# Problems For IIT- JEE (Mains)

Vectors

Only one choice is Correct

1. Which of the following is a vector:

(a) Energy (b) Power (c) Force (d) Mass

2. Identify the vector quantity:

(a) Time (b) Work (c) Heat (d) Angular momentum

3. Which of the following quantities is a vector:

(a) Displacement (b) Density (c) Volume (d) Temperature

4. Which of the following can be a vector:

(a) Area (b) Volume (c) Length (d) Pressure

5. Which of the following quantities is a vector:

(a) Mass of a radium nucleus (b) Charge on a proton (c) Wind velocity (d) Energy of a thermal neutron

6. Which of the following is not a vector:

(a) Linear momentum (b) Electric field (c) Kinetic energy (d) Acceleration

7. Identify the scalar quantity

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

8. Which of the following quantities is a scalar:

(a) Electric field (b) Electrostatic potential (C) Magnetic momentum (d) Acc.due to gravity

9. Angular momentum is:

(a) A scalar (b) A polar vector (c) An axial vector (d) A liner momentum

10 When a mass is rotating in a plane about a fixed point its angular momentum is directed along:

(a) The radius (b) The tangent to the orbit (c) The axis of rotation (d) Line at an angle of 450 to the axis of rotation

11 Angular displacement is:

(a) A scalar (c) A vector (b) Either (d) Neither

12 Moment of interia is :

(a) A scalar (c) A vector (b) Either (d) Neither

13 For the Fig. 2.37:

(a) A ⃗+B ⃗= C ⃗ (b) B ⃗+C ⃗= A ⃗ (c) C ⃗+A ⃗= B ⃗ (d) A ⃗+B ⃗+C ⃗= 0

14 A vector may change if :

(a) Frame of reference is translated (b) Frame of reference is rotated

(c) Vector is translated parallel to itself (d) Vector is rotated

15 When two vectors A ⃗ and B ⃗ of magnitude a and b are added, the magnitude of the resultant vector is always:

(a) equal to (a+b) (b) Less than (a+b) (c) greater than (a+b) (d) not greater than (a+b)

16 The rectangular components of force of 5 dyne are:

(a) 1 and 2 dyne (b) 2 and 3 dyne (c) 3 and 4 dyne (d) 2.5 and 2.5 dyne

17 To get a resultant displacement of 10m, two displacement vectors, one of magnitude 6 m and another of 8 m, should be combined:

(a) Parallel (b) Anti-parallel (c) At an angle 600 (d) Perpendicular to each

18 If the magnitude of vectors A ⃗, B ⃗ and C ⃗ are 12,5 and 13 units respectively and A ⃗+B ⃗ = C ⃗, the angle between vectors A ⃗ and B ⃗ is:

(a) 0 (b) π (c) π/2 (d) π/4

19 If A ⃗+B ⃗ = C ⃗ and the magnitudes of A ⃗,B ⃗ and C ⃗ are 5,4 and 3 units respectively, the angle between A ⃗ and C ⃗ is:

(a) Cos-1(3/5) (b) Cos-1(4/5) (c) π/2 (d) sin-1(3/4)

20 If two waves of same frequency and same amplitude respectively on superimposition produce a resultant wave of the same amplitude, the waves differ in phase by:

(a) Zero (b) π/4 (c) π/3 (d) 2π/3

21 The angle between (A ⃗ ×B ⃗) and (B ⃗×A) is:

(a) Zero (b) π (c) π/4 (d) π/2

22 The resultant of two equal force is double of either of the forces. The angle between them is:

(a) 1200 (b) 900 (c) 600 (d) 00

23 The resultant of two forces acting at an angle of 1500 is 10 kg wt. and is perpendicular to one of the force. The smaller force is:

(a) 10√3 kg wt (b) 20√3 kg wt (c) 20 kg wt (d) (20√3) kg wt

24 Two vector A ⃗ and B ⃗ are such that |A ⃗+B ⃗ | = |A ⃗-B ⃗ |. The angle between the vectors A ⃗ and B ⃗ is:

(a) 0 (b) π/3 (c) π/2 (d) π

⌈Hint:See solved Problem 4⌉

25 For the resultant of two vectors to be maximum, what must be the angle between them:

(a) 00 (b) 600 (c) 900 (d) 1800

26 Minimum number of unequal coplanar forces whose vector sum can be equal to zero is:

(a) Two (b) Three (c) Four (d) Any

27 Two vectors A ⃗ and B ⃗ lie in a plane, a third vector C ⃗ lies outside this plane, then the sum of these vectors A ⃗+B ⃗+C ⃗ :

(a) Can be zero (b) Can never be zero

(c) Lies in a plane containing A ⃗+B ⃗ (d) Lies in a plane containing A ⃗-B ⃗

28 Two forces of magnitude 7 newton and 5 newton act on a particle at an angle θ to each other, θ can have any value. The minimum magnitude of the resultant force is :

(a) 5 newton (b) 8 Newton (c) 12 Newton (d) 2 Newton

29. Two forces of 4 dyne and 3 dyne act upon a body. The resultant force on the body can only be:

(a) More than 3 dynes (b) More than 4 dynes (c) Between 3 and 4 dyne (d) Between 1 and 7 dyne

30 A force of 6 kg and another of 8 kg can be applied together to produce the effect of a single force of:

(a) 1 kg (b) 11 kg (c) 15 kg (d) 20 kg

31 Out of the following the resultant of which cannnot be 4 newton:

(a) 2 N and 2 N (b) 2 N and 4 N (c) 2N and 6 N (d) 2N and 8 N

32 In case of three vector quantities of same type, where resultant cannot be zero:

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

[Hint: If in a set a quantity has value in between Rmax and R min of remaining two, resultant can be zero ]

33 Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant of these forces will be

(a) Zero (b) 10 N (c) 20 N (d) 10√2 N

34 If n ⃗ is a unit vector in the direction of the vector A ⃗, then:

(a) n ⃗ = A ⃗/|A ⃗ | (b) n ⃗ = A ⃗|A ⃗ | (c) n ⃗ = A ⃗/|A ⃗ | (d) n ⃗ = n ⃗×n ⃗

35 An airplane is moving in a circular path with a sped 250 km/hr, what is the change in velocity in half revolution:

(a) 500 km/hr (b) 250 km/hr (c) 125 km/hr (d) Zero

36 A truck travelling due north at 50 km/hr west and travels at the same speed. What is the change in velocity :

(a) 50 km/hr north-west (b) 50√2 km/hr north-west (c) 50 km/hr south-wes (d) 50√2 km/hr south-west

37 A boat which has speed of 5km/hr in still water crosses a river of width 1 km along the shortest possbile path in 15 mintue. The velocity of the water in km/hr is:

(a) 1 (b) 3 (c) 4 (d) √14

38 A river is following from west to east at a speed of 5m/minute. A man on the south bank of the river, capable of swimming at 10m/minute in still water. Wants to swim the river in the shortest time. He should swim in a direction:

(a) Due north (b) 300 east of north (c) 300 west of north (d) 600 east of north

[HIint: See solved Problem 11]

39 I Started walking down a road to day-break facing the sun. After walking for some time, I turned to my, left, then I turned to the right once again. In which direction was I going then:

(a) East (b) North-west (c) North-east (d) South

40 A man travels 1 mile due east, then 5 mile due south, then 2 mile due east and finally 9 mile due north; how far is the from the starting point:

(a) 3 mile (b) 5 mile (C) 4 mile (D) Between 5 and 9 mile

41 I walked 4 mile, turned to my left and walked 6 mile, then turned to my right again and walk 4 mile . Which of the choice mentoins the distance from the starting points to the place where I stopped:

(a) 15 mile (b) 10 mile (c) 20 mile (d) 14 mile

42. A person moves 30 m north, then 20 m east, then 30√2 m south-west. His displacement from the original positioin is:

(a) 14 m south-west (b) 28 m south (c) 10 m west (d) 15 m east

43. A force F ⃗ = 6I ⃗-(8j) ⃗+10 k ⃗ newton produces and acceleratoin of 1 m/s2 in a body. The mass of body would be:

(a) 200 kg (b) 20 kg (c) 10√2 kg (d) 6√2 kg

44 The angle that the vector A ⃗ = (2i) ⃗+ (3j) ⃗ makes with y- axis is:

(a) tan-1 (3/2) (b) tan-1 (2/3) (c) sin-1 (2/3) (d) cos-1 (3/2)

45 If A ⃗ = (5i) ⃗+(7J) ⃗-(3k) ⃗ and B ⃗ = (2i) ⃗+(2J) ⃗-(ck) ⃗ are perpendicular vectors, the value of c is:

(a) -2 (b) 8 (c) -7 (d) -8

[Hint: Scalar product of perpendicular vectors is zero, i.e, A ⃗.B ⃗ = AxBx+AyBy+AzBz = 0, i.e. 10+14+3c = 0 or c = -8 ]

46 A vector perpendicular to ((4i) ⃗-(3J) ⃗) is:

(a) (4i) ⃗+(3J) ⃗ (b) (7k) ⃗ (c) (6i) ⃗ (d) (3i) ⃗-(4J) ⃗

47 The angle between the two vectors -(2i) ⃗+(3J) ⃗ + k ⃗ and i ⃗+(2J) ⃗-(4k) ⃗ is:

(a) 00 (b) 900 (c) 1800 (d) None

[Hint: θ= cos-1(A ⃗.B ⃗/AB); Here A ⃗.B ⃗ = 0, so θ= 900]

48 The angle between the vectors (i ⃗+J ⃗) and (J ⃗+k ⃗) is:

(a) 900 (b) 1800 (c) 00 (d) 600

49 A body constrained to move in y direction is subjected to a force given by F ⃗ = (-2i ⃗+15J ⃗+6k ⃗) N. what is the work done by this force in moving the body through a distance of 10 m along y-axis:

(a) 190J (b) 160 J (c) 150 J (d) 20 J

50 The torque on a magnet of magnetic moment M ⃗ in a field of induction B ⃗ is:

(a) τ ⃗ = M ⃗×B ⃗ (b) τ ⃗ = B ⃗×M ⃗ (c) τ = M ⃗.B ⃗ (d) τ = -M ⃗.B ⃗

51 A vector F ⃗1 is along the positive x-axis. If its vector product with another vector is zero, F ⃗2 is zero, then F ⃗2 could be:

(a) (4i) ⃗ (b) -((i) ⃗+(j)) ⃗ (c) (j ⃗+(k)) ⃗ (d) -(4j ⃗)

52 What is the torque of the force F ⃗ = ((2i) ⃗-(3j) ⃗+(4k)) ⃗ N acting at the point r ⃗ = ((3i) ⃗-(2j) ⃗+(3k)) ⃗ m about the origin:

(a) (6i) ⃗ – (6J) ⃗+(12k) ⃗ (b) 17i ⃗ – (6J) ⃗+13k ⃗ (c) 6i ⃗ – 6J ⃗+12k ⃗ (d) -17i ⃗ +6J ⃗+13k ⃗

53 In a cockwise system:

(a) J ⃗×k ⃗ = i ⃗ (b) i ⃗×i ⃗ = 0 (c) J ⃗×j ⃗ = 1 (d) k ⃗×i ⃗ = 1

54 The positoin vector of a particle is, r ⃗ = (a cosωt)i ⃗+(a sinωt) J ⃗ The velocity of the particle is:

(a) Parallel to position vector (b) Perpendicular to position vector

(c) Directed towards the origin (d) Directed away from the origion

55 The angles made by the vector 4i ⃗-3j ⃗+5 k ⃗ with z-axis is:

(a) 300 (b) 450 (c) 900 (d) 1200

[Hint: cos θ_Z = Rz/R]

56 A particle of mass m = 5 units is moving with a uniform speed v = 3√2 units in the XOY plane along the ine y = x+4 . The magnitude of the angular momentum of the particle about the origin is:

(a) 60 units (b) 40 √2units (c) Zero (d) 7.5 units

57 If I ⃗ denotes a unit vector along incident light ray, r ⃗ a unit vector along refracted ray into a medicum directed towards incidents medium, the law of refraction is:

(a) i ⃗.n ⃗ = μ(r ⃗.n ⃗) (b) (i ) ⃗×n ⃗ = μ(n ⃗×r ⃗) (c) (i ) ⃗×n ⃗ = μ(n ⃗×n ⃗) (d) (μ(i ) ⃗×n ⃗) = (r ⃗×n ⃗)

58 Three vectors A ⃗,B ⃗ and C ⃗ satisfy the relatoin A ⃗ . B ⃗ = 0 and A ⃗ . C ⃗ = 0 . The vector A ⃗ is parallel to:

(a) B ⃗ (b) C ⃗ (c) B ⃗. C ⃗ (d) B ⃗ ×C ⃗

59 The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is:

(a) 1200 (b) 600 (c) 900 (d) 1500

60 If vectors 2 i ⃗+2j ⃗ -2 k ⃗, 5 i ⃗ +y j ⃗ + k ⃗ and –i ⃗ +2j ⃗ +2 k ⃗ are coplanar, the value of y is:

(a) 81 (b) 36 (c) 23 (d) 9

61 A projectile of mass m is fired with velocity v at an angle of 450 with the horizontal from point A. Neglecting air resistance , the magnitude of change in momentum between the starting point A and the striking point B is:

(a) mv/√2 (b) 2mv (c) √2 mv (d) √2/mv

62 What is the value of liner velocity , if ω ⃗ = 3 i – 4j ̂+k ̂ and r ⃗ = 5 i ̂-6j ̂+6k ̂:

(a) 6 i ̂ + 2 j ̂ -3 k ̂ (b) 6 i ̂ – 2 j ̂ +8 k ̂ (c) 4 i ̂ – 13 j ̂ +6 k ̂ (d) -18 i ̂ – 13 j ̂ +2 k ̂

63 Two force of magnitude 30,60 and P newton acting at a point are in equlibrium if the angle between the first two is 600, the value of P is:

(a) 25√2 (b) 30√3 (c) 30√6 (d) 30√7

**ANSWERS**

1. (c) 2. (d) 3. (a) 4. (a) 5. (c) 6. (c) 7. (c) 8. (b) 9. (c) 10. (c) 11. (c) 12. (d) 13. (c) 14. (d) 15. (d) 16. (c) 17. (d) 18. (c) 19. (a) 20. (d) 21. (b) 22. (d) 23. (c) 24. (c) 25. (a) 26. (b) 27. (b) 28. (d) 29. (d) 30. (b) 31. (d) 32. (d) 33. (a) 34. (a) 35. (a) 36. (d) 37. (b) 38. (a) 39. (a) 40. (b) 41. (b) 42. (c) 43. (c) 44. (b) 45. (d) 46. (b) 47. (b) 48. (d) 49. (c) 50. (a) 51. (a) 52. (b) 53. (a) 54. (b) 55. (b) 56. (a) 57. (c) 58. (d) 59. (a) 60. (c) 61. (c) 62. (d) 63. (d)

Ramanujan Shodh Sansthan

(Mathematical and Physical Sciences)

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