/m3  with the same uniform speed. The material density of sphere ‘1 and 2’ are  8 × 103 kg/m3  and 11 × 103 kg/m3   The ratio of their radii is

48. A diatomic ideal gas is used in carnot engine as the working substance if during the adiabatic part of the cycle the volume of the gas increases from ‘V’ to ‘32V’. The efficiency of the engine is

49. The amount of radiation emitted by a perfectly black body is proportional to

50. A particle moves along X –axis in such a way that coordinate X varies with time t according to the equation . x = ( 2-5t+6t2)m The initial velocity of the particle is

51. One mole of an ideal gas at temperature ‘'T1' expands according to the law (P/V) = constant expression for the workdone when its final temperature becomes 'T2'  is

52. A single slit of width ‘0.1mm’ is illuminated by a parallel beam of light of wave length and diffraction bands are observed on a screen ‘0.5m’ from the slit. The distance of the third dark band from the central bright band is

53. For a projectile, its horizontal range and maximum vertical heights are equal, maximum height reached by it is (‘u’ is initial velocity of the projectile)

54. Calorie is defined as the amount of heat required to raise temperature of 1g of water by 10C and it is defined under which of the following conditions

55. A source and Listner both moving towards each other each with speed .frequency of the note emitted by the source is ‘600Hz’ Apparent wave length of sound wave received by the observer is  ( V = 330 m/ sec)

56. A wave represented by the given equation y = a cos(kx - ωt) is superposed with another wave to form a stationary wave such that the point x=0 is a node. The equation for the other wave is

57. The plane faces of two identical plano-convex lenses each having focal length of 40cm  are pressed against each other to form a usual convex lens. The distance from lens, at which an object must be placed to obtain a real, inverted image with magnification one is

58. Two infinitely long parallel wires having linear charge densities 'λ1'and 'λ2' respectively are placed at a distance ‘R’. The force per unit length on either wire will be (k = (1/4πε0))

59. An electric cell of e.m.f ‘E’ is connected across a copper wire of diameter ‘d’ and length 'l' the drift velocity of electron in the wire is 'vd' If the length and diameter of the wire are doubled the new drift velocity of electron is

60. In a large building there are 15 bulbs of ‘40w’ 5 bulbs of ‘100w’. 5 fans of ‘80w’ and 1 heater of ‘1kw’ . The voltage of electric mains is ‘220 volts’.The minimum capacity of the main fuse of the building will be

61. Which of the following combinations should be selected for better tuning of an L.C.R series circuit used for communication

62. A square coil of side ‘25cm’ having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant ‘t’ the ‘e.m.f’ induced in the coil is E= 200 sin100πt. The strength of the magnetic field is (in Tesla)

63. Magnetic moment and angular moment of revolving electron in a hydrogen atom ‘M’ and ‘L’ respectively then

64. A ‘2Mev’ proton is moving perpendicular to a uniform magnetic field of ‘2.5 Tesla’. The force on the proton is (mass of proton = 1.6 × 10-27 kg)

65. A voltage of peak value 283 volt and varying frequency is applied to a series L-C-R combination in which R =3 ohm, ‘L=25 mH and C = 40μF . The frequency of the source at which maximum power is dissipated in the circuit is

66. A paramagnetic sample shows a net magnetization of 8 A/m when placed in an external magnetic field of 0.6 T at a temperature of 4 K. When the same sample is placed in an external magnetic field of 0.2 T at a temperature of 16 K, the magnetization will be

67. The threshold frequency for a metallic surface corresponds to an energy of 6.2ev and the stopping potential for a radiation incident on this surface is ‘5volt’. The incident radiation lies in

68. The de-Broglie wave length of an electron in first Bohr orbit is

69. A nucleus of mass 'M + ∆m'  is at rest and decays into two daughter nuclei of equal mass '(M/2)' each speed of light is ‘C’. The speed of daughter nuclei is

70. The aperture of the objective lens of a telescope is made large so as to

71. For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

72. Two coherent sources of intensity ratio 1:4 produce an interference pattern the fringe visibility will be

73. Which logic gate is represented by the following combination of logic gates 74. The given graph represents V – I characteristic for a semiconductor device Which of the following statement is correct

75. If the velocity v of a particle moving along a straight line decreases linearly with its displacement ‘S’ from 20ms-1 to a value approaching zero at S=30m. Then acceleration of the particle at S=15m is 76. The velocity at the maximum height of a projectile is half of its initial velocity ‘u’. Its range on the horizontal plane is

77. A balloon of mass ‘m’ is found to accelerate up at the rate of g/6. The amount of water should be put inside the balloon so that it accelerates down at rate of g/6. (Assume buoyancy force remains the same)

78. The maximum value of ‘F’ for which both the blocks move together is 79. The Poisson’s ratio of a material is 0.4. If a force is applied to a wire of this material, there is a decrease of cross sectional area by 2%. The percentage increase in its length is

80. Pick out the wrong statement from the following.

81. Two identical containers each of volume V joined by a normal pipe contains gas at a
temperature T. If one of the containers is now maintained at the same temperature T while the other is maintained at 2T, the number of moles of gas in the container having temperature 2T will be

82. P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be

83. Mark out the incorrect statement regarding transverse standing waves on a string

84. A sonometer wire resonate with a given tuning fork forming standing wave with five antinode between the two bridges when a mass of 9kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same position of the bridges. The value of M is

85. In the figure shown a source of sound of frequency 510 Hz move with constant velocity Vs=20 m/ s in the direction shown. The wind is blowing at a constant velocity Vw=20 m/S towards an observer who is at rest at point B. Corresponding to the sound emitted by the source in initial position A, the frequency detected by the observer is equal to (speed of sound relative to air = 330 m/s) 86. For a prism kept in air it is found that for an angle of incidence 600, the angle of refraction ‘A’, angle of deviation ‘δ ’ and angle of emergence ‘e’ become equal. Then the refractive index of the prism is

87. The power of a lens having refractive index 1.25 is +3 diopters. When placed in a liquid its power is -2 diopters. The refractive index of the liquid is

88. The length of a potentiometer wire is l. A cell of emf ‘e’ is balanced at a length l/5 from the positive end of the wire. Assuming there is no contribution in resistance from any part of the circuit except the potentiometer wire, the balancing length for the same cell if length of the wire is increased by l/2 is

89. A uniform magnetic field B is directed out of the page. A metallic wire has the shape of a square frame and is placed in the field as shown. While the shape of the wire is steadily transformed into a circle in the same plane, the current in the frame 90. A variable frequency A.C. source is connected to a capacitor. How will the displacement current change with decrease in frequency?

91. In natural α -decay process occurring in different types of nuclei at rest. Which of the following
is correct?

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