#### NATURE OF PHYSICAL WORLD AND MEASURMENT NEET QUESTION AND JEE IMPORTANT ONE MARKS

11th Standard

Reg.No. :
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Physics

Time : 00:02:00 Hrs
Total Marks : 139
139 x 1 = 139
1. Find the value of one Au in 1000km

(a)

1.5 x 105m

(b)

2.5 x 106m

(c)

1.5 x 1011m

(d)

2.5 x 1010m

2. How many AU present in one light year?

(a)

6.30 x 104m

(b)

9.46 x 1015m

(c)

6.2 x 102m

(d)

9.4 x 1016m

3. How many um present in one metre?

(a)

10-6 $\mu$ m

(b)

106 $\mu$ m

(c)

10-3 $\mu$ m

(d)

10-2 $\mu$ m

4. The speed of an object v = 40 ms-1. The same quantity of speed in kmh-1 is,

(a)

60

(b)

160

(c)

40

(d)

144

5. The speed of an object v = 90km/h. The same quantity of speed in m/s is

(a)

90

(b)

25

(c)

45

(d)

180

6. 3.5 kg mass of a metal plate has the volume of 1.5 m3. Find the density of metal plate.

(a)

1.5 kg/m3

(b)

2.3 kg/m3

(c)

3.4 kg/m3

(d)

4.8 kg/m3

7. How many parsec are there in one kilometer?

(a)

3.084 x 10-16

(b)

3.084 x 108

(c)

3.24 x 10-14

(d)

None

8. The angle of an object is 18.2°. What is the angular diameter of the object in radians?

(a)

(b)

(c)

(d)

9. If h is planck's constant and $\lambda$ is wavelength, ${ h }/{ \lambda }$ has dimensions of

(a)

momentum

(b)

energy

(c)

mass

(d)

velocity

10. Velocity of sound in a gas is given by v = $\sqrt { \frac { \Upsilon \rho }{ \rho } }$. Dimensional formula for $\gamma$ is

(a)

[ MLT ]

(b)

${ M }^{ 0 }$ ${ L }^{ 0 }$ ${ T }^{ 0 }$ ]

(c)

${ M }^{ 0 }$L${ T }^{ 0 }$ ]

(d)

[ M${ L }^{ 0 }$ ${ T }^{ 0 }$]

11. If momentum ( p ), area ( A ) and time ( T ) are taken to be fundamental quantities, the energy has the dimensional formula

(a)

[p${ A }^{ -1 }$${ T }^{ 1 }$]

(b)

[${ p }^{ 2 }$$A^{ 1 }$${ T }^{ 1 }$]

(c)

[$p^{ 1 }$$A^{ -1/2 }$${ T }^{ 1 }$]

(d)

[$p^{ 1 }$$A^{ 1/2 }$${ T }^{ -1 }$]

12. The refractive index of a material is given by the equation n = A+$\frac { B }{ { \lambda }^{ 2 } }$, where A and B are constants. The dimensional formula for B is

(a)

${ M }^{ 0 }$${ L }^{ 2 }$T ]

(b)

${ M }^{ 0 }$${ L }^{ -2 }$${ T }^{ 0 }$]

(c)

${ M }^{ 0 }$${ L }^{ 2 }$${ T }^{ -2 }$ ]

(d)

${ M }^{ 0 }$${ L }^{ 2 }$${ T }^{ 0 }$ ]

13. If L is the inductance, C capacitance and R resistance the ratios L/R and R-C have the same dimensions as those of

(a)

frequency

(b)

time

(c)

energy

(d)

length

14. van der Waals, equation of state is ( p + $\frac { a }{ { v }^{ 2 } }$ ) ( v - b ) = nRT. The dimensions of a and b are

(a)

${ ML }^{ 3 }$${ T }^{ 2 }$], [ ${ ML }^{ 3 }$${ T }^{ 0 }$]

(b)

${ ML }^{ 5 }$${ T }^{ -2 }$] [ ${ M }^{ 0 }$${ L }^{ 3 }$${ T }^{ 0 }$]

(c)

${ M }^{ 2 }$${ LT }^{ 2 }$] [ ${ ML }^{ 3 }$${ T }^{ 2 }$]

(d)

${ ML }^{ 2 }$T ],  [${ ML }^{ 2 }$${ T }^{ 2 }$

15. Pascal-second has the dimensions of

(a)

force

(b)

energy

(c)

pressure

(d)

coefficient of viscosity

16. Dimensions of electrical resistance are

(a)

${ ML }^{ 2 }$${ T }^{ -3 }$${ A }^{ -1 }$ ]

(b)

${ ML }^{ 2 }$${ T }^{ -3 }$${ A }^{ -2 }$]

(c)

${ ML }^{ 3 }$${ T }^{ -3 }$${ A }^{ -2 }$]

(d)

${ ML }^{ 2 }$${ T }^{ 3 }$${ A }^{ 2 }$ ]

17. Dimensional formula for surface tension is

(a)

${ M }^{ 2 }$${ L }^{ 0 }$${ T }^{ -2 }$ ]

(b)

${ ML }^{ 0 }$ ${ T }^{ -2 }$]

(c)

${ M }^{ 0 }$${ LT }^{ -1 }$]

(d)

${ M }^{ 2 }$${ L }^{ 2 }$${ T }^{ -1 }$]

18. The quantity having the same units in all systems of units is

(a)

mass

(b)

time

(c)

length

(d)

temperature

19. Pressure gradient has the same dimensions as that of

(a)

(b)

(c)

(d)

None of these

20. Young's moduls of the material of a wire is 18 x ${ 10 }^{ 11 }$ dyne $cm^{ -2 }$. Its value in SI is

(a)

18 x $10^{ 15 }$ $Nm^{ -2 }$

(b)

18 x $10^{ 10 }$$Nm^{ -2 }$

(c)

18 x $10^{ 9 }$$Nm^{ -2 }$

(d)

18 x $10^{ 12 }$$Nm^{ -2 }$

21. In the equation y = a sin ( $\omega$t + kx ), the dimensional formula of  $\omega$ is

(a)

${ M }^{ 0 }$${ L }^{ 0 }$${ T }^{ -1 }$]

(b)

${ M }^{ 0 }$${ LT }^{ -1 }$ ]

(c)

$ML^{ 0 }$$T^{ 0 }$ ]

(d)

${ M }^{ 0 }$${ L }^{ -1 }$$T^{ 0 }$ ]

22. The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significiant figures and error is

(a)

( 164 $\pm$ 3 ) ${ cm }^{ 2 }$

(b)

( 163.62 $\pm$ 2.6 ) ${ cm }^{ 2 }$

(c)

( 163.6 $\pm$ 2.6 ) ${ cm }^{ 2 }$

(d)

( 163.62 $\pm$ 3 ) ${ cm }^{ 2 }$

23. If F = 6$\pi$${ \eta }^{ a }$${ r }^{ b }$${ v }^{ c }$, where, F = viscous force, $\eta$ = coefficient of viscosity, r = radius of spherical body, v = terminal velocity of the body The values of a, b and c are

(a)

a = 1, b = 2, c = 1

(b)

a = 1, b = 1, c = 1

(c)

a = 2, b =1, c = 1

(d)

a = 2, b = 1, c = 2

24. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%,3% and 4% respectively. Quantity p is calculated as follows
p = $\frac { { a }^{ 3 }{ b }^{ 2 } }{ cd }$%. Error in p is

(a)

14%

(b)

10%

(c)

7%

(d)

4%

25. The unit of thermal conductivity is

(a)

${ m }^{ -1 }$${ K }^{ -1 }$

(b)

${ JK }^{ -1 }$

(c)

WmK

(d)

JK

26. SI unit of permittivity is

(a)

$C^{ 2 }$$m^{ 2 }$$N^{ 2 }$

(b)

$C^{ 2 }$$m^{ -2 }$$N^{ -1 }$

(c)

$C^{ 2 }$$m^{ 2 }$$N^{ -1 }$

(d)

$C^{ -1 }$$m^{ 2 }$$N^{ 2 }$

27. A physical quantity is given by x = [ $M^{ a }$$L^{ b }$$T^{ c }$]. The percentage error in measurements of M, L and T are $\alpha$$\beta$ and  $\gamma$. then, the maximum % error in the quantity X is

(a)

a$\alpha$ + b$\beta$ + c$\gamma$

(b)

a$\alpha$ + b$\beta$ - c$\gamma$

(c)

$\frac { a }{ \alpha }$$\frac { b }{ \beta }$$\frac { c }{ \gamma }$

(d)

None of these

28. The dimensions of ${ { { (\mu }_{ 0 } }{ { \varepsilon }_{ 0 } }) }^{ -1/2 }$ are

(a)

${ L }^{ -1 }$T ]

(b)

${ LT }^{ -1 }$]

(c)

${ L }^{ -1/2 }$$T^{ 1/2 }$ ]

(d)

$L^{ 1/2 }$$T^{ -1/2 }$ ]

29. If L and C denote inductance and capacitance, then the dimensions of L-C are

(a)

$M^{ 0 }$$L^{ 0 }$$T^{ 2 }$ ]

(b)

$M^{ 2 }$$L^{ 0 }$$T^{ 2 }$]

(c)

$M^{ 0 }$$L^{ 2 }$$T^{ 2 }$ ]

(d)

$ML^{ 2 }$$T^{ 2 }$]

30. The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimensions of

(a)

frequency

(b)

velocity

(c)

angular momentum

(d)

time

31. In the relation $\rho$ = $\frac { \alpha }{ \beta }$${ e }^{ -\alpha z/k\theta }$$\rho$ is pressure, z is distance, k is boltzmann constant and $\theta$ is temperature. The dimensional formula of $\beta$ will be

(a)

${ M }^{ 0 }$${ L }^{ 2 }$${ T }^{ 0 }$]

(b)

${ ML }^{ 2 }$T ]

(c)

${ ML }^{ 0 }$${ T }^{ -1 }$]

(d)

${ M }^{ 0 }$${ L }^{ 2 }$${ T }^{ -1 }$]

32. "Parsec" is the unit of

(a)

time

(b)

distance

(c)

frequency

(d)

angular acceleration

33. 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

34. 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 mm

35. which of the following is the most precise device for measuring length?

(a)

a vernier calipers with 20 divisions on the sliding scale

(b)

an optical instrument that can measure length to within a wavelength of light

(c)

a screw gauge of pitch 1 mm and 100 divisions on the circular scale

(d)

All the above are equally precise

36. Dimensions of impulse are

(a)

$\left[ { M }^{ }{ L }^{ -2 }{ T }^{ -3 } \right]$

(b)

$\left[ { M }{ L }^{- 2 } \right]$

(c)

$\left[ { M }^{ }{ L }^{ }{ T }^{ -1} \right]$

(d)

$\left[ { M }^{ }{ L }^{}{ T }^{ -2 } \right]$

37. The dimensional formula for Young's modulus is

(a)

$\left[ { M }^{ }{ L }^{ -1 }{ T }^{ -2 } \right]$

(b)

$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ -2 } \right]$

(c)

$\left[ { M }^{ }{ L }^{ }{ T }^{ -2 } \right]$

(d)

$\left[ { M }^{ }{ L }^{ 2 }{ T }^{ -2 } \right]$

38. Which of the following is the dimensions of the coefficient of friction?

(a)

$\left[ { M }^{ 2 }{ L }^{ 2 }{ T }^{ } \right]$

(b)

$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 } \right]$

(c)

$\left[ { M }^{ }{ L }^{ 2 }{ T }^{ -2 } \right]$

(d)

$\left[ { M }^{ 2 }{ L }^{ 2 }{ T }^{ -2 } \right]$

39. The dimensional formula for the action will be

(a)

$\left[ { M }^{ }{ L }^{ }{ T }^{ -2 } \right]$

(b)

$\left[ { M }^{ 2 }{ L }^{ }{ T }^{-2 } \right]$

(c)

$\left[ { M }{ L }^{ 2}{ T }^{-1 } \right]$

(d)

$\left[ { M }^{ 2 }{ L }^{ 2 }{ T }^{ -2 } \right]$

40. Given that $y=a\quad cos\left( \frac { t }{ p } -qx \right)$ , where t represents time in following statements is true?

(a)

The units of x is same as that of q

(b)

The unit of x is same as that of p

(c)

The unit of t is same as that of q

(d)

The unit of t is same as that of p

41. The dimensional formula $\left[ M{ L }^{ 0 }{ T }^{ -3 } \right]$is more closely associated with

(a)

power

(b)

energy

(c)

intensity

(d)

42. Assuming that the mass m of the largest stone that can be moved by a flowering river depends upon the velocity v of the water, its density $\rho$ and the acceleration due to gravity g. Then, m is directly proportional to

(a)

${ v }^{ 3 }$

(b)

${ v }^{ 4 }$

(c)

${ v }^{ 5}$

(d)

${ v }^{ 6}$

43. If p represents radiation pressure, c represent speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x,y and z such that ${ p }^{ x }{ Q }^{ y }{ c }^{ z }$is dimensionless are

(a)

x=1,y=1,z=-1

(b)

x=1,y=-1,z=1

(c)

x=-1,y=1,z=1

(d)

x=1,y=1,z=1

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

(a)

$\left[ M{ L }^{ 3 }{ T }^{ -1 }{ Q }^{ -2 } \right]$

(b)

$\left[ M{ L }^{ 2}{ T }^{ -2 }{ Q }^{ 2 } \right]$

(c)

$\left[ M{ L }^{ }{ T }^{ -2 }{ Q }^{ -1 } \right]$

(d)

$\left[ M{ L }^{ 2 }{ T }^{ -2}{ Q }^{ -1 } \right]$

45. If C and R denote capacity and resistance, the dimensions of CR are

(a)

$\left[ { M }^{ 0 }{ L }^{ 0 }{ T } \right]$

(b)

$\left[ { M }{ L }^{ 0 }{ T } \right]$

(c)

$\left[ { M }^{ 0 }{ L }^{ 0 }{ { T }^{ 2 } } \right]$

(d)

not expressible in terms of M,L and L

46. The force F on a sphere of radius a moving in a medium with velocity v is given by F=6$\pi \quad \eta av$. The dimensions of $\eta$ are

(a)

$\left[ M{ L }^{ -3 } \right]$

(b)

$​​​​\left[ M{ L }^{ }{ T }^{ -2 } \right]$

(c)

$\left[ M{ T}^{ -1 } \right]$

(d)

$\left[ M{ L }^{ -1 }{ T }^{ -1 } \right]$

47. The equation of a wave is given by $y=a\quad sin\omega \left( \frac { x }{ v } -k \right)$ where $\omega$ is angular velocity and v is the linear velocity. The dimensions of k will be

(a)

$\left[ { T }^{ -2 } \right]$

(b)

$\left[ { T }^{ -1 } \right]$

(c)

$\left[ { T }^{ } \right]$

(d)

$\left[ { LT }^{ } \right]$

48. A force is given by F=at+b${ t }^{ 2 }$, where t is the time. The dimensions of a and b are

(a)

$\left[ ML{ T }^{ -4 } \right]$ and $\left[ ML{ T }^{ } \right]$

(b)

$\left[ ML{ T }^{ -1} \right]$ and $\left[ ML{ T }^{ 0} \right]$

(c)

$\left[ ML{ T }^{ -3 } \right]$ and $\left[ ML{ T }^{ -4 } \right]$

(d)

$\left[ ML{ T }^{ -3} \right]$ and $\left[ ML{ T }^{ 0 } \right]$

49. The dimension of $\frac { 1 }{ 2 } { \varepsilon }_{ 0 }{ E }^{ 2 }$(${ \varepsilon }_{ 0 }$ is the permittivity of the space and E is electric field), is

(a)

$\left[ M{ L }^{ 2 }{ T }^{ -1 } \right]$

(b)

$\left[ M{ L }^{ -1 }{ T }^{ -2 } \right]$

(c)

$\left[ M{ L }^{ 2 }{ T }^{ -2 } \right]$

(d)

$\left[ M{ L }^{ }{ T }^{ -1 } \right]$

50. The dimensions of $\frac { a }{ b }$in the equation $p=\frac { a-{ t }^{ 2 } }{ bx }$, where p is pressure, x is distance and t is time, are

(a)

$\left[ { M }^{ 2 }L{ T }^{ -3 } \right]$

(b)

$\left[ { M }^{ }{ T }^{ -2 } \right]$

(c)

$\left[ { }^{ }L{ T }^{ -3 } \right]$

(d)

$\left[ { M }{ L }^{ 3 }{ T }^{ -1 } \right]$

51. Dimension of velocity gradient is

(a)

$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ -1 } \right]$

(b)

$\left[ { M }^{ }{ L }^{ -1 }{ T }^{ -1 } \right]$

(c)

$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ -1 } \right]$

(d)

$\left[ { M }^{ }{ L }^{ 0 }{ T }^{ -1 } \right]$

52. The dimensional formula for emf e is MKS system will be

(a)

$\left[ { M }{ L }^{ 2 }{ T }^{ -2 }{ Q }^{ -1 } \right]$

(b)

$\left[ { M }{ L }^{ 2 }{ T }^{ -1 } \right]$

(c)

$\left[ { M }{ L }^{ -2 }{ Q }^{ -1 } \right]$

(d)

$\left[ { M }{ L }^{ }{ T }^{ -2 }{ Q }^{ -2 } \right]$

53. The velocity v of a particle at time t is given by $v=at+\frac { b }{ t+c }$, where a,b and c are constants. The dimensions of a,b and c are respectively

(a)

$\left[ L{ T }^{ -2 } \right]$$\left[ L \right]$ and $\left[ { T }\right]$

(b)

$\left[ { L }^{ 2 } \right]$,$\left[ { }^{ }{ T } \right]$ and $\left[ { L }^{ }{ T }^{ 2 } \right]$

(c)

$\left[ { L }^{ }{ T }^{ 2 } \right]$$\left[ { L }^{ }{ T }^{ } \right]$ and $\left[ { L } \right]$

(d)

$\left[ { L } \right]$,$\left[ { L }^{ }{ T }^{ } \right]$ and $\left[ { T }^{ 2 } \right]$

54. What is the units of $k=\frac { 1 }{ 4\pi { \varepsilon }_{ 0 } }$?

(a)

${ C }^{ 2 }{ N }^{ -1 }{ m }^{ -2 }$

(b)

${ N }^{ }{ m}^{ 2 }{ C }^{ -2 }$

(c)

${ N }^{ }{ m }^{ 2 }{ C }^{ 2 }$

(d)

Unitless

55. The length, breadth and thickness of a block are given by l=12 cm, b=6 cm and t=2.45 cm. The volume of the block according to the idea of significant figures should be

(a)

$1\times { 10 }^{ 2 }c{ m }^{ 3 }$

(b)

$2\times { 10 }^{ 2 }c{ m }^{ 3 }$

(c)

$1.763\times { 10 }^{ 2 }c{ m }^{ 3 }$

(d)

None of these

56. The length of a rod is $\left( 11.05\pm 0.2 \right)$cm. What is the length of the two rods?

(a)

$\left( 22.1\pm 0.05 \right)$cm

(b)

$\left( 22.1\pm 0.1 \right)$cm

(c)

$\left( 22.10\pm 0.05 \right)$cm

(d)

$\left( 22.10\pm 0.2 \right)$cm

57. The radius of a ball is $\left( 5.2\pm 0.2 \right)$cm. The percentage error in the volume of the ball is approximately

(a)

11%

(b)

4%

(c)

7%

(d)

9%

58. A physical quantity Q is calculated according to the expression $Q=\frac { { A }^{ 3 }{ B }^{ 3 } }{ C\sqrt { D } }$ If percentage errors in A,B,C,D are 2%, 1% 3% and 4% respectively. What is the percentage error in Q?

(a)

$\pm$8%

(b)

$\pm$10%

(c)

$\pm$14%

(d)

$\pm$12%

59. A body travels uniformly a distance of (13.8$\pm$0.2) m in a time (4.0$\pm$0.3) s. The velocity of the body within error limit is

(a)

​​​​​​(3.45$\pm$0.2)$m{ s }^{ -1 }$

(b)

(3.45$\pm$0.3)$m{ s }^{ -1 }$

(c)

(3.45$\pm$0.4)$m{ s }^{ -1 }$

(d)

(3.45$\pm$0.5)$m{ s }^{ -1 }$

60. The values of two resistors are $\left( 5.0\pm 0.2 \right) ㏀$ and $\left( 10.0\pm 0.1 \right) ㏀$. What is the percentage error in the equivalent resistance when they are connected in parallel?

(a)

2%

(b)

5%

(c)

7%

(d)

10%

61. A cuboid has volume $V=l\times 2l\times 3l$, 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 of V is

(a)

18%

(b)

6%

(c)

3%

(d)

1%

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

(a)

$3.6\times { 10 }^{ 4 }$J

(b)

$3.6\times { 10 }^{ 6 }$J

(c)

$7.3\times { 10 }^{ 6 }$J

(d)

None of these

63. With usual notation, the following equation, said to give the distance covered in the nth second i.e., ${ S }_{ n }=u+a\frac { (2n-1) }{ 2 }$is

(a)

numerically correct only

(b)

dimensionally correct only

(c)

both dimensionally and numerically only

(d)

neither numerically nor dimensionally correct

64. A quantity is given by $X=\frac { { \varepsilon }_{ 0 }lV }{ t }$, where V is the potential difference and l is the length. Then, X has dimensional formula same as that of

(a)

resistance

(b)

charge

(c)

voltage

(d)

current

65. The random error in the arithmetic means of 100 observations is x, then random error in the arithmetic mean of 400 observation would be

(a)

$4x$

(b)

$\frac { 1 }{ 4 } x$

(c)

$2x$

(d)

$\frac { 1 }{ 2 } x$

66. Given that $\int { \frac { dx }{ \sqrt { 2ax-{ x }^{ 2 } } } } ={ a }^{ n }\sin ^{ -1 }{ \left[ \frac { x-a }{ a } \right] }$ where a=constant. Using dimensior al analysis, the value of n is

(a)

1

(b)

zero

(c)

-1

(d)

None of these

67. If E=energy, g=gravitational constant, I=impulse and M=mass, then dimensions of $\frac { GI{ M }^{ 2 } }{ { E }^{ 2 } }$ are same as that of

(a)

time

(b)

mass

(c)

length

(d)

force

68. If force F, length L and time T are taken as fundamental units, the dimensional formula for mass will be

(a)

$\left[ F{ L }^{ -1 }{ T }^{ 2 } \right]$

(b)

$\left[ F{ L }^{ }{ T }^{ -2 } \right]$

(c)

$\left[ F{ L }^{ -1 }{ T }^{ -1 } \right]$

(d)

$\left[ F{ L }^{ 5 }{ T }^{ 2 } \right]$

69. Given that $y=A\quad sin\left[ \left( \frac { 2\pi }{ \lambda } \left( ct-x \right) \right) \right]$ , where y and x are measured in metre. Which of the following statements is true?

(a)

The unit of $\lambda$ is same as that of x and A

(b)

The unit of $\lambda$ is same as that of x but not of A

(c)

The unit of c is same as that of $\frac { 2\pi }{ \lambda }$

(d)

The unit of  (ct-x) is same as that of $\frac { 2\pi }{ \lambda }$

70. The frequency of vibration of string is given by $f=\frac { p }{ 2I } { \left[ \frac { F }{ m } \right] }^{ { 1 }/{ 2 } }$. Here, p is number of segments in the string and l is the length. The dimensional formula for m will be

(a)

$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ -1 } \right]$

(b)

$\left[ { M }^{ }{ L }^{ 0 }{ T }^{ -1 } \right]$

(c)

$\left[ { M }^{ }{ L }^{ -1 }{ T }^{ 0 } \right]$

(d)

$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 } \right]$

71. The sI unit of activity of a radioactive sample is

(a)

Curie

(b)

Rutherford

(c)

Becquerel

(d)

Millicurie

72. SI unit of power is

(a)

Joule

(b)

Erg

(c)

Newton

(d)

Watt

73. The SI unit of thermal conductivity is

(a)

$Js{ m }^{ -1 }{ K }^{ -1 }$

(b)

${ W}^{ -1 }{ m }^{ -1 }{ K }^{ -1 }$

(c)

${ W}^{ }{ m }^{ -1 }{ K }^{ -1 }$

(d)

${ W}^{ }{ m }^{ -2 }{ K }^{ -1 }$

74. Surface tension has the same dimensions as that of

(a)

coefficient of viscosity

(b)

impulse

(c)

momentum

(d)

spring constant

(e)

frequency

75. The dimension of impulse is

(a)

$\left[ { ML }^{ }{ T }^{ -{ 1 }} \right]$

(b)

$\left[ { ML }^{ { 2 } }{ T }^{ -{ 1 }} \right]$

(c)

$\left[ { ML }^{ -{ 1 } }{ T }^{ -{ 1 } } \right]$

(d)

$\left[ { M}^{ }{ T }^{ -{ 1 } } \right]$

76. If C be the capacitance and V be the electric potential, then the dimensional formula of $C{ V }^{ 2 }$is

(a)

$\left[ M{ L }^{ 2 }{ T }^{ -2 }{ A }^{ 0 } \right]$

(b)

$\left[ M{ L }^{ }{ T }^{ -2 }{ A }^{ -1 } \right]$

(c)

$\left[ { M}^{ 0 }{ L }^{ }{ T }^{ -2 }{ A }^{ 0 } \right]$

(d)

$\left[ { M}^{ }{ L }^{ -3 }{ T }^{ }{ A }^{ } \right]$

77. What is the dimension of surface tension?

(a)

$\left[ M{ L }^{ }{ T }^{ 0 } \right]$

(b)

$\left[ M{ L }^{ }{ T }^{ -1 } \right]$

(c)

$\left[ M{ L }^{ 0 }{ T }^{ -2 } \right]$

(d)

$\left[ M{ L }^{ 0}{ T }^{ -2 } \right]$

78. The unit of magnetic moment is

(a)

$T{ J }^{ -1 }$

(b)

$J{ T}^{ -1 }$

(c)

$A{ m }^{ -2 }$

(d)

$A{ m }^{ -1 }$

79. Unit of electrical conductivity is

(a)

ohm

(b)

siemen

(c)

m/mho

(d)

mho/m

80. From the dimensional consideration which of the following equation is correct?

(a)

$T=2\pi \sqrt { \frac { { R }^{ 3 } }{ GM } }$

(b)

$T=2\pi \sqrt { \frac { GM } {{ R }^{ 3 } }}$

(c)

$T=2\pi \sqrt { \frac { GM } {{ R }^{ 2 } }}$

(d)

$T=2\pi \sqrt { \frac { { R }^{ 2 } }{ GM } }$

81. If force F, length L and time T be considered fundamental units, then units of mass will be

(a)

$\left[ FL{ T }^{ -2 } \right]$

(b)

$\left[ F{ L }^{ -2 }{ T }^{ -1 } \right]$

(c)

$\left[ F{ L }^{ -1 }{ T }^{ 2 } \right]$

(d)

$\left[ { F }^{ 2 }{ L }{ T }^{ -2 } \right]$

82. Dimensions of capacitance is

(a)

$\left[ { M }^{ -1 }{ { L }^{ -2 } }{ T }^{ 4 }{ A }^{ 2 } \right]$

(b)

$\left[ { M }^{ }{ { L }^{ } }{ T }^{ -3 }{ A }^{ -1 } \right]$

(c)

$\left[ { M }^{ }{ { L }^{ 2 } }{ T }^{ -3 }{ A }^{-1 } \right]$

(d)

$\left[ { M }^{ -1 }{ { L }^{ -2 } }{ T }^{ 3 }{ A }^{ -1 } \right]$

83. A uniform wire of length L, diameter D and density $\rho$ is stretched under a tension T. The correct relation between its fundamental frequency f, the length L and the diameter D is

(a)

$f\propto \frac { 1 }{ LD }$

(b)

$f\propto \frac { 1 }{ L\sqrt { D } }$

(c)

$f\propto \frac { 1 }{ { D }^{ 2 } }$

(d)

$f\propto \frac { 1 }{L { D }^{ 2 } }$

84. The dimensions of resistance are same as those of.......... where h is the Planck's constant, e is the charge.

(a)

$\frac { { h }^{ 2 } }{ { e }^{ 2 } }$

(b)

$\frac { { h }^{ 2 } }{ { e }^{ } }$

(c)

$\frac { { h }^{ } }{ { e }^{ 2 } }$

(d)

$\frac { { h }^{ } }{ { e }^{ } }$

85. The equation of state of some gases can be expressed as $\left( p+\frac { a }{ { V }^{ 2 } } \right) (V-b)=RT$ where, p is absolute the pressure, V is the volume, T is absolute temperature and a and b are constants. The dimensional formula of a is

(a)

$\left[ { M }^{ }{ L }^{ 5 }{ T }^{ -2 } \right]$

(b)

$\left[ { M }^{ -1 }{ L }^{ 5 }{ T }^{ -2 } \right]$

(c)

$\left[ { M }^{ }{ L }^{ -1 }{ T }^{ -2 } \right]$

(d)

$\left[ { M }^{ }{ L }^{ -5 }{ T }^{ -2 } \right]$

86. The relation $p=\frac { \alpha }{ \beta } { e }^{ -\frac { \alpha Z }{ k\theta } }$, where p is pressure, Z is distance, k is Boltzmann constant and $\theta$ is temperature. The dimensional formula of $\beta$ will be

(a)

$\left[ { M }^{ 0 }{ L }^{ 2 }{ T }^{ 0 } \right]$

(b)

$\left[ { M }^{ }{ L }^{ 2 }{ T }^{ } \right]$

(c)

$\left[ { M }^{ }{ L }^{ 0 }{ T }^{ -1} \right]$

(d)

$\left[ { M }^{ 0 }{ L }^{ 2 }{ T }^{ -1 } \right]$

87. The dimension of electromotive force in terms of current A is

(a)

$\left[ { M }{ L }^{ -2 }{ A }^{ -2 } \right]$

(b)

$\left[ { { M } }{ L }^{ 2 }{ { T }^{ -2 }A }^{ -2 } \right]$

(c)

$\left[ { { M } }{ L }^{ 2 }{ { T }^{ -2 }A }^{ -2 } \right]$

(d)

$\left[ { { M } }{ L }^{ 2 }{ { T }^{ -3 }A }^{ -1 } \right]$

88. The dimensional formula of $\frac { 1 }{ { \mu }_{ 0 }{ \varepsilon }_{ 0 } }$is

(a)

$\left[ { M }^{ 0 }{ L}{ T }^{ -2 } \right]$

(b)

$\left[ { M }^{ 0 }{ L }^{ -2 }{ T }^{ -2 } \right]$

(c)

$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ -1 } \right]$

(d)

$\left[ { M }^{ 0 }{ L }^{ 2 }{ T }^{ -2 } \right]$

89. If $p=\frac { RT }{ V-b } { e }^{ -{ \alpha V }/{ RT } }$, then dimensional formula of $\alpha$ is

(a)

p

(b)

R

(c)

T

(d)

V

90. Velocity v is given by $v=a{ t }^{ 2 }+bt+c$, where t is time. What are the dimensions of a, b and c respectively?

(a)

$\left[ L{ T }^{ -3 } \right]$$\left[ L{ T }^{ -2 } \right]$and $\left[ L{ T }^{ -1 } \right]$

(b)

$\left[ L{ T }^{ -1 } \right]$$\left[ L{ T }^{ -2 } \right]$and $\left[ L{ T }^{ -3 } \right]$

(c)

$\left[ L{ T }^{ -2 } \right]$$\left[ L{ T }^{ -3 } \right]$and $\left[ L{ T }^{ -1 } \right]$

(d)

$\left[ L{ T }^{ -1 } \right]$$\left[ L{ T }^{ -3 } \right]$and $\left[ L{ T }^{ -2 } \right]$

91. If E,M,L and G denote energy, mass, angular momentum and gravitation constant respectively, then the quantity $\left( { { E }^{ 2 }{ L }^{ 2 } }/{ { M }^{ 5 }{ G }^{ 2 } } \right)$ has the dimensions of

(a)

angle

(b)

length

(c)

mass

(d)

None of these

92. A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 10%, then the rate of flow of liquid will change nearly by

(a)

+10%

(b)

+46%

(c)

-10%

(d)

-40%

93. If momentum is increased by 20%, then kinetic energy increase by

(a)

48%

(b)

44%

(c)

40%

(d)

36%

94. If increase in linear momentum of a body is 50%, then change in its kinetic energy is

(a)

25%

(b)

125%

(c)

150%

(d)

50%

95. At constant temperature, the volume of a gas is to be decreased by 4%. The pressure must be increased by

(a)

4%

(b)

4.16%

(c)

8%

(d)

3.86%

96. Choose the incorrect statement out of the following.

(a)

Every measurement by any measuring instrument has some errors

(b)

Every calculated physical quantity that is based on measured values has some error

(c)

A measurement can have more accuracy but less precision and vice versa

(d)

The percentage error is different from relative error

97. Which one of the following quantities has not been expressed in proper units?

(a)

Torque Newton metre

(b)

Stress Newton metre${ }^{ -2 }$

(c)

Modulus of elasticity Newton metre${ }^{ -2 }$

(d)

Power Newton metre/second${ }^{ -1 }$

(e)

Surface tension Newton metre${ }^{ -2 }$

98. The unit of specific conductivity is

(a)

${ \Omega -cm }^{ -1 }$

(b)

${ \Omega -cm }^{ -2 }$

(c)

${ \Omega^{ -1 } -cm }$

(d)

${ { \Omega }^{ -1 }-cm }^{ -1 }$

99. An object is moving through the liquid. The viscous damping force action on it is proportional to the velocity. Then dimensional formula of constant of proportionality is

(a)

$\left[ { M }^{ }{ L }^{ -1}{ T }^{ -1 } \right]$

(b)

$\left[ { M }^{ }{ L }^{ }{ T }^{ -1 } \right]$

(c)

$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ -1 } \right]$

(d)

$\left[ { M }^{ }{ L }^{ 0 }{ T }^{ -1 } \right]$

100. By what percentage should the pressure of a given mass of a gas be increased, so as to decrease its volume by 10% at a constant temperature?

(a)

5%

(b)

7.2%

(c)

12.5%

(d)

11.1%

101. Percentage error in the measurement of mass and speed are 2% and 3% respectively. The error in the estimation of kinetic energy obtained by measuring mass and speed will be

(a)

12%

(b)

10%

(c)

2%

(d)

8%

102. If the length of a seconds pendulum is increased by 2% then in a day the pendulum

(a)

loses 764 s

(b)

loses 924 s

(c)

gains 236 s

(d)

loses 864 s

(e)

gains 346 s

103. The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is

(a)

663.821

(b)

664

(c)

663.8

(d)

663.82

104. The numbers 2.745 and 2.735 on rounding off to 3 Significant figures will give

(a)

2.75 and 2.74

(b)

2.74 and 2.73

(c)

2.75 and 2.73

(d)

2.74 and 2.74

105. The mass and volume of a body are 4.237 g and 2.5 cm3, respectively. The density of the material of the body in correct significant figures is

(a)

1.6048 g cm-3

(b)

1.69 g cm-3

(c)

1.7 g cm-3

(d)

1.695 g cm-3

106. Measure of two quantities along with the precision of respective measuring instrument is A = 2.5ms-1 ± 0.5ms-1, B = 0.10 s ± 0.01 s, The value of AB will be

(a)

(0.25 ± 0.08) m

(b)

(0.25 ± 0.5) m

(c)

(0.25 ± 0.05) m

(d)

(0.25 ± 0.135) m

107. The mean length of an object is 5 ern. Which of the following measurements is most accurate?

(a)

4.9 cm

(b)

4.805 cm

(c)

5.25 cm

(d)

5.4 cm

108. Young's modulus of steel is 1.9$\times$1011 Nm-2. When expressed in CGS units of dyne/cm2 ,It will be equal to (1N = 105 dyne,1m2 = 104 cm2)

(a)

$1.9\times 10^{ 10 }$

(b)

$1.9\times 10^{ 11 }$

(c)

$1.9\times 10^{ 12 }$

(d)

$1.9\times 10^{ 13 }$

109. You measure two quantities as A = 1.0 rn ± 0.2 m, B = 2.0m ± 0.2 m, We should report correct value for $\sqrt { AB }$ as

(a)

1.4m ± 0.4m

(b)

1.41m ± 0.15m

(c)

1.4 m ± 0.3 m

(d)

1.4m ± 0.2m

110. In terms of time t and distance x, the force F is given by F = Asin Ct + B cosDx, then dimensions of $\frac { A }{ B }$ and $\frac { C }{ D }$ are given by

(a)

[M0L0T2], [M0LT-1]

(b)

[MLT-2], [M0L0T-1]

(c)

[MLT-2], [M0L-1T0]

(d)

[M0LT-1], [M0L0T0]]

111. The scalar quantity among the following is

(a)

weight of body

(b)

(c)

elementary area

(d)

magnetic field strength

(e)

electric potential

112. The wrong unit conversion among the following is

(a)

1 angstrom = 10-10m

(b)

1 fermi = 10-15m

(c)

1 light year = 9.46 $\times$ 1015m

(d)

1 parsec = 3.08 $\times$ 1016m

(e)

1 astronomical unit = 1.496 $\times$ 10-11m

113. The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)" and (average velocity)m of the liquid. Which one of the following relation is correct?

(a)

m = n

(b)

m = - n

(c)

m2 = n

(d)

m = - n2

114. The ratio of the dimensions of Planck's constant and that of moment of inertia has the dimensions of

(a)

angular momentum

(b)

time

(c)

velocity

(d)

frequency

115. In terms of basic units of mass (M), length (L), time (T) and charge (Q), the dimensions of magnetic permeability of vacuum (${ \mu }_{ 0 }$) would be

(a)

[MLQ-2]

(b)

[LT-1Q-1]

(c)

[ML2T-1Q-2]

(d)

[LTQ-1]

116. The dimensional formula for electric flux is

(a)

[ML3I-1T-3]

(b)

[M2L2I-1T-2]

(c)

[ML3I1T-3]

(d)

[ML-3I-1T-3]

117. If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

(a)

[Ev-2T-1]

(b)

[Ev-1T-2]

(c)

[Ev-2T-2]

(d)

[E-2v-1T-3]

118. The three physical quantities x,  y and z have units g cm2 ,g s-1 and cms-2 ,respectIvely. The relation between x, y and z is

(a)

x = yz2

(b)

x = y2z

(c)

y2 = x z

(d)

z = xy

119. The unit of universal gas constant is

(a)

watt / K

(b)

dyne / $^{ \circ }C$

(c)

erg/K

(d)

newton / $^{ \circ }R$

120. Unit of emf is

(a)

joule / ampere

(b)

volt / ampere

(c)

$\frac { henry-ampere }{ second }$

(d)

Joule/coulomb

121. The dimensional formula for Reynold's number is

(a)

[L0M0T0]

(b)

[LMT]

(c)

[L-1MT]

(d)

[LMT-1]

122. The relation between force F and density d is F =$\frac { x }{ \sqrt { d } }$. The dimension of x is

(a)

[L-1/2M3/2T-2]

(b)

[L-1/2M1/2T-2]

(c)

[L-1M3/2T-2]

(d)

[L-1M1/2T-2]

123. In which of the following pairs, the two physical quantities have different dimensions?

(a)

Planck's constant and angular momentum

(b)

Impulse and linear momentum

(c)

Moment of inertia and moment of a force

(d)

Energy and torque

124. If the absolute errors in two physical quantities A and B are a and b respectively, then the absolute error in the value of A-B is

(a)

b-a

(b)

a$\neq$b

(c)

a+b

(d)

a-b

125. If force (F), velocity (v) and time (1) are taken as fundamental units, then the dimensions of mass is

(a)

[FvT-1]

(b)

[FvT-2]

(c)

[Fv-1T-1]

(d)

[Fv-1T]

126. If the unit of force is kN, the length is 1 km and time 100 s, then what will be the unit of mass?

(a)

1000 kg

(b)

1 kg

(c)

10000 kg

(d)

100 kg

127. The dimensional formula of magnetic flux is

(a)

$\left[ ML^{ 2 }T^{ -2 }A^{ -1 } \right]$

(b)

$\left[ ML^{ 2 }T^{ -3 }A^{ -1 } \right]$

(c)

$\left[ M^{ -1 }L^{ -2 }T^{ 2 }A \right]$

(d)

$\left[ ML^{ 3 }T^{ -2 }A^{ -1 } \right]$

128. The dimensional formula for electric field is

(a)

[ML2T-3A-1]

(b)

[ML2T-3A-2]

(c)

[MLT-3A-1]

(d)

[M0L0T0A0]

129. If n denotes a positive integer, h the Planck's constant, q the charge and B the magnetic field, then the quantity $\left[ \frac { nh }{ 2\pi qB } \right]$ has the dimension of

(a)

area

(b)

length

(c)

speed

(d)

acceleration

130. In an experiment four quantities a, b, c and dare measured with percentage error 1%, 2%, 3% and 4%, respectively. Quantity P is calculated as follows $P=\frac { a^{ 2 }{ b }^{ 2 } }{ cd }$%, Error in P is

(a)

14%

(b)

10%

(c)

7%

(d)

4%

131. Which of the following physical quantity unit is not a fundamental unit?

(a)

Length

(b)

Mass

(c)

Magnetic field

(d)

Current

132. The dimensional formula for rate of doing work is

(a)

[ML2T-3]

(b)

[ML-3T2]

(c)

[M2L2T2]

(d)

[MLT-2]

(e)

[M3L3T3]

133. The density of glass is 2.8 gram/cc in CGS system. The value of density in SI unit is

(a)

2.8$\times$10-3

(b)

2.8$\times$10-2

(c)

2.8$\times$102

(d)

2.8$\times$106

(e)

2.8$\times$103

134. The dimensional formula of electric potential

(a)

[ML2T-3A-1]

(b)

[M-1L2T-2A]

(c)

[M-1L2T-2A-1]

(d)

[ML2T-2A]

135. In the equation$\left( \frac { 1 }{ p\beta } \right) =\frac { y }{ { k }_{ B }T }$ , where p is the pressure, y is the distance, kB is Boltzmann constant and T is the temperature. Dimensions of  $\beta$ are

(a)

[M-1L1T2]

(b)

[M0L2T0]

(c)

[M1L-1T-2]

(d)

[M0L0T0]

136. Which one of the following is not correct?

(a)

Dimensional formula of thermal conductivity (K) is [M1L1T-3K-1]

(b)

Dimensional formula of potential (V) is [M1L2T3A-1]

(c)

Dimensional formula of permeability of free space $\left( { \mu }_{ 0 } \right)$ is [M1L1T-2A-2]

(d)

Dimensional formula of RC is [M0L0T-1]

137. A physical quantity X is defined by the formula $X=\frac { { IFv }^{ 2 } }{ { WL }^{ 3 } }$where I is moment of inertia, F is force, v is velocity, W is work and L is length, the dimensions of X are

(a)

[MLT-2]

(b)

[MT-2]

(c)

[ML2T-3]

(d)

[LT-1]

138. A physical quantity X is given by
$\\ \\ X=\frac { { 2k }^{ 3 }{ l }^{ 2 } }{ m\sqrt { n } }$
The percentage error in the measurements of k, l, m, and n are 1%,2%,3% and 4%, respectively. The value of X is uncertain by

(a)

8%

(b)

10%

(c)

12%

(d)

None of these

139. The quantities A and B~are related, by the relation, m = A/B, where m i~.th'J'linear density and A is the force. The dimensions of B are of

(a)

pressure

(b)

latent heat

(c)

work

(d)

None of these