Vector

Easy
1. The vector projection of a vector on y-axis is
10. A hall has the dimensions A fly
(a) 5 (b) 4 starting at one corner ends up at a diametrically opposite
(c)3 (d) Zero corner. What is the magnitude of its displacement
2. Position of a particle in a rectangular-co-ordinate system is (3, (a) 17 m (b) 26 m
2, 5). Then its position vector will be (c) 36 m (d) 20 m
(a) (b)
(c) (d) None of these 11. 100 coplanar forces each equal to 10 N act on a body. Each
force makes angle with the preceding force. What is the
3. If a particle moves from point P (2,3,5) to point Q (3,4,5). Its resultant of the forces
displacement vector be (a) 1000 N (b) 500 N
(a) (b) (c) 250 N (d) Zero
(c) (d)
12. The magnitude of a given vector with end points (4, – 4, 0)
and (– 2, – 2, 0) must be
4. A force of 5 N acts on a particle along a direction making an
angle of 60° with vertical. Its vertical component be (a) 6 (b)
(a) 10 N (b) 3 N (c) 4 (d)
(c) 4 N (d) 2.5 N

5. If and the vector having the 13. The expression is a

same magnitude as B and parallel to A is
(a) Unit vector (b)Null vector
(a) (b)
(c)Vector of magnitude (d)none
(c) (d)
14. Given vector the angle between and y-axis is

6. Vector makes equal angles with x,y and z axis. Value of its (a) (b)
components (in terms of magnitude of ) will be (c) (d)

(a) (b)
15. The unit vector along is
(a) (b)
(c) (d)

(c) (d)
7. If the direction of cosines of the vector
are
16. A vector is represented by . Its length in XY
(a) (b) plane is
(a) 2 (b)
(c) (d)

(c) (d)

17. Five equal forces of 10 N each are applied at one point and all
8. The vector that must be added to the vector and
are lying in one plane. If the angles between them are equal,
so that the resultant vector is a unit vector the resultant force will be
along the y-axis is (a) Zero (b) 10 N
(a) (b) (c) 20 N (d)
(c) (d) Null vector
18. The angle made by the vector with x- axis is
9. How many minimum number of coplanar vectors having (a) 90° (b) 45°
different magnitudes can be added to give zero resultant (c) 22.5° (d) 30°
(a) 2 (b) 3
(c) 4 (d) 5
Vector
Easy
19. Any vector in an arbitrary direction can always be replaced by
two (or three) (c) (d)
(a) Parallel vectors which have the original vector as their
resultant
28. Surface area is
(b) Mutually perpendicular vectors which have the original
vector as their resultant (a) Scalar (b)Vector
(c) Arbitrary vectors which have the original vector as (c) Neither scalar nor vector (d)Both scalar and vector
their resultant
(d) It is not possible to resolve a vector 29. With respect to a rectangular cartesian coordinate system,
three vectors are expressed as
20. Angular momentum is
, and where are
(a) A scalar (b) A polar vector
unit vectors, along the X, Y and Z-axis respectively. The unit
(c) An axial vector (d) None of these
vectors along the direction of sum of these vector is

21. Which of the following is a vector (a) (b)

(a) Pressure (b) Surface tension
(c) Moment of inertia (d) None of these
(c) (d)

22. If then which of the following is NOT correct

(a) (b) 30. The angle between the two vectors and
(c) (d) is
(a) 60° (b) Zero
23. The position vector of a particle is (c) 90° (d) None of these
. The velocity of the particle
is
31. The position vector of a particle is determined by the
(a) Parallel to the position vector
expression
(b) Perpendicular to the position vector
(c) Directed towards the origin The distance traversed in first 10 sec is
(d) Directed away from the origin (a) 500 m (b) 300 m
(c) 150 m (d) 100 m
24. Which of the following is a scalar quantity
(a) Displacement (b) Electric field
32. Unit vector parallel to the resultant of vectors
(c) Acceleration (d) Work
and will be

25. If a unit vector is represented by , then the

(a) (b)
value of ‘c’ is
(a) 1 (b)
(c) (d) None of these
(c) (d)

26. A boy walks uniformally along the sides of a rectangular park

33. The component of vector along the vector
of size 400 m× 300 m, starting from one corner to the other
corner diagonally opposite. Which of the following statement is
is incorrect
(a) (b)
(a) He has travelled a distance of 700m
(b) His displacement is 700 m
(c) (d) 5
(c) His displacement is 500 m
(d)His velocity is not uniform throughout the walk
27. The unit vector parallel to the resultant of the vectors
and is 34. The angle between the two vectors and
will be
(a) (b)
Vector
Easy
(a) 90° (b) 0° 43. A particle is simultaneously acted by two forces equal to 4 N
(c) 60° (d) 45° and 3 N. The net force on the particle is
(a) 7 N (b) 5 N
(c) 1 N (d) Between 1 N and 7 N
35. There are two force vectors, one of 5 N and other of 12 N at
what angle the two vectors be added to get resultant vector of
17 N, 7 N and 13 N respectively 44. Two vectors and lie in a plane, another vector lies
(a) 0°, 180° and 90° (b) 0°, 90° and 180° outside this plane, then the resultant of these three vectors i.e.,
(c) 0°, 90° and 90° (d) 180°, 0° and 90°
(a) Can be zero (b)Cannot be zero
36. If and then magnitude and (c) Lies in the plane containing (d)Lies in the plane
direction of will be containing

(a) (b)
45. If the resultant of the two forces has a magnitude smaller than
(c) (d) the magnitude of larger force, the two forces must be
(a) Different both in magnitude and direction
37. A truck travelling due north at 20 m/s turns west and travels at (b) Mutually perpendicular to one another
the same speed. The change in its velocity be (c) Possess extremely small magnitude
(a) 40 m/sN–W (b) m/s N–W (d) Point in opposite directions
(c) 40 m/s S–W (d) m/sS–W
46. Forces and act on a point mass in two mutually
38. If the sum of two unit vectors is a unit vector, then magnitude perpendicular directions. The resultant force on the point
of difference is mass will be
(a) (b) (a) (b)

(c) (d) (c) (d)

39. and , Value of 47. If the angle between and is

would be (a) 60° (b) 0°
(c) 120° (d) 90°
(a) (b)
(c) (d)
48. Let the angle between two nonzero vectors and be
120° and resultant be
40. An object of m kg with speed of vm/s strikes a wall at an
angle  and rebounds at the same speed and same angle. The (a) must be equal to (b) must be less
magnitude of the change in momentum of the object will be than
(a) (b) (c) must be greater than (d) may be
(c) 0 (d) equal to

49. The magnitude of vector and are respectively 12, 5

and 13 units and then the angle between and
is
(a) 0 (b)
(c) (d)
41. Two forces, each of magnitude F have a resultant of the same
magnitude F. The angle between the two forces is
50. Magnitude of vector which comes on addition of two vectors,
(a) 45° (b) 120°
and is
(c) 150° (d) 60°
(a) (b)
(c) (d)

42. For the resultant of the two vectors to be maximum, what

must be the angle between them 51. A particle has displacement of 12 m towards east and 5 m
towards north then 6 m vertically upward. The sum of these
(a) 0° (b) 60°
displacements is
(c) 90° (d) 180°
(a) 12 (b) 10.04 m
Vector
Easy
(c) 14.31 m (d) None of these 60. The resultant of two vectors A and B is perpendicular to the
vector A and its magnitude is equal to half the magnitude of
52. The three vectors and vector B. The angle between A and B is
(a) 120° (b) 150°
form
(c) 135° (d) None of these
(a) An equilateral triangle (b) Isosceles triangle
(c) A right angled triangle (d) No triangle
61. What vector must be added to the two vectors
53. For the figure and so that the resultant may be a unit vector
(a) along x-axis
(b) (a) (b)

(c) (c) (d)

(d)
62. What is the angle between and the resultant of

54. Let then and

(a) is always greater then (a) Zero (b)

(b) It is possible to have and (c) (d)

(c) C is always equal to A + B
(d) C is never equal to A + B 63. The resultant of and is perpendicular to . What is the
angle between and
55. The value of the sum of two vectors and with as the (a) (b)
angle between them is
(c) (d)
(a) (b)
64. Maximum and minimum magnitudes of the resultant of two
(c) (d) vectors of magnitudes P and Q are in the ratio Which of
the following relations is true
(a) (b)
(c) (d) None of these
56. Following sets of three forces act on a body. Whose resultant
cannot be zero
(a) 10, 10, 10 (b) 10, 10, 20 65. The resultant of two vectors and is If Q is doubled,
(c) 10, 20, 23 (d) 10, 20, 40 the new resultant is perpendicular to P. Then R equals
(a) P (b) (P+Q)
57. When three forces of 50 N, 30 N and 15 N act on a body, then (c) Q (d) (P–Q)
the body is
(a) At rest (b) Moving with a uniform 66. Two forces, and are acting on a body. One force is
velocity double that of the other force and the resultant is equal to the
(c) In equilibrium (d) Moving with an greater force. Then the angle between the two forces is
acceleration (a) (b)
(c) (d)
58. The sum of two forces acting at a point is 16 N. If the
resultant force is 8 N and its direction is perpendicular to
minimum force then the forces are 67. Given that and that is to . Further if
(a) 6 N and 10 N (b) 8 N and 8 N then what is the angle between and
(c) 4 N and 12 N (d) 2 N and 14 N
(a) (b)
59. If vectors P, Q and R have magnitude 5, 12 and 13 units and
the angle between Q and R is (c) (d)

(a) (b)
68. A body is at rest under the action of three forces, two of
(c) (d) which are the third force is
(a) (b)
Vector
Easy
(c) (d)
77. Which pair of the following forces will never give
69. A plane is revolving around the earth with a speed of 100 resultant force of 2 N
km/hr at a constant height from the surface of earth. The (a) 2 N and 2 N (b) 1 N and 1 N
change in the velocity as it travels half circle is
(a)200 km/hr (b) 150 km/hr
(c) 1 N and 3 N (d) 1 N and 4 N
(c) (d) 0
78. Two forces 3N and 2 N are at an angle  such that the
70. What displacement must be added to the displacement resultant is R. The first force is now increased to 6N and the
resultant become 2R. The value of  is
to give a displacement of 7.0 m pointing in
the x- direction (a) 30° (b) 60°
(a) (b) (c) 90° (d) 120°

(c) (d)
79. Three concurrent forces of the same magnitude are in
equilibrium. What is the angle between the forces ? Also
71. A body moves due East with velocity 20 km/hour and then name the triangle formed by the forces as sides
due North with velocity 15 km/hour. The resultant velocity (a) 60° equilateral triangle (b)120° equilateral triangle
(a) 5 km/hour (b) 15 km/hour (c) 120°, 30°, 30° an isosceles triangle(d) 120° an obtuse
(c) 20 km/hour (d) 25 km/hour angled triangle

72. The magnitudes of vectors and are 3, 4 and 5 units 80. If , then angle between and
respectively. If , the angle between and is will be
(a) 90° (b) 120°
(a) (b) (c) 0° (d) 60°

(c) (d) 81. The maximum and minimum magnitude of the resultant
of two given vectors are 17 units and 7 unit
respectively. If these two vectors are at right angles to
73. While travelling from one station to another, a car travels 75 each other, the magnitude of their resultant is
km North, 60 km North-east and 20 km East. The minimum (a) 14 (b) 16
distance between the two stations is
(c) 18 (d) 13
(a) 72 km (b) 112 km
(c) 132 km (d) 155 km
82. The vector sum of two forces is perpendicular to their vector
differences. In that case, the forces
74. A scooter going due east at 10 ms–1 turns right through an (a) Are equal to each other in magnitude
angle of 90°. If the speed of the scooter remains unchanged in (b) Are not equal to each other in magnitude
taking turn, the change is the velocity of the scooter is
(c) Cannot be predicted
(a)20.0 ms–1 south eastern direction(b)Zero
(d) Are equal to each other
(c) 10.0 ms–1 in southern direction(d)14.14 ms–1 in south-
west direction
83. y component of velocity is 20 and x component of velocity is
10. The direction of motion of the body with the horizontal at
75. A person goes 10 km north and 20 km east. What will be this instant is
displacement from initial point
(a) (b)
(a) 22.36 km (b) 2 km
(c) 45° (d) 0°
(c) 5 km (d) 20 km

84. Two forces of 12 N and 8 N act upon a body. The resultant

76. Two forces and force on the body has maximum value of
(a) 4 N (b) 0 N
act on a single point. The
(c) 20 N (d) 8 N
angle between and is nearly
(a) 30° (b) 45° 85. Two equal forces (P each) act at a point inclined to each other
(c) 60° (d) 90° at an angle of 120°. The magnitude of their resultant is
Vector
Easy
(a) (b)
(c) (d) 2P 94. If then the angle between A and B is

(a) / 2 (b
86. The vectors and are added. The magnitude of
/ 3
the sum of these vector is
(c)  (d) / 4
(a) (b) 38
(c) 238 (d) 560
95. If and then value of
will be
87. Two vectors are such that .
Then (a) (b)
(a) (b) (c) (d)
(c) (d)
96. The torque of the force acting at the
88. If a vector is perpendicular to the vector point m about the origin be
. Then the value of is (a) (b)
(c) (d)
(a) –1 (b)

(c) (d) 1
97. If then which of the following statements is
wrong
89. If two vectors and are parallel (a) (b)
to each other then value of  be (c) (d)
(a) 0 (b) 2
(c) 3 (d) 4 98. If a particle of mass m is moving with constant velocity v
parallel to x-axis in x-y plane as shown in fig. Its angular
momentum with respect to origin at any time t will be
90. A body, acted upon by a force of 50 N is displaced through a
distance 10 meter in a direction making an angle of 60° with (a) (b)
the force. The work done by the force be (c) (d)
(a) 200 J (b) 100 J
(c) 300 (d) 250 J 99. Consider two vectors and The
magnitude of the scalar product of these vectors is
91. A particle moves from position to (a) 20 (b) 23
due to a uniform force of (c) (d) 26
If the displacement in meters then work
done will be 100.Consider a vector Another vector that is
(a) 100 J (b) 200 J perpendicular to is
(c) 300 J (d) 250 J (a) (b)
(c) (d)
92. If for two vector and , sum is perpendicular to the
difference . The ratio of their magnitude is 101. Two vectors and are at right angles to each
(a) 1 (b) 2
other, when
(c) 3 (d) None of these
(a) (b)
(c) (d)
93. The angle between the vectors and is The value of
the triple product is 102.If and is finite, then

(a) (b) Zero (a) is parallel to (b)

(c) (d)
Vector
Easy
(c) and are mutually perpendicular(d) (c) 160 J (d) 190 J

112.A particle moves in the x-y plane under the action of a force
such that the value of its linear momentum at anytimet is
103.A force Newton is applied over a particle
The angle between and at
which displaces it from its origin to the point
a given time t. will be
metres. The work done on the particle is
(a) – 7 J (b) +13 J (a) (b)
(c) +7 J (d) +11 J (c) (d)

104.The angle between two vectors and 113.The area of the parallelogram represented by the vectors
is and is
(a) 0° (b) 90° (a) 14 units (b) 7.5 units
(c) 180° (d) None of the above (c) 10 units (d) 5 units

105.The angle between the vectors and is 114.A vector is along the positive X-axis. If its vector product
(a) 30° (b) 45° with another vector is zero then could be
(c) 60° (d) 90°
(a) (b)

106.A particle moves with a velocity under (c) (d)

the influence of a constant force
The instantaneous power 115.If for two vectors and the vectors
applied to the particle is (a) Are perpendicular to each other(b)Are parallel to each
(a) 35 J/s (b) 45 J/s other
(c) 25 J/s (d) 195 J/s (c) Act at an angle of 60° (d)Act at an angle of 30°

107.If then angle between and is 116.The angle between vectors and is
(a) 0° (b) 30° (a) Zero (b) 
(c) 45° (d) 60° (c) (d)

108.A force acting on a body, produces a 117.What is the angle between and
displacement Work done by the force is
(a) 10 units (b) 18 units (a) 0 (b)
(c) 11 units (d) 5 units
(c) (d)
109.The angle between the two vectors and
will be
118.The resultant of the two vectors having magnitude 2 and 3 is
(a) Zero (b) 45° 1. What is their cross product
(c) 90° (d) 180° (a) 6 (b) 3
(c) 1 (d) 0
110.The vector and are
perpendicular to each other. The positive value of a is 119.Let be any vector. Another
(a) 3 (b) 4 vector which is normal to A is
(c) 9 (d) 13
(a) (b)

111.A body, constrained to move in the Y-direction is subjected to (c) (d)

a force given by
What is the work done by this force in moving the body a 120.The angle between two vectors given by and
distance 10 m along the Y-axis is
(a) 20 J (b) 150 J
Vector
Easy
(a) 0.5 units (b) 1 unit
(a) (b) (c) 2 units (d) 4 units

(c) (d) 130.What is the unit vector perpendicular to the following vectors
and

(a) (b)
121.A vector points vertically upward and points towards
north. The vector product is
(c) (d)
(a) Zero (b) Along west
(c) Along east (d) Vertically downward
131.The area of the parallelogram whose sides are represented by
122.Angle between the vectors and is the vectors and is
(a) 90° (b) 0° (a) sq.unit (b) sq.unit
(c) 180° (d) 60° (c) sq.unit (d) sq.unit

123.The position vectors of points A, B, C and D are

132.The position of a particle is given by
momentum The angular momentum is
and then the displacement vectors AB and CD
perpendicular to
are
(a) Perpendicular (b)Parallel (a) x-axis (b) y-axis
(c) Antiparallel (d)Inclined at an angle of (c) z-axis (d) Line at equal angles to all
60° the three axes

124.If force and displacement then 133.Two vector A and B have equal magnitudes. Then the vector
the work done is A + B is perpendicular to
(a) (b) (a) (b) A – B
(c) (d) (c) 3A – 3B (d) All of these

125.If then angle between and will be 134.Find the torque of a force acting at the
(a) 30° (b) 45° point
(c) 60° (d) 90°
(a) (b
126.In an clockwise system
(a) (b) (c) (d)
(c) (d)

127.The linear velocity of a rotating body is given by

135.The value of is
where is the angular velocity and is the radius vector. The
(a) 0 (b)
angular velocity of a body is and the radius
vector then is (c) (d)
(a) units (b) units
(c) units (d) units 136.If and are perpendicular vectors and vector
and The value of a is
128.Three vectors and satisfy the relation and (a) – 2 (b) 8
The vector is parallel to (c) – 7 (d) – 8
(a) (b)
(c) (d) 137.A force vector applied on a mass is represented as
and accelerates with .
What will be the mass of the body in kg.
129.The diagonals of a parallelogram are and What is the
area of the parallelogram
Vector
Easy
(a) (b) (c) + 13 J (d) – 7 J
(c) (d)10
146.If a vector is parallel to another vector then the resultant
138.Two adjacent sides of a parallelogram are represented by the of the vector will be equal to
two vectors and . What is the area of (a) A (b)
parallelogram (c) Zero vector (d) Zero
(a) 8 (b)
(c) (d) 192 147.P, Q and R are three coplanar forces acting at a point and are
in equilibrium. Given P = 1.9318 kg wt, 0.9659, the
value of R is ( inkg wt)
139.The position vectors of radius are and
while those of linear momentum are Then the (a) 0.9659
angular momentum is (b) 2
(a) (b) (c) 1
(c) (d) (d)

140.What is the value of linear velocity, if and

148.A body is in equilibrium under the action of three coplanar
forces P, Q and R as shown in the figure. Select the correct
(a) (b) statement
(c) (d) (a)

(b)
141.Dot product of two mutual perpendicular vector is
(a) 0 (b) 1 (c)
(c)  (d) None of these
(d)
142.When then
(a) and are perpendicular to each other 149.If a body is in equilibrium under a set of non-collinear forces,
(b) and act in the same direction then the minimum number of forces has to be
(a) Four (b) Three
(c) and act in the opposite direction
(c) Two (d) Five
(d) and can act in any direction
150.How many minimum number of non-zero vectors in different
143.If then the value of is planes can be added to give zero resultant
(a) 2 (b) 3
(a) (b) (c) 4 (d) 5

(c) (d) 151.As shown in figure the tension in the horizontal cord is 30 N.
The weight W and tension in the string OA in Newton are

144.A force acting on a particle causes a

(a) 30 30
displacement in its own direction. If the
(b) 30 60
work done is 6J, then the value of c will be
(c) 60 30
(a) 12 (b) 6
(d) None of these
(c) 1 (d) 0

152.Two cars are moving in the same direction with the same
145.A force is applied over a particle which speed 30 km/hr. They are separated by a distance of 5 km, the
displaces it from its original position to the point speed of a car moving in the opposite direction if it meets
m. The work done on the particle is these two cars at an interval of 4 minutes, will be
(a) + 11 J (b) + 7 J (a) 40 km/hr (b) 45 km/hr
Vector
Easy
(c) 30 km/hr (d) 15 km/hr 160.A man sitting in a bus travelling in a direction from west to
east with a speed of 40 km/h observes that the rain-drops are
153.A man standing on a road hold his umbrella at 30° with the falling vertically down. To the another man standing on
vertical to keep the rain away. He throws the umbrella and ground the rain will appear
starts running at 10 km/hr. He finds that raindrops are hitting (a) To fall vertically down
his head vertically, the speed of raindrops with respect to the
(b) To fall at an angle going from west to east
road will be
(a) 10 km/hr (b) 20 km/hr (c) To fall at an angle going from east to west
(c) 30 km/hr (d) 40 km/hr (d) The information given is insufficient to decide the
direction of rain.
154.A boat is moving with a velocity 3i + 4j with respect to ground.
The water in the river is moving with a velocity – 3i – 4jwith 161.A boat takes two hours to travel 8 km and back in still water.
respect to ground. The relative velocity of the boat with If the velocity of water is 4 km/h, the time taken for going
respect to water is upstream 8 km and coming back is
(a) 8j (b) – 6i – 8j
(a) 2h
(c) 6i +8j (d)
(b) 2h 40 min
(c) 1h 20 min
155.A 150 m long train is moving to north at a speed of 10 m/s. A
parrot flying towards south with a speed of 5 m/s crosses the (d) Cannot be estimated with the information given
train. The time taken by the parrot the cross to train would be:
162.A 120 m long train is moving towards west with a speed of 10
(a) 30 s (b) 15 s m/s. A bird flying towards east with a speed of 5 m/s crosses
(c) 8 s (d) 10 s the train. The time taken by the bird to cross the train will be
(a) 16 sec (b) 12 sec
156.A river is flowing from east to west at a speed of 5 m/min. A
man on south bank of river, capable of swimming 10m/min in (c) 10 sec (d) 8 sec
still water, wants to swim across the river in shortest time. He
should swim [BHU 1998] 163.A boat crosses a river with a velocity of 8 km/h. If the
(a) Due north resulting velocity of boat is 10 km/h then the velocity of river
(b) Due north-east water is
(c) Due north-east with double the speed of river (a) 4 km/h (b) 6 km/h
(d) None of these
(c) 8 km/h (d) 10 km/h

157.A person aiming to reach the exactly opposite point on the

bank of a stream is swimming with a speed of 0.5 m/s at an 164.If a vector making angles , , and  respectively with the
0
angle of 120 with the direction of flow of water. The speed X, Y and Z axes respectively.
of water in the stream is
Then
(a) 1 m/s (b) 0.5 m/s
(c) 0.25 m/s (d) 0.433 m/s (a) 0 (b) 1
(c) 2 (d) 3
158.A moves with 65 km/h while B is coming back of A with 80
km/h. The relative velocity of B with respect to A is 165.If the resultant of n forces of different magnitudes acting at a
(a) 80 km/h (b) 60 km/h point is zero, then the minimum value of n is
(c) 15 km/h (d) 145 km/h (a) 1 (b) 2
(c) 3 (d) 4
159.A thief is running away on a straight road on a jeep moving
with a speed of 9 m/s. A police man chases him on a motor
cycle moving at a speed of 10 m/s. If the instantaneous 166.Can the resultant of 2 vectors be zero
separation of jeep from the motor cycle is 100 m, how long (a) Yes, when the 2 vectors are same in magnitude and
will it take for the policemen to catch the thief direction
(a) 1 second (b) 19 second
(b) No
(c) 90 second (d) 100 second
(c) Yes, when the 2 vectors are same in magnitude but
opposite in sense
Vector
Easy
(d) Yes, when the 2 vectors are same in magnitude making

an angle of with each other 173.A force (where K is a positive constant)

acts on a particle moving in the x-y plane. Starting from the
origin, the particle is taken along the positive x- axis to the
167.The sum of the magnitudes of two forces acting at point is 18 point (a, 0) and then parallel to the y-axis to the point (a, a).
and the magnitude of their resultant is 12. If the resultant is at The total work done by the forces on the particle is
90° with the force of smaller magnitude, what are the, (a) (b)
magnitudes of forces (c) (d)
(a) 12, 5 (b) 14, 4
(c) 5, 13 (d) 10, 8 174.The vectors from origin to the points A and B are
and respectively. The
168.A vector is turned without a change in its length through a area of the triangle OAB be
small angle The value of and are respectively
(a) sq.unit (b) sq.unit
(a) (b)
(c) 0, 0 (d) None of these (c) sq.unit (d) sq.unit

169. Find the resultant of three vectors and 175.A metal sphere is hung by a string fixed to a wall. The sphere
shown in the following figure. Radius of the circle is pushed away from the wall by a stick. The forces acting on
C the sphere are shown in the second diagram. Which of the
is R. B
following statements is wrong
(a) 2R 45o
45o (a)
A
(b) O
(b)
(c) (c)
(d) (d)

170. Figure shows ABCDEF as a regular hexagon. 176.The speed of a boat is 5 km/h in still water. It crosses a river
of width 1 km along the shortest possible path in 15 minutes.
What is the value of E D
The velocity of the river water is
(a) (a) 1 km/h (b) 3 km/h
(b) F C (c) 4 km/h (d) 5 km/h
O
(c)
177.A man crosses a 320 m wide river perpendicular to the current
(d) A B
in 4 minutes. If in still water he can swim with a speed 5/3
times that of the current, then the speed of the current, in
171.The length of second's hand in watch is 1 cm. The change in m/min is
velocity of its tip in 15 seconds is (a) 30 (b) 40
(c) 50 (d) 60.
(a) Zero (b)
178. represents a unit vector when c is
(c) (d) (a) – 0.2 (b)
(c) (d) 0

172. A particle moves towards east with velocity 5 m/s.

After 10 seconds its direction changes towards north 179.The angles which a vector makes with X, Y and
with same velocity. The average acceleration of the Z axes respectively are
particle is (a) 60°, 60°, 60° (b) 45°, 45°, 45°
(c) 60°, 60°, 45° (d) 45°, 45°, 60°
(a) Zero (b)
180.The value of a unit vector in the direction of vector
(c) (d) is
Vector
Easy
(a) (b) 187.The resultant of is On reversing the vector the
(c) (d) resultant becomes What is the value of
(a) (b)
181.Which of the following is independent of the choice of co-
ordinate system (c) (d)

(a) (b)
188. Figure below shows a body of mass M moving
(c) (d) None of these with the uniform speed on a circular path of radius, R.
What is the
P2 change in acceleration in going from to
182.A car travels 6 km towards north at an angle of 45° to the east v
and then travels distance of 4 km towards north at an angle of
135° to the east. How far is the point from the starting point. P1
R
What angle does the straight line joining its initial and final
position makes with the east
(a) and (b)

(c) and (d)

(a) Zero (b)

(c) (d)
183.Given that = 0 out of three vectors two are equal in
magnitude and the magnitude of third vector is times that
of either of the two having equal magnitude. Then the angles 189. A particle is moving on a circular path of radius r
between vectors are given by with uniform velocity v. The change in velocity when
(a) 30°, 60°, 90° (b) 45°, 45°, 90° P
the particle moves from P to Q is
(c) 45°, 60°, 90° (d) 90°, 135°, 135° r
O 40o v

184.Two forces and act along the lines x = 0

Q
and y = 0 respectively. Then the resultant of forces would be v
(a) (b)
(c) (d)
(a) (b)
185.At what angle must the two forces (x + y) and (x – y) act so (c) (d)
that the resultant may be
190. and are two vectors.
(a) (b) The angle between them will be
(a) 0° (b) 45°
(c) 60° (d) 90°
(c) (d)

191.If and then projection of

on will be
186.Following forces start acting on a particle at rest at the origin
of the co-ordinate system simultaneously
(a) (b)
, ,
and then the (c) (d)
particle will move
(a) In x – y plane (b) In y – z plane
(c) In x – z plane (d) Along x -axis 192.In above example a unit vector perpendicular to both and
will be

(a) (b)
Vector
Easy
(c) Both (a) and (b) (d) None of these
200.A steam boat goes across a lake and comes back (a) On a
193.Two constant forces (N) and quite day when the water is still and (b) On a rough day when
there is uniform air current so as to help the journey onward
(N) act on a body and displace it from the and to impede the journey back. If the speed of the launch on
position (m) to the position both days was same, in which case it will complete the
journey in lesser time
(m). What is the work done
(a) Case (a) (b) Case (b)
(a) 9 J (b) 41 J
(c) Same in both (d) Nothing can be predicted
(c) – 3 J (d) None of these

201.To a person, going eastward in a car with a velocity of 25

194.For any two vectors and , if the
km/hr, a train appears to move towards north with a velocity
magnitude of is equal to
of km/hr. The actual velocity of the train will be
(a) (b)
(a) 25 km/hr (b) 50 km/hr

(c) (d) (c) 5 km/hr (d) km/hr

202.A swimmer can swim in still water with speed  and the river
195.Which of the following is the unit vector perpendicular to is flowing with velocity v/2. To cross the river in shortest
and distance, he should swim making angle  with the upstream.
What is the ratio of the time taken to swim across the shortest
(a) (b) time to that is swimming across over shortest distance
(a) cos  (b) sin 
(c) (d) (c) tan  (d) cot 

203.A bus is moving with a velocity 10 m/s on a straightroad. A

196.Two vectors and will be
scooterist wishes to overtake the bus in 100 s.
parallel if
If the bus is at a distance of 1km from the scooterist, with
(a) b = 0 (b) b = 1
what velocity should the scooterist chase the bus
(c) b = 2 (d) b= – 4
(a) 50 m/s (b) 40 m/s
(c) 30 m/s (d) 20 m/s
197.Which of the following is not true ? If and
where A and B are the magnitudes of and

(a) (b)

(c) (d) A = 5

198.The area of the triangle formed by and is

(a) 3 sq.unit (b) sq. unit

(c) sq. unit (d) sq. unit

199.Two trains along the same straight rails moving with constant
speed 60 km/hr and 30 km/hr
respectively towards each other. If at time , the
distance between them is 90 km,
the time when they collide is
(a) 1 hr (b) 2 hr
(c) 3 hr (d) 4 hr
 208. The time period of a simple pendulum is
204. The period of oscillation of a simple
given by . The measured value of the
pendulum is . Measured value of is
length of pendulumis known to a
from meterscale having a minimum division accuracy. The time for oscillations of the
of and time of one complete oscillation is pendulum is found to be secondusing a clock
measured fromstopwatch of of resolution. The percentage accuracy in the
resolution. The percentage error in the
determination of using this pendulum is .The
determination of ' will be
value of to the nearest integer is:-
(a) (b)
(a) (b) (c) (d)
(c) (d)

205. In an octagon of equal side, what is

209. If two vectors and
the sum of If
are perpendicular to each other.
Then, the value of m will be:
(a)1 (b)-l
(c) - 3 (d) 2

(a) (b)
(c) (d)

206. The pitch of the screw guage is and there

are divisions on the circular scale. When
nothing is put inbetween the jaws, the zero of
the circular scale lines divisions below the
reference line. When a wire isplaced between the
jaws, the first linear scale division is clearly
visible while division on circular
scalecoincides with the reference line. The radius
of the wire is:
(a) (b)
(c) (d)

207. A wire of has a length of . It is stretched

till its length increases by . The percentage
change in aresistance to the nearest integer is:
(a) (b)
(c) (d)

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