Vectors Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The length of second’s hand in watch is 1 cm. The change
in velocity of its tip in 15 seconds is
(a) zero (b) cm/sec
302
p
(c)
cm/sec
30
p
(d)
2
cm/sec
30
p
Q.2 A particle moves towards east with velocity 5 m/s. After
10 seconds its direction changes towards north with same
velocity. The average acceleration of the particle is
(a) zero (b)
2
1
m/s N-W
2
(c)
2
1
m/s N-E
2
(d)
2
1
m/s S-W
2
Q.3 A force 
ˆˆ
() =-+
ur
F K yi xj (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 point (a, 0) and then parallel to the y-axis to the point
(a, a). The total work done by the forces 
ur
F on the particle
is
(a) – 2 Ka
2
(b) 2 Ka
2
(c) – Ka
2
(d) Ka
2
Page 2


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The length of second’s hand in watch is 1 cm. The change
in velocity of its tip in 15 seconds is
(a) zero (b) cm/sec
302
p
(c)
cm/sec
30
p
(d)
2
cm/sec
30
p
Q.2 A particle moves towards east with velocity 5 m/s. After
10 seconds its direction changes towards north with same
velocity. The average acceleration of the particle is
(a) zero (b)
2
1
m/s N-W
2
(c)
2
1
m/s N-E
2
(d)
2
1
m/s S-W
2
Q.3 A force 
ˆˆ
() =-+
ur
F K yi xj (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 point (a, 0) and then parallel to the y-axis to the point
(a, a). The total work done by the forces 
ur
F on the particle
is
(a) – 2 Ka
2
(b) 2 Ka
2
(c) – Ka
2
(d) Ka
2
2
DPP/ P 05
Q.4 A metal sphere is hung by a string fixed to a wall. The
sphere is pushed away from the wall by a stick. The forces
acting on the sphere are shown in the second diagram.
Which of the following statements is wrong?
q
q
W
P
(a) P = W tan q (b)
0 + +=
r rr
T PW
(c) T
2
 = P
2
 + W
2
(d) T = P + W
Q.5 The speed of a boat is 5km/h in still water. It crosses a
river of width 1 km along the shortest possible path in 15
minutes. The velocity of the river water is
(a) 1 km/h (b) 3 km/h
(c) 4 km/h (d) 5 km/h
Q.6 A man crosses a 320 m wide river perpendicular to the
current 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 m/min is
(a) 30 (b) 40
(c) 50 (d) 60
Q.7 P, Q and R are three coplanar forces acting at a point and
are in equilibrium. Given P = 1.9318 kg wt, sin q
1
 = 0.9659,
the value of R is (in kg wt)
P Q
R
150°
2
q
1
q
(a) 0.9659 (b)2
(c)1 (d)
1
2
Q.8 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
A
W
30 N
O
30°
(a)
30 3,30
(b)
30 3,60
(c)
60 3,30
(d) None of these
Q.9 A boat is moving with a velocity 
ˆˆ
34 ij + with respect to
ground. The water in the river is moving with a velocity
– 
ˆˆ
34 ij - with respect to ground. The relative velocity of
the boat with respect to water is
(a) ˆ
8 j (b) ˆˆ
68 ij -- (c) ˆˆ
68 ij + (d)
ˆ
52i
Q.10 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
angle of 120° with the direction of flow of water. The speed
of water in the stream is
(a) 1 m/s (b) 0.5 m/s (c) 0.25 m/s(d)   0.433 m/s
Q.11 A man can swim with velocity v relative to water. He has to
cross a river of width d flowing with a velocity u (u > v).
The distance through which he is carried down stream by
the river is x. Which of the following statements is correct?
(a) If he crosses the river in minimum time 
=
du
x
v
(b) x cannot be less than 
du
v
(c) For x to be minimum he has to swim in a direction making
an angle of 
1
sin
2
v
u
,
æö ?
÷ ç
, ÷
ç
÷ ç
èø
 with the direction of the
flow of water.
(d) x will be maximum if he swims in a direction making
an angle of 
1
sin
2
-
p æö
+
ç÷
èø
v
u
 with direction of the flow of
water.
Page 3


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The length of second’s hand in watch is 1 cm. The change
in velocity of its tip in 15 seconds is
(a) zero (b) cm/sec
302
p
(c)
cm/sec
30
p
(d)
2
cm/sec
30
p
Q.2 A particle moves towards east with velocity 5 m/s. After
10 seconds its direction changes towards north with same
velocity. The average acceleration of the particle is
(a) zero (b)
2
1
m/s N-W
2
(c)
2
1
m/s N-E
2
(d)
2
1
m/s S-W
2
Q.3 A force 
ˆˆ
() =-+
ur
F K yi xj (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 point (a, 0) and then parallel to the y-axis to the point
(a, a). The total work done by the forces 
ur
F on the particle
is
(a) – 2 Ka
2
(b) 2 Ka
2
(c) – Ka
2
(d) Ka
2
2
DPP/ P 05
Q.4 A metal sphere is hung by a string fixed to a wall. The
sphere is pushed away from the wall by a stick. The forces
acting on the sphere are shown in the second diagram.
Which of the following statements is wrong?
q
q
W
P
(a) P = W tan q (b)
0 + +=
r rr
T PW
(c) T
2
 = P
2
 + W
2
(d) T = P + W
Q.5 The speed of a boat is 5km/h in still water. It crosses a
river of width 1 km along the shortest possible path in 15
minutes. The velocity of the river water is
(a) 1 km/h (b) 3 km/h
(c) 4 km/h (d) 5 km/h
Q.6 A man crosses a 320 m wide river perpendicular to the
current 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 m/min is
(a) 30 (b) 40
(c) 50 (d) 60
Q.7 P, Q and R are three coplanar forces acting at a point and
are in equilibrium. Given P = 1.9318 kg wt, sin q
1
 = 0.9659,
the value of R is (in kg wt)
P Q
R
150°
2
q
1
q
(a) 0.9659 (b)2
(c)1 (d)
1
2
Q.8 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
A
W
30 N
O
30°
(a)
30 3,30
(b)
30 3,60
(c)
60 3,30
(d) None of these
Q.9 A boat is moving with a velocity 
ˆˆ
34 ij + with respect to
ground. The water in the river is moving with a velocity
– 
ˆˆ
34 ij - with respect to ground. The relative velocity of
the boat with respect to water is
(a) ˆ
8 j (b) ˆˆ
68 ij -- (c) ˆˆ
68 ij + (d)
ˆ
52i
Q.10 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
angle of 120° with the direction of flow of water. The speed
of water in the stream is
(a) 1 m/s (b) 0.5 m/s (c) 0.25 m/s(d)   0.433 m/s
Q.11 A man can swim with velocity v relative to water. He has to
cross a river of width d flowing with a velocity u (u > v).
The distance through which he is carried down stream by
the river is x. Which of the following statements is correct?
(a) If he crosses the river in minimum time 
=
du
x
v
(b) x cannot be less than 
du
v
(c) For x to be minimum he has to swim in a direction making
an angle of 
1
sin
2
v
u
,
æö ?
÷ ç
, ÷
ç
÷ ç
èø
 with the direction of the
flow of water.
(d) x will be maximum if he swims in a direction making
an angle of 
1
sin
2
-
p æö
+
ç÷
èø
v
u
 with direction of the flow of
water.
DPP/ P 05
3
Q.12 A 120 m long train is moving towards west with a speed of
10 m/s. A bird flying towards east with a speed of 5 m/s
crosses the train. The time taken by the bird to cross the
train will be
(a) 16 sec (b) 12 sec (c) 10 sec (d) 8 sec
Q.13 What is the value of linear velocity, if 
$ $
34 i jk w= -+
ur
$
 and
$ $
5 66 r i jk = -+
r
$
(a)
$ $
6 23 i jk -+
$
(b)
$ $
6 28 i jk -+
$
(c)
$ $
4 136 i jk -+
$
(d)
$ $
18 132 i jk - -+
$
Q.14 If | | 3 ., A B AB ´=
ur ur ur u r
 then the value of || AB +
ur ur
 is
(a)
1/2
22
3
AB
AB
æö
++
ç÷
èø
(b) A + B
(c)
2 2 1/2
( 3) A B AB ++ (d)
2 2 1/2
() A B AB ++
Q.15 Find the torque of a force 
$ $
35 F i jk =- ++
ur
$
 acting at a point
$ $
73 r i jk = ++
r
$
(a)
$ $
14 38 16 i jk -+
$
(b)
$ $
4 46 i jk ++
$
(c)
$ $
21 44 i jk ++
$
(d)
$ $
14 34 16 i jk - +-
$
Q.16 If | | | . |, B AB A´=
ur ur ur ur
 then angle between A
ur
 and B
ur
 will be
(a) 30° (b) 45° (c) 60° (d) 90°
Q.17The vector 
$ $
3 P ai ajk = ++
ur
$
 and 
$ $
2 Q ai jk = --
ur
$
 are
perpendicular to each other. The positive value of a is
(a)3 (b)4
(c)9 (d) 13
Q.18A particle moves from position 
$ $
3 26 i jk +-
$
 to
$ $
14 13 9 i jk ++
$
 due to a uniform force of 
$ $
(4 3). i j kN ++
$
If the displacement in metres then work done will be
(a) 100 J (b) 200 J (c) 300 J d) 250 J
Q.19The three vectors 
ˆˆ ˆ ˆ ˆˆ
3 2 , 35 A i j kB i jk = - + = -+
u r ur
 and
ˆ ˆˆ
24 C i jk = +-
ur
 form
(a) an equilateral triangle (b) isosceles triangle
(c) a right angled triangle (d) no triangle
Q.20 Two forces 
1
ˆ ˆˆ
5 10 20 F i jk = +-
r
 and 
2
ˆ ˆˆ
10 5 15 F i jk = --
r
act on a single point. The angle between 
1
F
r
 and 
2
F
r
 is nearly
(a) 30° (b) 45°
(c) 60° (d) 90°
Q.21 With respect to a rectangular cartesian coordinate system,
three vectors are expressed as
ˆ ˆ ˆˆ
4 , 3 2, a i jb ij = - =-+
r
r
 and ˆ
ck =-
r
where 
ˆ ˆˆ
,, i jk are unit vectors, along the X, Y and Z-axis
respectively . The unit vectors ˆ r along the direction of sum
of these vector is
(a)
1
ˆ ˆˆ
ˆ ()
3
r i jk = +- (b)
1
ˆ ˆˆ
ˆ ()
2
r i jk = +-
(c)
1
ˆ ˆˆ
ˆ()
3
r i jk = -+ (d)
1
ˆ ˆˆ
ˆ ()
2
r i jk = ++
DIRECTIONS (Q.22-Q.24) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 A boy walks uniformally along the sides of a rectangular
park of size 400 m × 300 m, starting from one corner to
the other corner diagonally opposite. Which of the
following  statements is correct?
(1) He has travelled a distance of  700 m
(2) His displacement is 500 m
(3) His velocity is not uniform throughout the walk
(4) His displacement is 700 m
Q.23The three vectors 
ˆ ˆ ˆ ˆ ˆˆ
A 3i 2j k, B i 3j 5k = - - = -+
r r
 and
ˆˆˆ
C 2i – j 4k =-
r
 does not form
(1) an equilateral triangle (2) isosceles triangle
(3) a right angled triangle (4) no triangle
Page 4


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The length of second’s hand in watch is 1 cm. The change
in velocity of its tip in 15 seconds is
(a) zero (b) cm/sec
302
p
(c)
cm/sec
30
p
(d)
2
cm/sec
30
p
Q.2 A particle moves towards east with velocity 5 m/s. After
10 seconds its direction changes towards north with same
velocity. The average acceleration of the particle is
(a) zero (b)
2
1
m/s N-W
2
(c)
2
1
m/s N-E
2
(d)
2
1
m/s S-W
2
Q.3 A force 
ˆˆ
() =-+
ur
F K yi xj (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 point (a, 0) and then parallel to the y-axis to the point
(a, a). The total work done by the forces 
ur
F on the particle
is
(a) – 2 Ka
2
(b) 2 Ka
2
(c) – Ka
2
(d) Ka
2
2
DPP/ P 05
Q.4 A metal sphere is hung by a string fixed to a wall. The
sphere is pushed away from the wall by a stick. The forces
acting on the sphere are shown in the second diagram.
Which of the following statements is wrong?
q
q
W
P
(a) P = W tan q (b)
0 + +=
r rr
T PW
(c) T
2
 = P
2
 + W
2
(d) T = P + W
Q.5 The speed of a boat is 5km/h in still water. It crosses a
river of width 1 km along the shortest possible path in 15
minutes. The velocity of the river water is
(a) 1 km/h (b) 3 km/h
(c) 4 km/h (d) 5 km/h
Q.6 A man crosses a 320 m wide river perpendicular to the
current 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 m/min is
(a) 30 (b) 40
(c) 50 (d) 60
Q.7 P, Q and R are three coplanar forces acting at a point and
are in equilibrium. Given P = 1.9318 kg wt, sin q
1
 = 0.9659,
the value of R is (in kg wt)
P Q
R
150°
2
q
1
q
(a) 0.9659 (b)2
(c)1 (d)
1
2
Q.8 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
A
W
30 N
O
30°
(a)
30 3,30
(b)
30 3,60
(c)
60 3,30
(d) None of these
Q.9 A boat is moving with a velocity 
ˆˆ
34 ij + with respect to
ground. The water in the river is moving with a velocity
– 
ˆˆ
34 ij - with respect to ground. The relative velocity of
the boat with respect to water is
(a) ˆ
8 j (b) ˆˆ
68 ij -- (c) ˆˆ
68 ij + (d)
ˆ
52i
Q.10 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
angle of 120° with the direction of flow of water. The speed
of water in the stream is
(a) 1 m/s (b) 0.5 m/s (c) 0.25 m/s(d)   0.433 m/s
Q.11 A man can swim with velocity v relative to water. He has to
cross a river of width d flowing with a velocity u (u > v).
The distance through which he is carried down stream by
the river is x. Which of the following statements is correct?
(a) If he crosses the river in minimum time 
=
du
x
v
(b) x cannot be less than 
du
v
(c) For x to be minimum he has to swim in a direction making
an angle of 
1
sin
2
v
u
,
æö ?
÷ ç
, ÷
ç
÷ ç
èø
 with the direction of the
flow of water.
(d) x will be maximum if he swims in a direction making
an angle of 
1
sin
2
-
p æö
+
ç÷
èø
v
u
 with direction of the flow of
water.
DPP/ P 05
3
Q.12 A 120 m long train is moving towards west with a speed of
10 m/s. A bird flying towards east with a speed of 5 m/s
crosses the train. The time taken by the bird to cross the
train will be
(a) 16 sec (b) 12 sec (c) 10 sec (d) 8 sec
Q.13 What is the value of linear velocity, if 
$ $
34 i jk w= -+
ur
$
 and
$ $
5 66 r i jk = -+
r
$
(a)
$ $
6 23 i jk -+
$
(b)
$ $
6 28 i jk -+
$
(c)
$ $
4 136 i jk -+
$
(d)
$ $
18 132 i jk - -+
$
Q.14 If | | 3 ., A B AB ´=
ur ur ur u r
 then the value of || AB +
ur ur
 is
(a)
1/2
22
3
AB
AB
æö
++
ç÷
èø
(b) A + B
(c)
2 2 1/2
( 3) A B AB ++ (d)
2 2 1/2
() A B AB ++
Q.15 Find the torque of a force 
$ $
35 F i jk =- ++
ur
$
 acting at a point
$ $
73 r i jk = ++
r
$
(a)
$ $
14 38 16 i jk -+
$
(b)
$ $
4 46 i jk ++
$
(c)
$ $
21 44 i jk ++
$
(d)
$ $
14 34 16 i jk - +-
$
Q.16 If | | | . |, B AB A´=
ur ur ur ur
 then angle between A
ur
 and B
ur
 will be
(a) 30° (b) 45° (c) 60° (d) 90°
Q.17The vector 
$ $
3 P ai ajk = ++
ur
$
 and 
$ $
2 Q ai jk = --
ur
$
 are
perpendicular to each other. The positive value of a is
(a)3 (b)4
(c)9 (d) 13
Q.18A particle moves from position 
$ $
3 26 i jk +-
$
 to
$ $
14 13 9 i jk ++
$
 due to a uniform force of 
$ $
(4 3). i j kN ++
$
If the displacement in metres then work done will be
(a) 100 J (b) 200 J (c) 300 J d) 250 J
Q.19The three vectors 
ˆˆ ˆ ˆ ˆˆ
3 2 , 35 A i j kB i jk = - + = -+
u r ur
 and
ˆ ˆˆ
24 C i jk = +-
ur
 form
(a) an equilateral triangle (b) isosceles triangle
(c) a right angled triangle (d) no triangle
Q.20 Two forces 
1
ˆ ˆˆ
5 10 20 F i jk = +-
r
 and 
2
ˆ ˆˆ
10 5 15 F i jk = --
r
act on a single point. The angle between 
1
F
r
 and 
2
F
r
 is nearly
(a) 30° (b) 45°
(c) 60° (d) 90°
Q.21 With respect to a rectangular cartesian coordinate system,
three vectors are expressed as
ˆ ˆ ˆˆ
4 , 3 2, a i jb ij = - =-+
r
r
 and ˆ
ck =-
r
where 
ˆ ˆˆ
,, i jk are unit vectors, along the X, Y and Z-axis
respectively . The unit vectors ˆ r along the direction of sum
of these vector is
(a)
1
ˆ ˆˆ
ˆ ()
3
r i jk = +- (b)
1
ˆ ˆˆ
ˆ ()
2
r i jk = +-
(c)
1
ˆ ˆˆ
ˆ()
3
r i jk = -+ (d)
1
ˆ ˆˆ
ˆ ()
2
r i jk = ++
DIRECTIONS (Q.22-Q.24) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 A boy walks uniformally along the sides of a rectangular
park of size 400 m × 300 m, starting from one corner to
the other corner diagonally opposite. Which of the
following  statements is correct?
(1) He has travelled a distance of  700 m
(2) His displacement is 500 m
(3) His velocity is not uniform throughout the walk
(4) His displacement is 700 m
Q.23The three vectors 
ˆ ˆ ˆ ˆ ˆˆ
A 3i 2j k, B i 3j 5k = - - = -+
r r
 and
ˆˆˆ
C 2i – j 4k =-
r
 does not form
(1) an equilateral triangle (2) isosceles triangle
(3) a right angled triangle (4) no triangle
4
DPP/ P 05
DIRECTIONS (Q.28-Q.29) : Each of these qu estions contains two
statements: S tatement-1 (Assertion) and S tatement-2 (Reason).
Each of these questions has four alternative choices, only one of
which is the co rrect answer . Y ou hav e to select the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.28 Statement-1:If , A B AB + =-
rr rr
 then angle between A
r
and B
r
 is 90°
Statement-2 : A B BA +=+
rr rr
Q.29 Statement-1 : The sum of two vectors can be zero.
Statement-2 : Two vectors cancel each other, when they
are equal and opposite.
Q.24 If for two vectors A
r
 and B,A B0 ´<
r rr
, which of the following
is not correct?
(1) They are perpendicular to each other
(2) They act at an angle of 60°
(3) They act at an angle of 30°
(4) They are parallel to each other
DIRECTIONS (Q.25-Q.27) : Read the passage given below
and answer the questions that follows :
ˆ ˆˆ
2 A i jk = ++
r
 and 
ˆ ˆˆ
B i jk = ++
r
 are two vectors.
Q.25 The unit vector perpendicular to A
r
 is
(a)
ˆ ˆ
2
jk -+
(b)
ˆ ˆ
2
jk --
(c)
ˆ ˆ
2
ik +
(d)
ˆ ˆ
2
ik -
Q.26 The unit vector parallel to A
r
 is
(a)
ˆ ˆˆ
23
2
i jk -+
(b)
ˆ ˆˆ
2
6
i jk ++
(c)
ˆ ˆˆ
2
5
i jk --
(d)
ˆ ˆˆ
22
6
i jk +-
Q.27 The unit vector perpendicular to B
r
 is
(a)
ˆ ˆ
3
jk --
(b)
ˆ ˆ
2
jk -+
(c)
ˆ ˆ
3
ik -
(d)
ˆ ˆ
2
ik +