3.1 light year distance is equal to 

(a) 9.46 1010 ⋅ km (b) 9.46 1012 ⋅ km 

(c) 9.46 109 ⋅ km (d) 9.46 1015 ⋅ km

4. Parallactic second is equal to 

(a) 9.4605 1015 ⋅ m (b) 3.07 1016 ⋅ m 

(c) 1.496 1011 ⋅ m (d) 3 108 ⋅ m

5. A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the sun and the earth in terms of the new unit, if light takes 8 min and 20 s to cover this distance? 

(a) 300 (b) 400 (c) 500 (d) 600 

6. A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair is 3.5 mm. What is the estimate on the thickness of the hair? 

(a) 0.0035 mm (b) 0.035 mm 

(c) 0.01 m (d) 0.7 m

7. The dimensions of impulse are equal to that of

(a) force (b) linear momentum (c) pressure (d) angular momentum 

8. The dimensional formula for molar thermal capacity is same as that of 

(a) gas constant (b) specific heat 

(c) Boltzmann’s constant (d) Stefan’s constant 

9.  In measuring electric energy, 1kWh is equal to

  (a) 3.6 10 J 4 ⋅

(b) 3.6 10 J 6 ⋅ 

(c) 7.3 10 J 6 ⋅

(d) None of these 

10. Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant? (a) Acceleration due to gravity 

(b) Surface tension of water 

(c) Weight of a standard kilogram mass 

(d) The velocity of light in vacuum 

11. The square root of the product of inductance and capacitance has the dimensions of 

(a) length 

(b) time 

(c) mass 

(d) no dimension 

12.  With usual notation, the following equation, said to give the distance covered in the nth second, i.e. s u an 

n = +( ) 2 1 −2is 

(a) numerically correct only 

(b) dimensionally correct only 

(c) both dimensionally and numerically only 

(d) neither numerically nor dimensionally correct

33. [ML T A ] 2 3 1 − − is the dimensional formula for 

(a) capacitance (b) resistance 

(c) resistivity (d) potential difference 

34. The dimensional formula [ML T ] 0 3−is more closely associated with 

(a) power 

(b) energy 

(c) intensity 

(d) velocity gradient

35. Assuming that the mass mof the largest stone that can be moved by a flowing river depends upon the velocity v of the water, its density ρand the acceleration due to gravity g. Then, mis directly proportional to 

(a) v3(b) v4 

(c) v5(d) v6 

36. The units of length, velocity and force are doubled. Which of the following is the correct change in the other units? 

(a) Unit of time is doubled 

(b) Unit of mass is doubled 

(c) Unit of momentum is doubled 

(d) Unit of energy is doubled

37. The dimensional representation of specific resistance in terms of charge Q is 

(a) [ML T Q ] 3 1 2 − − (b) [ML T Q ] 2 2 2 − 

(c) [MLT Q ] − − 2 1 (d) [ML T Q ] 2 2 1 − − 

38. IfC and R denote capacity and resistance, the dimensions of CR are 

(a) [M L T] 0 0 

(b) [ML T] 0 

(c) [M L T ] 0 0 2 

39. Multiply 107.88 by 0.610 and express the result with correct number of significant figures. 

(a) 65.8068 (b) 64.807 (c) 65.81 (d) 65.8 

40. The unit of permittivity of free space, ε0is (a) coulomb/newton-metre 

(b) newton-metre 2/coulomb2 

(c) coulomb2/newton-metre 2 

(d) coulomb2/(newton-metre) 2

41.  Three measurements are made as 18.425 cm, 7.21 cm and 5.0 cm. The addition should be written as 

(a) 30.635 cm (b) 30.64 cm (c) 30.63 cm (d) 30.6 cm

42. The radius of a thin wire is 0.16 mm. The area of cross-section of the wire in mm2 with correct number of significant figures is 

(a) 0.08 (b) 0.080 

(c) 0.0804 (d) 0.080384 

43 . The mass of a box is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box to correct significant figures is 

(a) 2.3 kg (b) 2.34 kg 

(c) 2.3432 kg (d) 2.31 kg 

44 .  The length of a rod is (11.05 0.2) cm ± . What is the length of the two rods? 

(a) (22.1 0.05) cm ± 

(b) (22.1 0.1) cm ± 

(c) (22.10 0.05) cm ± 

(d) (22.10 0.2) cm ± 

45.  Pressure gradient has the same dimensions as that of

(a) velocity gradient

(b) potential gradient

(c) energy gradient

(d) None of these 

46 .  Which one of the following have same dimensions?

(a) Torque and force 

(b) Potential energy and force 

(c) Torque and potential energy 

(d) Planck’s constant and linear momentum 

47. 58. The significant figures of the number 6.0023 is

(a) 2

(b) 5 

(c) 4

(d) 1 

48. In which of the following numerical values, all zeros are significant? 

(a) 0.2020

(b) 20.2 

(c) 2020

(d) None of these 

49.  If the error in measuring diameter of a circle is 4%, the error in measuring radius of the circle would be

(a) 2%

(b) 8% 

(c) 4%

(d) 1% 

50. A cuboid has volumeV l l l = ⋅ ⋅ 2 3 , where l is the length of one side. If the relative percentage error in the measurement of l is 1%, then the relative percentage error in measurement ofV is 

(a) 18%

(b) 6% 

(c) 3%

(d) 1%