VECTORS

PHYSICS
XI (A1 & B)

Believe In Excellence

CONTENTS

LEVEL # I - 2-4
LEVEL # II - 5-6
LEVEL # III - 7 - 11

ANSWER KEY - 12

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 LEVEL-I
1. A force of 6 kg and another of 8 kg can be 8. Two vectors have magnitudes 3 unit and 4
applied together to produce the effect of a single unit respectively. What should be the angle
force of- between them if the magnitude of the resultant
(A) 1kg (B) 11kg is -
(C) 15 kg (D) 20 kg (i) 1 unit (ii) 5 unit (iii) 7 unit
(A) 180º, 90º, 0º
2. If the magnitudes of the vectors A, B and C (B) 80º, 70º, 0º
are 6, 8, 10 units respectively and if A + B = (C) 90º, 170º, 50º
(D) None of these
C, then the angle between A and C is -
(A) /2 (B) arc cos (0. 6)
9. In a two dimensional motion of a particle, the
(C) arc tan (0.75) (D) /4
particle moves from point A, position vector r1
to point B position vector r2. If the magnitude
3. Angle between (P + Q) and (P – Q) will be- of these vector are respectively r1 = 3 and r2 =
(A) 0º only 4 and the angle they make with the x-axis are
(B) 90º only 1=75º,2=15º respectively, then magnitude of
(C) 180º only the displacement vector is-
(D) between 0º and 180º
(A) 3 (B) 13 (C) 5 (D) 1
(both the values inclusive)

10. A blind person after walking 10 steps in one

4. What is the resultant of three coplanar forces:
direction, each of length 80 cm, turns randomly
300 N at 0°, 400 N at 30º and 400 N at 150º ?
to the left or to the right by 90º. After walking
(A) 500 N (B) 700 N a total of 40 steps the maximum possible
(C) 1100N (D) 300 N displacement of the person from his starting
position could be -
5. A child pulls a box with a force of 200 N at an (A) 320 m (B) 32 m
angle of 60º above the horizontal. Then the (C) 16/ 2 m (D) 16 2 m
horizontal and vertical components of the force
are- 11. If the angle between vector a and b is an
F
(A) 100 N, 175 N acute angle, then the difference a – b is -
60º
(B) 86.6 N, 100 N (A) the main diagonal of the parallelogram
(C) 100 N, 86.6 N (B) the minor diagonal of the parallelogram
(D) 100 N, 0 N (C) any of the above
(D) none of the above
6. The value of a unit vector in the direction of 12. For the figure –
vector A = 5 î – 12 ĵ , is - (A) A + B = C
(B) B + C = A
C B
(A) î (B) ĵ (C) C + A = B
(D) A + B + C = 0 A
(C) ( î  ˆj) / 13 (D) (5 î – 12 ĵ )/13
13. The resultant of two vectors A and B is
perpendicular to the vector A and its magnitude
7. Two forces of 4 dyne and 3 dyne act upon a body. is equal to half the magnitude of vector B.
The resultant force on the body can only be – The angle between A and B is -
(A) more than 3 dynes (A) 120º
(B) more than 4 dynes (B) 150º R

(C) between 3 and 4 dynes (C) 135º B

(D) between 1 and 7 dynes (D) None of these

A

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14. Which of the sets given below may represent  
22. The vector sum of two vectors A and B is
the magnitudes of three vectors adding to zero?
maximum, then the angle  between two vectors is
(A) 2, 4, 8 (B) 4, 8, 16
(A) 0º (B) 30º
(C) 1, 2, 1 (D) 0.5, 1, 2
(C) 45º (D) 60º
15. The forces, each numerically equal to 5 N, are
   
acting as shown in the Figure. Find the angle 23. If P  Q  P  Q and  is the angle between
between forces?  
(A) 60 P and Q , then
(B) 120 5N
(A)  = 0º (B)  = 90º
(C) 30 (C) P = 0 (D) Q = 0
(D) 150 60º
5N
24. The sum and difference of two perpendicular
16. Rain is falling vertically down wards with a speed vectors of equal lengths are
5 m/s. If unit vector along upward is defined (A) of equal lengths and have an acute angle
as ĵ , represent velocity of rain in vector form. between them
(A) –5 ĵ (B) 5 ĵ (B) of equal lengths and have an obtuse angle
between them
(C) 5 î (D) –5 î (C) also perpendicular to each other and are
of different lengths
  (D) also perpendicular to each other and are
17. Two forces F1 and F2 are acting at right angles
of equal lengths
to each other, find their resultant ?

(A) 2
F1  F2
2
(B) 2
F1  F2
2 25. Two vectors A and B lie in X-Y plane. The
vector B is perpendicular to vector A. If A = î
(C) F1 + F2 (D) F1 – F2
+ ĵ , then B may be -

18. Two forces, F1 and F2 are acting on a body. (A) î  ˆj (B)  î  ĵ

One force is double that of the other force (C) –2 î + 2 ĵ (D) Any of the above
and the resultant is equal to the greater force.
Then the angle between the two forces is -
26. Two constant forces F1 = 2 î – 3 ĵ + 3 k̂ (N)
(A) cos–1 (1/2) (B) cos–1 (–1/2)
(C) cos–1 (–1/4) (D) cos–1 (1/4)
and F2 = î + ĵ – 2 k̂ (N) act on a body and
 
19. Two force of F1  500 N due east and F2  250 N displace it from the position r1= î + 2 ĵ – 2 k̂
 
due north. Find magnitude of F2  F1 ? (m) to the position r2 = 7 î + 10 ĵ + 5 k̂ (m).

(A) 250 5N (B) 250 N What is the work done ?

(A) 9 Joule (B) 41 Joule
(C) 625 N (D) 750 N
(C) –3 Joule (D) None of these
20. The vector sum of the forces of 10 N and 6 N can
be 27. The two vectors A = 2î  ˆj  3k̂ and
(A) 2N (B) 8N
B = 7 î  5 ĵ  3k̂ are -
(C) 18N (D) 20N
(A) parallel (B) perpendicular
21. The vector sum of two force P and Q is minimum (C) anti-parallel (D) none of these
when the angle  between their positive directions, is
  28. Angle that the vector A = 2 î + 3 ĵ makes with
(A) (B)
4 3 y-axis is –
 (A) tan–1 3/2 (B) tan–1 2/3
(C) (D) 
2 (C) sin–1 2/3 (D) cos–1 3/2

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29. A vector perpendicular to ( 4î  3 ĵ) is – 34. The magnitude of scalar product of two vectors
is 8 and that of vector product is 8 3 . The
(A) 4î  3ˆj (B) 7 k̂
angle between them is
(C) 6î (D) 3î  4 ĵ (A) 30º (B) 60º
(C) 120º (D) 150º
30. Two vectors P = 2î  bĵ  2k̂ and Q  î  ˆj  k̂ will
35. Which of the following sets of displacements
be perpendicular if - might be capable of bringing a car to its
(A) b = 0 (B) b = 1 returning point ?
(C) b = 2 (D) b = – 4 (A) 5, 10, 30 and 50 km
(B) 5, 9, 9 and 16 km
31. A vector A points. vertically upward and, B points (C) 40, 40, 90 and 200 km
towards north. The vector product A × B is- (D) 10, 20, 40 and 90 km
(A) along west (B) along east
(C) zero (D) vertically downward 36. Match the statements given in column-I with
statements given in column-II
32. The linear velocity of a rotating body is given Column - I Column - II
by v =  × r, where  is the angular velocity     
(A) If | A |  | B | and | A  B |  | A | then (p) 90º
and r is the radius vector. The angular velocity
 
angle between A and B is
of a body  = î  2 ĵ  2k̂ and their radius vector
(B) Magnitude of resultant of two (q) 120º
 
r = 4 ĵ – 3 k̂ , |v| is - forces | F1 |  8N and | F2 |  4 N may be
 
(A) (C) Angle between A  2 î  2 ĵ & B  3 k̂ is (r) 12 N
29 units (B) 31 units
(D) Magnitude of resultant of vectors (s) 14
(C) 37 units (D) 41 units  
A  2 î  ĵ & B  3 k̂ is

  
33. Vectors A,B and C are shown in figure. Find
angle between
y

B 
45º A
30º
x
60º

C

     
(i) A and B (ii) A and C (iii) B and C .

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 LEVEL-II
1. A vector is not changed if -  
11. The vector A and B are such that-
(A) It is rotated through an arbitrary angle    
(B) It is multiplied by an arbitrary scale AB AB
   
(C) It is cross multiplied by a unit vector (A) A  B  0 (B) A  B  0
(D) It is a slide parallel to itself 
(C) A  0

(D) B  0
2. The component of a vector is -
12. The vector sum of N coplanar forces, each of
(A) always less than its magnitude
magnitude F, when each force is making an
(B) always greater than its magnitude
(C) always equal to its magnitude 2
angle of with that preceding it, is -
(D) none of these N
NF
3. If the resultant of two forces of magnitudes P (A) F (B) NF (C) (D) Zero
2
and Q acting at a point at an angle of 60º is
7 Q , then P/Q is 13. Three forces P, Q & R are acting at a point in
(A) 1 (B) 3/2 (C) 2 (D) 4 the plane. The angle between P & Q and Q & R
are 150º & 120º respectively, then for
  equilibrium, forces P, Q & R are in the ratio
4. The resultant of A and B makes an angle 
  (A) 1 : 2 : 3 (B) 1 : 2 : 3
with A and  with B , then -
(A)  <  (B) if A < B (C) 3 : 2 : 1 (D) 3 :2:1
(C) if A > B (D) if A = B
14. In an equilateral ABC, AL, BM and CN are
5. A person moves 30 m north, then 20 m east medians. Forces alo ng BC and BA
represented by them will have a resultant
then 30 2 m south-west . His displacement
represented by -
from the original position - (A) 2AL (B) 2BM (C) 2CN (D) AC
(A) 14 m south-west (B) 28 m south
(C) 10 m west (D) 15 m East 15. Two forces each of magnitude F have a
resultant of the same magnitude F. The angle
between the two forces is -
6. A man moves towards 3m north then 4m
(A) 45º (B) 120º (C) 150º (D) 60º
towards east and finally 5m towards 37º south
of west. His displacement from origin is 16. The resultant of two forces, one double the
other in magnitude is perpendicular to the
(A) 5 2 m (B) 0 m (C) 1 m (D) 12 m
smaller of the two forces. The angle between
the two forces is
7. I started walking down a road to day-break (A) 150º (B) 90º (C) 60º (D) 120º
facing the sun. After walking for some-time, I
17. A particle is moving on a circular path with
turned to my left, then I turned to the right
constant speed v. What is the change in its
once again. In which direction was I going then?
velocity after it has described an angle of 60º?
(A) East (B) North-west
(C) North-east (D) South (A) v 2 (B) v 3 (C) v (D) 2 v

8. How many minimum number of vectors in 18. The magnitude of the vector product of two
 
different planes can be added to give zero vectors A and B may be -
resultant ? (a) Greater than AB (b) Equal to AB
(A) 2 (B) 3 (C) 4 (D) 5 (c) Less than AB (d) Equal to Zero
(A) a, b, c (B) b, c, d
9. Minimum number of unequal forces whose (C) a, c, d (D) a, b, d
vector sum can equal to zero is -
(A) two (B) three (C) four (D) any   
19. Three vectors A, B and C satisfy the relation
          
10. If | A  B |  | A |  | B | , the angle between A and B A.B =0 and A.C = 0. The vector A is parallel to
     
is - (A) B (B) C (C) B . C (D) B  C
(A) 60º (B) 0º (C) 120º (D) 90º

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20. The angle between the two vectors
29. A unit vector along the direction î  ĵ  k̂ has a
 2î  3ˆj  k̂ and î  2ˆj  4k̂ is - magnitude -
(A) 0º (B) 90º (C) 180º (D) None
(A) 3 (B) 2 (C) 1 (D) 0
21. A body constrained to move in y direction is
subj ected to a force given by 30. A man moves towards 3m north then 4m towards east
 and finally 5m towards 37º south of west. His displace-
F  (2î  15 ĵ  6k̂ ) N. What is the work done by
ment from origin is
this force in moving the body through a
distance of 10 m along y-axis ? (A) 5 2 m (B) 0 m
(A) 190 J (B) 160 J (C) 150 J (D) 20 J
(C) 1 m (D) 12 m

22. If the angle between the unit vectors a and

31. Three forces P, Q & R are acting at a point in the
b is 60º, then | a – b | is plane. The angle between P & Q and Q & R are 150º &
(A) 0 (B) 1 (C) 2 (D) 4 120º respectively, then for equilibrium, forces P, Q & R
are in the ratio
 
23. A vector A points vertically upward and B points
  (A) 1 : 2 : 3 (B) 1 : 2 : 3
towards north. The vector product A  B is-
(A) along west (B) along east (C) 3 : 2 : 1 (D) 3 :2:1
(C) zero (D) vertically downward

    32. When two forces of magnitude P and Q are

24. What is the angle between ( P  Q) and (P  Q) ? perpendicular to each other, their resultant is
of magnitude R. When they are at an angle of
 
(A) 0 (B) (C) (D)  180º to each other their resultant is of magni-
2 4
R
tude . Find the ratio of P and Q.
 2
25. Which of the following is not true ? If A  3î  4ˆj

and B  6î  8 ĵ where A and B are the 33. If the four forces as shown are in equilibrium
 
magnitudes of A and B ?  
Express F1 & F2 in unit vector form.
  A 1
(A) A  B = 0 (B)  F2
B 2 15 N
 
(C) A.B  48 (D) A = 5 °
30 10 N
     
26. For any two vectors A and B , if A.B  | A  B | ,
37° 30°
  
the magnitude of C  A  B is equal to -

(A) A 2  B2 (B) A + B
F1
AB
(C) A 2  B2  (D) A 2  B 2  2 AB
2
34. A particle is acted upon by the
 
forces F1  2 i  aj  3k , F2  5 i  cj  bk ,
27. If vectors A = î + 2 ĵ + 4 k̂ and B = 5 î represent
 
the two sides of a triangle, then the third side F3  b i  5 j  7k , F4  c i  6 j  ak . Find the val-
of the triangle has length equal to - ues of the constants a, b, c in order that the
(A) 56 (B) 21 (C) 5 (D) 6 particle will be in equilibrium.


28. A vector is along the positive x-axis. If its 35. A vector A of length 10 units makes an angle
 
vector product with another vector F2 is zero,
of 60º with the vector B of length 6 units.

then F2 could be - Find the magnitude of the vector difference
  
(A) 4 ĵ (B)  (î  ĵ) (C) (ˆj  k̂ ) (D) (4î ) A – B & the angle it makes with vector A .

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 LEVEL – III PREVIOUS YEARS
1. Angular momentum is : [AIPMT 1993]     
(A) Axial vector (B) Polar vector 8. If A  B = A = B then angle between A
(C) Scalar (D) None of these

and B will be :– [AIPMT 2001]
2. A force vector applied on a mass is represented
(A) 90° (B) 120°

as F  6 ˆi  8 ˆj  10kˆ and the mass accelerates (C) 0° (D) 60°
with 1m/s2. What will be the mass of the body ?
[AIPMT 1996] 9. The vector sum of two forces is perpendicular
to their vector difference. In that case, the
(A) 10 2 kg (B) 2 10 kg
force :
(C) 10 kg (D) 20 kg (A) Are equal to each other. [AIPMT 2003]
(B) Are equal to each other in magnitude.

3. Find the torque of a force F  2ˆi  ˆj  4kˆ acting (C) Are not equal to each other in magnitude.
 (D) Cannot be predicted.
at the point r  7ˆi  3 ˆj  kˆ : [CET 98, AIPMT 97]
     
(A) 14 ˆi  38 ˆj  16kˆ (B) 4 ˆi  4 ˆj  6kˆ If A  B =
10. 3 A . B , then the value of A  B
(C) 14 ˆi  38 ˆj  16kˆ (D) 11iˆ  26 ˆj  kˆ is : [AIPMT 2004]

FA  B
(A) G
I
AB
1/ 2

4. If a unit vector is represented by 0.5 i  0.8 j  ck ,

H
2 2
 J
3K
then the value of 'c' is : [AIPMT 1999]
(B) A + B
(A) 1 (B) 0.11
(C) (A2 + B2 + 3 AB)
1/2
(C) 0.01 (D) 0 .39
(D) (A2+B2+AB)1/2

5. 
For a body, angular velocity (  ) = î –2 ˆj + 3 k̂
11. ˆ is perpendicular to
If a vector (2 ˆi  3 ˆj  8k)

and radius vector ( r ) = î + ˆj + k̂ , then its
ˆ , then the value of 
the vector (4 ˆj  4 ˆi  k)
velocity is : [AIPMT 1999]

(A) –5 î + 2 ˆj + 3 k̂ (B) –5 î + 2 ˆj – 3 k̂ is :
(A) –1 (B) 1/2 [AIPMT 2005]
(C) –5 î – 2 ˆj + 3 k̂ (D) –5 î – 2 ˆj – 3 k̂ (C) –1/2 (D) 1

 
6.

What is the value of linear velocity, if   3ˆi  4 ˆj  kˆ 12. If the angle between the vectors A and B is ,
  

and r  5 ˆi  6 ˆj  6 kˆ ? [KCET 2000, AIPMT 1999] 
the value of the product B  A .A is equal to 
(A) 4 ˆi  13 ˆj  6kˆ (B) 6 ˆi  2 ˆj  3kˆ [AIPMT 2005]
(A) BA2 cos (B) BA2 sin
(C) 6 ˆi  2 ˆj  8kˆ (D) 18 ˆi  13 ˆj  2kˆ (C) BA2 sin cos (D) zero

 13. If |A × B| = 3A B, then the value of

7. If F = (60 î + 15 ˆj - 3 k̂ ) N and v = (2 î - 4 ˆj + 5 k̂ ) |A + B| is [CBSE AIPMT 2005]
m/s, then instantaneous power is : 1/2
[AIPMT 2000]  2 2 AB 
(A) (A2 + B2 + AB)1/2 (B)  A  B  
(A) 195 watt (B) 45 watt.  3
(C) 75 watt (D) 100 watt
 
1/2
(C) A + B (D) A2  B2  3AB

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  
14. The vecto rs A and B are such that  
21. A force of (3 i  4 j) newton acts on a body
    
A  B  A  B . The angle between vectors A
 
 and displaces it by (3 i  4 j) metre. The work
and B is - [RPMT 1999, AIPMT 2006]
done by the force is : [AIIMS 2001]
(A) 90° (B) 60°
(A) 10J (B) 12J
(C) 75° (D) 45°
(C) 19J (D) 25J

15. A particle is moving such that its position  

coordinates (x, y) are (2m, 3m) at time 22. The vector P  aiˆ  ajˆ  3kˆ and Q  aiˆ  2 ˆj  kˆ are
t = 0, (6m, 7m) at time t = 2 s and (13m, 14 perpendicular to each other. The positive value
m) at time t = 5 s. Average velocity vector of a is : [EAMCET 1998, AIIMS 2002]
( av) from t = 0 to 5 s is [CBSE AIPMT 2014] (A) 3 (B) 2
(C) 1 (D) zero
(A)
1
5
 
13iˆ  14j
ˆ (B)
3

7 ˆ ˆ
ij 
23. The direction of the angular velocity vector is
along : [AIIMS 2004]

(C) 2 ˆi  ˆj (D)
5

11 ˆ ˆ
ij  (A) the tangent to the circular path
(B) the inward radius
(C) the outward radius
16. The angle between the two vectors (D) the axis of rotation
       
A  3 i  4 j 5 k and B  3 i  4 j 5 k will be :  
24. A and B are two vectors and  is the angle
[AIIMS 1996]  
d i
 
(A) zero (B) 180° between them, if A  B = 3 A. B the value
(C) 90° (D) 45° of  is :- [AIPMT 2007]
(A) 90° (B) 60°
17. The forces, which meet at one point but their (C) 45° (D) 30°
lines of action do not lie in one plane, are called :
[AIIMS 1996] 25. A car travels 6 km towards the north at an angle
(A) non-coplanar and non-concurrent forces 45° to the East and then travels distance of 4 km
(B) coplanar and non-concurrent forces towards the north at an angle 135° to the east.
(C) non-coplanar and concurrent forces How far is the point from the starting point ? What
(D) coplanar and concurrent forces angle does the straight line joining its initial and final
positions makes with the east ? [AIIMS 2008]
18. What happens, when we multiply a vector by (– 2) ? (A) 50 km and tan (5)
–1

[AIIMS 1997]
(A) direction reverses and unit changes (B) 10 km and tan ( 5 )
–1

(B) direction reverses and magnitude is doubled (C) 52 km and tan (5)
–1

(C) direction remains unchanged and unit

changes (D) 52 km and tan
–1
 5
(D) none of these

    26. There are N coplanar vectors each of

19. If P.Q = PQ, then angle between P and Q is : magnitude V. Each vector is inclined to the
(A) 0° (B) 30° [AIIMS 1999] 2
(C) 45° (D) 60° preceding vector at angle . What is the
N
magnitude of their resultant ? [AIIMS 2009]
20. Two vectors of equal magnitude have a resultant
equal to either of them in magnitude . The angle V
(A) (B) V
between them is : [AIIMS 2001] N
(A) 60° (B) 90° N
(C) 105° (D) 120° (C) Zero (D)
V

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    
27. The angle made by the vector A  ˆi  ˆj with x- 35. If vectors P , Q and R have magnitudes 5,
  
axis is [EAMCET 1996] 12 and 13 units and P  Q  R , the angle
(A) 90° (B) 45°  
(C) 22.5° (D) 30° between Q and R is : [CEET 1998]

1  5  1  5 
28. If the sum of two unit vectors is a unit vector, (A) Cos   (B) Cos  
then the magnitude of their difference is :  12   13 
[MANIPAL-1996]
1  12  1  2 
(A) 2 (B) 3 (C) Cos   (D) Cos  
 13   13 

1
(C) (D) 5 36. If two numerically equal forces P and P acting
2
at a point produce a resultant force of
magnitude P itself, then the angle between the
29. Which of the following is a vector quantity ? two original forces is : [CEET 1999]
[AFMC 1997] (A) 0° (B) 60°
(A) Temperature (B) Surface tension (C) 90° (D) 120°
(C) Calorie (D) Force
     
   37. If A  B  C and A  B  C then the angle
30. The magnitudes of vectors A , B and C are
 
   between A and B is : [EAMCET 1999]
respectively 12, 5 and 13 units and A  B  C ,
  (A) 45° (B) 60°
then the angle between A and B is : (C) 90° (D) 120°
(A) 0 (B) 45° [CPMT 1997]
(C) /2 (D) /4 38. The angle between two vectors given by
ˆ and (7ˆi  4 ˆj  4 k)
(6 ˆi  6 ˆj  3k) ˆ is [EAMCET 99]
31. The angle between two vectors 2ˆi  3ˆj  kˆ  1  1  1  5 
(A) cos   (B) cos  
 3  3
 
and 3ˆi  6kˆ is : [CPMT 1997]

(A) 0° (B) 45° 1  2  1

 5
(C) sin   (D) sin  3 
(C) 60° (D) 90°  3  

32. Let A  ˆiACos  ˆjASin  , be any vector. Another
39. Which of the following vector identities is false ?
  [BHU 1999]
vector B which is normal to A is : [BHU 1997]
       
(A) P  Q  Q  P (B) P  Q  Q  P
(A) ˆiBCos  ˆjBSin  (B) ˆiBSin   ˆjBCos
       
(C) P.Q  Q.P (D) P  Q  Q  P
(C) ˆiBSin   ˆjBCos (D) ˆiACos  ˆjASin 

33. Which of the following is a scalar quantity ? 40. Which of the following is a scalar quantity ?
[AFMC 1998] [RPMT 1999]
(A) current (B) velocity
(A) Displacement (B) Electric Field
(C) force (D) acceleration
(C) Acceleration (D) Work
34. The sum of magnitudes of two forces acting
at a point is 16N. If the resultant force is 8N 41.  
If n̂  aiˆ  bjˆ is perpendicular to the vector ˆi  ˆj ,
and its direction is perpendicular to smaller
then the value of a and b may be : [RPMT 1999]
force, then the forces are : [CEET 1998]
(A) 1, 0 (B) –2, 0
(A) 6N & 10N (B) 8N & 8N
(C) 4N & 12N (D) 2N & 14N 1 1
(C) 3, 0 (D) , 
2 2

RPS M GARH PAGE # 9

42. Which of the following pair of forces will never 49. The unit vector parallel to the resultant of the
give resultant force of 2 N : [HP PMT 1999]  
vectors A  4 ˆi  3 ˆj  6 kˆ and B  ˆi  3 ˆj  8kˆ is :
(A) 2 N and 2 N (B) 1 N and 1 N
(C) 1 N and 3 N (D) 1 N and 4 N 1 ˆ
(A) 3 i  6 ˆj  2 kˆ  [EAMCET 2000]
7 

43. The vector B is directed vertically upwards
 1 ˆ
and the vector C points towards south, then (B) 3 i  6 ˆj  2kˆ 
7 
 
B  C will be : [RPMT 1999]
1  ˆ
(A) in west (C) 3 i  6 ˆj  2kˆ 
49  
(B) in east
(C) zero 1  ˆ
(D) 3 i  6 ˆj  2kˆ 
(D) vertically downwards 49  

44. A vector of length is turned through the angle  

 about its tail. What is the change in the 50. A vector A points vertically upward and B
position vector of its head ? [VBET-1999]  
points towards north. The vector product A  B
(A) cos  (B) 2sin 
is [UPSEAT 2000]
(C) 2cos  (D) sin
(A) zero (B) along west
(C) along east (D) vertically downward
45. Force 3N, 4N and 12N act at a point in mutually
perpendicular directions. The magnitude of the
51. Which of the following sets of concurrent forces
resultant force is : [CMC Vellore 1999]
may be in equilibrium ? [KCET 2000]
(A) 19 N (B) 13 N
(A) F1 = 3N, F2 = 5N, F3 = 1N
(C) 11 N (D) 5 N
(B) F1 = 3N, F2 = 5N, F3 = 9N
(C) F1 = 3N, F2 = 5N, F3 = 6N
46. The magnitude of a vector cannot be :
(D) F1 = 3N, F2 = 5N, F3 =15N
[CMC Ludhiana 1999]
(A) positive (B) unity  
52. If three vectors satisfy the relation A.B  0
(C) negative (D) zero
  
and A.C  0 , then A can be parallel to
   
47.  
The angle between vectors A  B and B  A   
[KCET 2003]
(A) C (B) B
is : [CMC Ludhiana 2000]
   
(C) B  C (D) B.C

(A) rad (B) rad
2
53. What is the projection of 3ˆi  4 kˆ on the y-axis ?

(C) rad (D) zero (A) 3 (B) 4 [RPMT 2004]
4
 (C) 5 (D) zero

48. A and B are two vectors. Now indicate the
wrong statement in the following : 54. Square of the resultant of two forces of equal
[CMC Vellore 2000] magnitude is equal to three times the product
        of their magnitude. The angle between them is
(A) A.B  B.A (B) A  B  B  A
        (A) 0° (B) 45° [KCET 2005]
(C) A  B  B  A (D) A  B  B  A (C) 60° (D) 90°

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55. A particle moves with a velocity 59. A police jeep is chasing with velocity of 45 kmh–1,
v a thief in another jeep moving with velocity 153
kmh–1. Police fires a bullet with muzzle velocity of
 
= 5jˆ  3jˆ  6kˆ ms–1 under influence of a contant 180 ms–1. The velocity with which will strike the
car of the thief, is [Manipal 2006]
ˆ  20k
force F = 10 î  10 ˆ N. Theinstantanceous (A) 150 ms–1 (B) 27 ms–1
power applied to the particle is [Manipal 2005] (C) 450 ms–1 (D) 250 ms–1
(A) 200 Js–1 (B) 40 Js–1
(C) 140 Js –1
(D) 170 Js–1 60. Two forces of 12 N and 8 N act upon a body.
The resultant force on the body has a maximum
56. A rive is flowing from west to east with a speed value of [Manipal 2008]
of 5 m min–1 A man can swin in still water with (A) 4 N (B) zero
a velocity 10 m min–1. In which directions, (C) 20 N (D) 8 N
should the man swin so as to take the shortest
possible path to go the south ? [BHU 2005] 61. A proton in a cyclotron changes its velocity
(A) 30° east of south (B) 60° east of south from 30 kmh–1 the north of 45 kmh–1 the east
(C) 60° west of south (D) 30° east of north in 20 s. What is the magnitude of average
acceleration during this time ? [Manipal 2008]
57. The vectors fro origin to the points A and B (A) 2.5 kms–2 (B) 12.5 kms–2
(C) 22.5 kms–2 (D) 32.5 kms–2
are A = 3 î – 6 ĵ +2 k̂ and B = 2 î + ĵ – 2 k̂ ,
respectively. The area of the OAB is 62. Rain is falling vertically downwards with a
[BHU 2005] velocity of 4kmh–1. A man walks in the rain
5 2 with a velocity of 3 kmh–1. The raindrops will
(A) 17 (B) 17 fall on the man with a velocity of [BHU 2008]
2 5
(A) 1 kmh–1 (B) 3 kmh–1
3 5 (C) 4 kmh –1
(D) 5 kmh–1
(C) 17 (D) 17
5 3
63. A train of 150m length is going towards North
58. Minimum numbers of unequal vectors which can directions at a speed of 10ms–1. A parrot flies
give zeo resultant are [AFMC 2005] at a speed of 5 ms–1 towards South direction
(A) two (B) three parallel to the railway track. The time taken by
(C) four (D) more than four parrot to cross the train is equal to [BHU 2008]
(A) 12 s (B) 8 s
(C) 15 s (D) 10 s

RPS M GARH PAGE # 11

 ANSWER-KEY
Level -I
1. B 2. B 3. D 4. A 5. A 6. D 7. D 8. A

9. B 10. D 11. B 12. C 13. B 14. C 15. B 16. A

17. A 18. C 19. A 20. B 21. D 22. A 23. B 24. D

25. D 26. A 27. B 28. B 29. C 30. D 31.A 32. A

33. (i) 105º, (ii) 150º, (iii) 105º 34. (B) 35. (B) 36. (A)  Q, (B)  R, (C)  P, (D)  S

Level-II
1. D 2. D 3. C 4. C 5. C 6. B 7. A 8. C

9. B 10. C 11. D 12. D 13. D 14. B 15. B 16.D

17. C 18. B 19. D 20. B 21. C 22. B 23. A 24.B

25. C 26. D 27. A 28. D 29. C 30. B 31. D

 
32. 2 ± 3 33. F1 = –(12 3 – 1) j & F2 = (12 – 5 3 ) i + (12 3 – 15) j
7
34. a = – 7, b = – 3, c = – 4 35. 2 19 ; cos–1
2 19

Level-III
1. A 2. A 3. D 4. B 5. A 6. D 7. B 8. B

9. B 10. D 11. C 12. D 13. A 14. A 15.D 16.C

17. C 18. B 19. A 20. D 21. D 22. A 23.D 24.B

25. C 26. C 27. B 28. B 29. D 30. C 31.D 32.C

33. D 34. A 35. C 36. D 37. D 38. D 39.B 40.A

41. D 42. D 43. B 44. B 45. B 46. C 47.A 48.C

49. A 50. B 51. C 52. C 53. D 54. C 55.C 56.A

57. A 58. A 59. A 60. C 61. A 62. D 63.D

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