8/6/2019 xi test

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UNITS, DIMENSIONS, ERRORS AND VECTORS

1. One nanometre is equal to

(a) mm109 (b) mm10 6 (c) mm107 (d) mm10

9

2. The unit of temperature in .I.S system is

(a) Degree centigrade (b) Degree Celsius (c) Kelvin (d) Degree Fahrenheit

3. Which of the following is NOT the unit of energy ?

(a) Nm (b) J (c) Wh (d) kW

4. Temperature can be expressed as a derived unit in terms of

(a) Mass & length (b) Length & time (c) Mass, length & time (d) none of the above

5. Which of the following is the unit of latent heat ?

(a) J (b)1moleJ (c) 1kgJ (d) 11molkgJ

6. The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pairs

(a) Torque and work (b) Angular momentum and work

(c) Energy and Young's modulus (d) None of the above

7. Which of the following have the same dimensions as r/v2 ? Here v is the speed of the particle describing a circular path of radius r .

(a) Acceleration (b) Momentum (c) Force (d) Impulse

8. Given that g is acceleration due to gravity and R is the radius of the earth. Then2/1]R/g[ possesses the dimensions of

(a) Orbital speed (b) Angular speed (c) Escape velocity (d) Time period

9. The dimensional formula for .s.m.r . (root mean square) velocity is

(a) 1oLTM (b) 2oo TLM

(c) 1oo TLM (d) 3MLT

10. The intensity of a wave is defined as the energy transmitted per unit area per second. Which of the following represents the dimensional

formula for the intensity of the wave ?

(a) 2MT (b) 3MT (c) 1MT (d) TML4

11. The frequency of oscillation of a stretched string is given byl2

1f =

2/1]/F[ . Here =l length and =F force.

What is the dimensional formula for ?(a) 1MLT (b)

01TML (c) 001 TLM (d) 000 TLM

12. Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by22

Ax

BxK = . The dimensions ofB

are the same as that of

(a) time/work (b) distancework (c) distancework/ (d) timework

13. In the relation )kxt(cosay = , the dimensional formula for k is

(a) LTM0 (b) 010 TLM (c) 10LTM (d) 110 TLM

14. Given that the displacement of an oscillating particle is given by ]DCtBx[sinAy = . The dimensional formula of ( )ABCD is

(a) 010 TLM (b)100 TLM (c) 110 TLM (d) 000 TLM

Chapter - 1

BY:- Er.chandan singh

8/6/2019 xi test

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15. The equation of state of some gases can be expressed as ( ) RTbVV

ap

2=

+ . Here, p is the pressure, V the volume, T the

absolute temperature, and R,b,a are constants. The dimensions of ' a ' are

(a) 25

TML

(b) 21

TLM

(c) 030

TLM(d) 060

TLM

16. Suppose, the torque acting on a body is given by = /MIKL . Where =L angular momentum, =I moment of inertia, =

angular speed. The dimensional formula forKM is same as that for

(a) 2time (b) 4time (c) 2time (d) 4time

17. The dimensions of voltage in terms ofMLTA are

(a) 132 ATML (b)232 ATML (c) 132 ATML (d) ATML

32

18. If force ( )F , acceleration ( )A , time ( )T are used as fundamental units, the dimensional formula for length will be

(a) 20ATF (b) 20TFA (c) 02TFA (d) FAT

19. If area ( )A , velocity ( )V and density ( )D are taken as the fundamental units, what is the dimensional formula for force ?

(a) DAV2 (b) VDA2 (c)2DVA (d) DVA

20. Energy E , velocity V and time T are taken as the fundamental units. What is the dimensional formula for energy per unit area ?

(a) EVT (b)11 TEV (c) 22 TEV (d) 21 TEV

21. The least count of instrument is .cm01.0 Taking all precautions, the most permissible error in the measurement can be

(a) cm005.0 (b) cm001.0 (c) cm01.0 (d) cm02.0

22. Error in the measurement of radius of a sphere is %.1 Then error in the measurement of volume is

(a) %1 (b) %5 (c) %3 d) 8 %

23. The percentage errors in the measurement of mass and speed are %1 and %2 respectively. What is the percentage error in the kinetic

energy ?

(a) %5 (b) %5.2 (c) %3 (d) %5.1

24. An experiment measures quantities c,b,a and then x is calculated as .c/abx32

=

If the percentage errors in c,b,a are %3%,1 and %2 respectively,, the percentage error in x can be

(a) %13 (b) %7 (c) %4 (d) %1

25. If b/ax = and a and b are the errors in the measurement ofa and b respectively, then the maximum percentage error in thevalue of x will be

(a) 100b

b

a

a

+

(b) 100b

b

a

a

(c) 100ba

b

ba

a

+

(d) 100ba

b

ba

a

26. If bax = and a and b are the errors in the measurement of a and b respectively, then the maximum percentage error in thevalue of x will be

(a) 100b

b

a

a

+

(b) 100b

b

a

a

(c) 100ba

b

ba

a

+

(d) 100ba

b

ba

a

BY:- Er.chandan singh

8/6/2019 xi test

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27. What is the number of significant figures in 0310.0 ?

(a) 2 (b) 3 (c) 4 (d) 5

28. What is the number of significant figures in 0.200 ?

(a) 1 (b) 2 (c) 3 (d) 4

29. What is the number of significant figures in 310310.0 ?(a) 2 (b) 3 (c) 4 (d) 6

30. Which of the following expresses the most accurate measurement of length of a rod ?

(a) mm0.500 (b) mm500 (c) cm50 (d) m5.0

31. The diameter of a wire is measured with a screw gauge having least count mm01.0 . Which of the following correctly expresses the

diameter?

(a) cm20.0 (b) m002.0 (c) mm00.2 (d) cm2.0

32. What is the number of significant figures in 510)80.420.3( + ?

(a) 5 (b) 4 (c) 3 (d) 2

33. Taking into account the significant figures, what should be the value of 0099.099.9 ?

(a) 9999.9 (b) 00.10 (c) 0.10 (d) 10

34. If the value of r is 845.10 ohm and the value of current is 23.3 amp., the potential is 02935.35 . Its value in significant number would be

(a) V50.3 (b) V0.35 (c) V029.35 (d) V030.35

35. The volume of one sphere is cc76.1 . The volume of25 such spheres (according to the idea of significant figure) is

(a) cc00.44 (b) cc0.44 (c) cc44 (d) cc100.44 2

36. What is the angle between kji ++ and i ?

(a) 6/ (b) 4/ (c) 3/ (d) none of the above

37. A point of application of a force k2j3i5F +=r

is moved from k4j7i2r1 ++=r

to k3j2i5r2 ++=r

. The work done is

(a) 22 units (b) 22 units (c) 11 units (d) 0 units.

38. The vector sum ofn coplanar forces, each of magnitude F , when each force is making an angle of n/2 with the proceeding one, is

(a) zero (b) nF (c) 2/F (d) 2/nF

39. Out of the following sets of forces, the resultant of which cannot be zero

(a) 10,10,10 (b) 20,10,10 (c) 20,20,10 (d) 40,20,10

40. A vector of magnitude a is rotated through angle . What is the magnitude of the change in the vector ?

(a) 2/sina2 (b) 2/cosa2 (c) sina2 (d) cosa2

BY:- Er.chandan singh

8/6/2019 xi test

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ANSWERS

1. b 2. c 3. d 4. d 5. c 6. a 7. a 8. b 9. a 10. b

11. b 12. b 13. b 14. b 15. a 16. d 17. c 18. a 19. a 20. c

21. a 22. c 23. a 24. a 25. a 26. c 27. b 28. d 29. b 30. a

31. c 32. c 33. b 34. b 35. b 36. d 37. a 38. a 39. d 40. a

41. c 42. b 43. c 44. c 45. d

41. The vectors A and B are such that |BA||BA|rrrr

=+ . Then the angle between the two vectors wil l be

(a) o0 (b)o60 (c) o90 (d)

o180

42. Given that QPQP rrrr =+ . This can be true when

(a) 0Prr

= (b) 0Qrr

=

(c) neitherPr

norQr

is a null vector (d) Pr

is perpendicular to Qr

43. Given that RQPrrr

=+ and 222 RQP =+ . The angle between Pr

and Qr

is

(a) 0 (b) 4/ (c) 2/ (d)

44. Given that RQPrrr

=+ . Also, RQP == . What should be the angle between Pr

and Qr

?

(a) 0 (b) 3/ (c) 3/2 (d)

45. Three vectors B,Arr

and Cr

satisfy the relation 0BA =rr

and 0CA =rr

. The vectorAr

is parallel to

(a) B (b) C (c) CBrr

(d) CBrr

BY:- Er.chandan singh