# Jee 2014 Booklet1 Hwt Introduction to Vectors & Forces

August 28, 2017 | Author: varunkohliin | Category: Euclidean Vector, Norm (Mathematics), Angle, Force, Mathematical Analysis

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Jee 2014 Booklet1 Hwt Introduction to Vectors & Forces...

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Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

What happens if a vector is multiplied by a number 2 ? (A) The magnitude of the vector is doubled but its direction remains the same (B) The magnitude of the vector remains the same but its direction is reversed (C) The magnitude of the vector is doubled and its direction is reversed (D) Neither the magnitude nor the direction of the vector undergo any change

2.

The magnitude of the resultant of two vectors of magnitude of the resultant of two vectors of magnitudes 3 units and 4 units in 5 units. What is the angle between two vectors ? (A)

3.

 4

(B)

 2

3 4

(C)

(D)

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. What is the angle between the two vectors? (A)

60

(B)

90

120

(C)

(D)

150

4.

The magnitudes of four pairs of displacement vectors are given. Which pairs of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm ? (A) 2 cm, 3 cm (B) 1 cm, 3 cm (C) 1 cm, 5 cm (D) 1 cm, 7 cm

5.

If the sum A + B of two vectors A and B equals the difference A  B between them, then : (A) (C)

6.

8.

(B) (D)

B is a null vector neither A nor B is a null vector

The resultant of two vectors A and B subtends an angle of 45 with either of them. The magnitude of the resultant is : (A)

7.

A is a null vector both A and B are null vectors

zero

(B)

2 A

(C)

A

(D)

2A

A and B are two vectors in a plane at an angle of 60 with each other. C is another vector perpendicular to the plane containing vectors A and B. Which of the following relations is possible ? (A) A+B=C (B) A + C=B (C) A×B=C (D) A×C=B Vector C is the sum of two vectors A and B and vector D is the cross product of vectors A and B. What is the angle between vectors C and D ? (A)

zero

(B)

60

90

(C)

(D)

180

9.

The resultant of two vectors of magnitudes 3 units and 4 units is 1 unit. What is the magnitude of their cross product ? (A) 12 units (B) 7 units (C) 1 unit (D) zero

10.

Three vectors A, B and C are related as A + B = C. If vector C is perpendicular to vector A and the magnitude of C is equal to the magnitude of A, what will be the angle between vectors A and B ? (A)

45

VMC/Introduction to Vectors

(B)

90

135

(C)

41

(D)

180

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The magnitude of the resultant of (A + B) and  A  B  is : (C)

A2  B 2

(D)

What is the angle between the resultant vector and vector A ?  A (A) zero (B) (C) cos 1   B

B cos 1    A

(D)

(A) 2.

3.

2A

(B)

2B

1 (B) (C) 2 The angle  between the vector ˆi  ˆj  kˆ and vector ˆi is given by :

3

 3  1   1    cos 1  (C)   cos 1    sin 1    (B)   3  3  2  Given that 0.2 ˆi  0.6 ˆj  akˆ is a unit vector. What is the value of a ?

(A) 5.

(A) 6.

8.

10.

(B)

0 .4

(C)

0 .6

1 ˆ ˆ i  j  2

(B)

3 ˆ ˆ i  j  2

5 ˆ ˆ i  j  2

(C)

   Figure shows three vectors a , b and c . If RQ = 2PR, which of the following relations is correct ?    (A) 2a + c = 3b    (B) a + 3c = 2b    0 (C) 3a – c = 2b    (D) a + 2c = 3b

2

(D)

 3   sin 1    2 

(D)

0 .8

(D)

7 ˆ ˆ i  j  2

Q  a

 b

R  c

P

The magnitudes of vectors A, B and C are respectively 12, 5 and 13 units and A + B = C. The angle between A and B is.   (D) 2 4 The sum of magnitude of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to the smaller force, then the forces are (A) 6 N and 10 N (B) 8 N and 8 N (C) 4 N and 12 N (D) 2 N and 14 N

(A) 9.

0 .3

(D)

Given A  2 ˆi  3 ˆj and B  ˆi  ˆj . The component of vector A along vector B is : (A)

7.

 A B  cos 1    A B

If ˆi and ˆj are unit vectors along x-axis and y-axis respectively, the magnitude of vector ˆi  ˆj will be : (A)

4.

A2  B 2

zero

(B)

(C)

Two vectors C = A + B and D and A  B are perpendicular to each other. Then (A) A is parallel to B (B) A is perpendicular to B (C) B is a null vector (D) A and B have a equal magnitudes

VMC/Introduction to Vectors

42

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A vector A is along the positive z-axis and its vector product with another vector B is zero, then vector B could be : ˆi  ˆj ˆj  kˆ (A) (B) (C) (D) 4 ˆi  7 kˆ

2.

A body, initially at rest, is acted upon by four forces F1  ˆi  kˆ , F2  2 ˆj  3kˆ , F3  3ˆi and F4  3 ˆj  4ˆi . In which plane will the body move ? (A)

3.

x  y plane

x  z plane

(B)

y  z plane

(C)

(D)

None of these

A is a vector which when added to the resultant of vectors 2ˆi  3 ˆj  4kˆ and ˆi  5 ˆj  2kˆ yields a unit vector along the y-axis. Then vector A is : (A)

4.

3ˆi  ˆj  6kˆ

(B)

3ˆi  ˆj  6kˆ

(C)

(D)

3ˆi  ˆj  6kˆ

The angle between two vectors A and B is  . Vector R is the resultant of the two vectors. If R makes an angle (A)

5.

3ˆi  ˆj  6kˆ

A = 2B

A

(B)

B 2

(C)

A=B

(D)

 with A, then : 2

AB = 1

What is the torque of a force F  2ˆi  3 ˆj  4kˆ Newton acting at a point r  3i  2 j  3kˆ metre about the origin ? (B) (C) (D) 6ˆi  6 ˆj  12kˆ 14ˆi  6 ˆj  13kˆ 6ˆi  6 ˆj  12kˆ 17ˆi  6 ˆj  13kˆ   Two vectors A1 and A2 each of magnitude A are inclined to each other such that their resultant is equal to 3 A . Then the resultant of   A1 and  A2 is : (A)

6.

(A) 7.

8.

9.

(B)

3A

(C)

2A

(D)

A

(A)

2

(B)

8

(C) 7   The area of a parallelogram whose adjacent sides are P  2ˆi  3 ˆj and Q  ˆi  4 ˆj is :

(D)

8

(A)

5 square units

(B)

15 square units

(D)

25 square units

(C)

20 square units

  If A  ˆi  2 ˆj  3kˆ and B  3ˆi  2 ˆj  kˆ , then the area of parallelogram formed from these vectors as the adjacent sides will be :

(A) 10.

2A

    If A and B are perpendicular vectors, where A  5ˆi  7 ˆj  3kˆ and B  2ˆi  2 ˆj  akˆ , then the value of a is :

2 3 square unit

(B)

4 3 square units (C)

6 3 square unit

(D)

8 3 square units

  The vectors P  aiˆ  ajˆ  3kˆ and Q  aiˆ  2 ˆj  kˆ are perpendicular to each other. The positive value of a is :

(A)

3

VMC/Introduction to Vectors

(B)

2

(C)

1

43

(D)

0

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

     Given A  3i  ˆj  7kˆ . When a vector B is added to A , we get a unit vector along X-axis. Then B is : ˆi  2 ˆj  3kˆ

(C) (D) 2ˆi  ˆj  7kˆ ˆi  3kˆ  4 ˆj 4ˆi  2 ˆj  3kˆ    The magnitude of the X and Y components of A are 7 and 6. Also the magnitude of X and Y components of A  B are 11 and 9  respectively. What is the magnitude of B ? (A) 5 (B) 6 (C) 8 (D) 9 (A)

2.

3.

The angle between the z-axis and the vector ˆi  ˆj  2kˆ is : 30

(A) 4.

(B)

7.

(D)

If the resultant of two forces (A + B) and  A  B  is

2

F

60

5F

F

2

    

(C)

(C)

 A2  B 2  cos 1   2 2  2 A B 

1

 2 A2  B 2  cos 1   A2  B 2  

    

PQ

    If P  2ˆi  3 ˆj  kˆ and Q  3ˆi  2 ˆj, then P  Q is :

zero

(C) 12 (D) 15     The magnitude of the two vectors a and b are a and b respectively. The magnitude vector product of a and b cannot be :

(B)

6

equal to zero (B) less than ab (C) equal to ab   Given r  4 ˆj and P  2ˆi  3 ˆj  kˆ . The angular momentum is  L  r  p  . 4ˆi  8kˆ

(A) 10.

   (D)  

(D)

(A) 9.

90

(D)

A  B , then the angle between these forces is :

 A2  B 2   A2  B 2   1  (A) cos 1   (B) cos   2 A2  B 2  A  B2          If P  Q  0, then | P  Q | is :   (A) (B) zero | P || Q |

(A) 8.

60

(C)

3F

6.

45

Two forces, each equal to F, act as shown in figure. Their resultant is : F (A) (B) F 2 (C)

5.

(B)

(B)

8ˆi  4kˆ

8 ˆj

(C)

(D)

greater than ab

(D)

9kˆ

A force of 10ˆi  3 ˆj  6kˆ N acts on a body of mass 100 g and displaces it from 6ˆi  5 ˆj  3kˆ m to 10ˆi  2 ˆj  7 kˆ m . The work done

is : W  F , S (A)

21 J

VMC/Introduction to Vectors

(B)

121 J

(C)

361 J

44

(D)

1000 J

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME : ROLL NO.

TIME : 25 MINUTES

TEST CODE : V&F  START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

3.

4.

5.

6.

7.

8.

9.

  Projection of P on Q is :    ˆ ˆ PQ Pˆ  Q PQ (A) (B) (C) (D)   Given A  4ˆi  6 ˆj and B  2ˆi  3 ˆj . Which of the following is correct ?       | A| 1   (A) (B) (C) (D) A B  0 A.B  24 |B| 2       If A.B  0 and A  B  1, then A and B are definitely : (A) perpendicular unit vectors (B) parallel unit vectors (C) parallel (D) perpendicular

  A and B are anti-parallel

   The torque of a force F   3ˆi  ˆj  5kˆ acting at a point is  . If the position vector of the point is 7ˆi  3 ˆj  kˆ , then  of this force about origin is : (A) (B) (C) (D) 7ˆi  8 ˆj  9kˆ 14ˆi  ˆj  3kˆ 2ˆi  3 ˆj  8kˆ 14ˆi  38 ˆj  16kˆ

Following forces start acting on a particle at rest at the origin of the co-ordinate system   F1  5ˆi  5 ˆj  5kˆ , F2  2ˆi  8 ˆj  6kˆ , F3  6ˆi  4 ˆj  7 kˆ , F4  ˆi  3 ˆj  2kˆ . The particle will move : (A) in x-y plane (B) in y-z plane (C) in x-z plane (D) along x-axis

simultaneously

Force is inclined at 60 to be the horizontal. If its rectangular component in the horizontal direction is 50 N, then component of the force in the vertical direction is : (A) 25 N (B) 75 N (C) 87 N (D) 100 N

T

A small sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall  by a stick. The force acting on the sphere are show in figure. Which of the following statements is wrong ? P    (A) (B) T  P W 0 P  W tan (C) T2 = P2 + W2 (D) T=P+W W    The X and Y components of vector A have numerical values 6 and 6 respectively and that of A  B have numerical values 10 and 9.  What is the numerical value of B ? (A) 2 (B) 3 (C) 4 (D) 5

A man, using a 70 kg garden roller on a level surface exerts a force of 200 N at 45 to the ground. What is the vertical force of the roller on the ground, if the pushes the roller ? ( g 10 ms 2 ) (A) 70 N (B) 200 N

10.

  PQ

(C)

  If the vectors A  2ˆi  4 ˆj and B  5ˆi  p ˆj are parallel then p = (A) 10 (B) –10 (C)

VMC/Introduction to Vectors

45

560 N

(D)

840 N

4

(D)

–4

HWT/Physics

Vidyamandir Classes DATE :

  MARKS :    9 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 9 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Given that T1  100 N , then find T2 : (A) (C)

A 100 N 3 200 N

(B)

100 3N

50N

(D)

60 

30 

B

T2

T1 C

72 N

G 2.

Three forces of magnitudes 6 N, 6 N and figure. Resultant of these forces is : (A) 12 N along OB (C) 18 N along OC

3.

(C)

5.

18 N along OA 12 N along OE

1 N , 60 2 N , 90

(B)

2 N , 60

(D)

2 N , 90

F

 O

2N

 2N

10

(B)

10

(C)

5



(D)

15

In a two dimensional motion of a particle, the particle moves from point A, position vector   r1 to point B, position vector r2 . If the magnitudes of these vectors are respectively,

 r1

A

1

 r2

B

then find the magnitude of the displacement vector. 2 (A) 15 (B) (C) 17 (D) 13 15     The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half of the magnitude of vector B .   Then the angle between A and B is : (A)

9.

6N

B

6N A

2N

r1 = 3 and r2 = 4 and the angles they make with the x-axis are 1  75 and 15 , respectively,

8.

E C

7.

F

D

        If A1 and A2 are two non-collinear unit vectors and if | A1  A2 |  3 , then the value of A1  A2 . 2 A1  A2 is : (A) 1 (B) 1/2 (C) 3/2 (D) 2   A vector A when added to the vector B  3ˆi  4 ˆj yields a resultant vector that is in the positive y direction and has a magnitude equal   to that of B . Find the magnitude of A .

(A) 6.

(B) (D)

Four concurrent coplanar forces in Newton are acting at a point and keep it in equilibrium figure. Then values of F and  are : (A)

4.

72 N act at a corner of a cube along three sides as shown in

30

(B)

45

150

(C)

(D)

120

The magnitude of resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of the sides of an equilateral triangle taken in order is : (A) zero (B) (C) (D) 2 2 unit 4 3 unit 3 unit     Two vectors A and B are inclined to each other at an angle  . Which of the following is the unit vector perpendicular to both A and B ?     ˆ  Bˆ ˆ  Bˆ A B A A B A   (A) (B) (C) (D) sin AB sin AB cos A B

VMC/Introduction to Vectors

46

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A sphere is placed between 2 inclined planes as shown. Find N1 and N2. (A) (C)

2.

N1 

100 100 N ; N2  N 2 2

(B)

N1 

50 N ; N 2  50 N 3

(D)

Sphere 100 N

N1  50 N ; N 2  50 3 N

N1

60

N1 = 50 N ; N2 = 50 N

30

N2

A block of 50 N is pressed normally against a wall as shown. The frictional force acting on the block is : S  1

F = 100N (A) 3.

4.

(A)

0.025

(B)

0.2

(C)

0.33

(D)

0.25

(B)

100 N

(C)

5N

(D)

10 N

400 N rough W

B

A swimmer wants to directly reach the point B starting from A, The river is 2 flowing along x-axis. If the velocity of the swimmer is times the 3 velocity of the river, find the angle  from the line AB at which his swimming effort should be directed. 60

30

(B)

45

(C)

45

A (D)

y x

65

A man walking with 3 m/s feels the rain falling vertically with a speed of 4 m/s. Find the angle which the rainfall makes with the vertical according to a stationary observer : (A)

6.

50 N

For W = 100 N, the 400 N block just starts sliding. Find the coefficient of static friction.

(A) 5.

50N

37

53

(B)

The tension in string OA is : (A)

50 N

(B)

35 3 N

(C) (D)

100 N 75 N

VMC/Introduction to Vectors

3 tan 1   5

(C)

(D)

5 tan 1   3

30

A

O 50 3 N

47

HWT/Physics

Vidyamandir Classes 7.

8.

9.

10.

Find  if the system is in equilibrium. (A)

45

(B)

30

(C)

60

(D)

75

The force F for which the block starts moving is : (A) 31.25 N (C) 22.7 N

3m

m

m F

(B) (D)

25 N 41.7 N

S 

1 2

50 N

5 m/s

The magnitude of v AB is : (A)

5 m/s

(B)

5 3 m/ s

(C)

5 2 m/s

(D)

None of these

vB

60 vA

5 m/s

The block shown is moving with constant velocity. Find k between the block and the surface. (A)

tan

(B)

cot 

(C)

sin 

(D)

cos 

VMC/Introduction to Vectors

37

m

v

48

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

The frictional force on the 100 N block is: 37

50N

100N

 s  0 .5

(A) 2.

30 N

(B)

50 N

(C)

40

(D)

65 N

(C)

30 ˆi

(D)

30 ˆi

50 m

(D)

0m

vBA  ?

A

20m/s

B

10m/s

Y

X (A) 3.

10 ˆi

(B)

The shortest distance between the car and the motorcycle will be :

M 100 mtrs

(A) 4.

30 m/s

30 m/s Car

100 m

(B)

50 2 m

(C)

A force F   3ˆi  7 ˆj  N moves a body from (1m, 1m, 1m) to (2m, 3m, 4m). The work done by this force is: (A)

5.

10 ˆi

17 J

(B)

20 J

(C)

34 J

(D)

40 J

(C)

90

(D)

Not possible

Find  so that the swimmer directly lands on the point B.

B vSR = 2m/s

vR = 2m/s

A (A) 6.

45

(B)

30

The swimmer can swim in still water with a speed of 2.5 m/s. What is the shortest time taken by him to swim across the river?

10m vR = 2m/s (A)

4 seconds

VMC/Introduction to Vectors

(B)

5 seconds

(C)

6.7 seconds

49

(D)

8 seconds

HWT/Physics

Vidyamandir Classes 7.

If | a |  | b | , then the angle between a  b and a  b is: (A)

8.

0

(B)

90

180

(C)

45

(D)

A particle is moving on a circular path with constant speed v. The magnitude of the change in its velocity after it has described an angle of 90 is: (A)

v

(B)

2v

(C)

0

(D)

3v

Paragraph for Q.9 - 10 2 blocks A and B of weight 10 kg and 5 kg respectively are placed on a smooth inclined

B A

plane as shown. The system is in equilibrium. If the angle of inclination is increased, the 37

block B starts slipping. 9.

Find  s between A and B. (A)

10.

0.75

The tension in the string is: (A) 29.4 N

VMC/Introduction to Vectors

(B)

1.33

(C)

0.50

(D)

0.33

(B)

39.2 N

(C)

58.8 N

(D)

88.2 N

50

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A rod of weight W is supported horizontally by 2 strings: one at a distance L/3 and the other at a distance L/2 from the centre of the rod. The tensions T1 and T2 are given by :

2.

W W ; T2  3 2

(A)

T1 

(B)

W W T1  ; T2  2 2

(C)

W W T1  ; T2  4 4 T1 

(D)

5.

6.

T1

T2

a  b   c  d   ? (A)

 kˆ

(B)

28kˆ

(C)

19 kˆ

(D)

19 kˆ

A particle is moving on a circular path with a constant speed v. The magnitude of the change in its velocity after it has described an angle of 90 is :

L/3

(A)

L/2

3W 2W ; T2  5 5

(C) 7.

A 10 kg steel ball is suspended by 2 strings as shown. The tensions in the 2 strings are: (g = 9.8 m/s2)

v

v 2

(B)

v 2

(D)

2v

Following forces start acting on a particle at rest at the origin of the coordinate system simultaneously. F1  2ˆi  3 ˆj  kˆ F2   ˆi  2 ˆj  kˆ F3  4ˆi  4 ˆj  4kˆ

45

Then the particle will move : (A) (B) ln x  y plane

60

(A)

196 N and 98 N

(B)

98 3 N and 98 2 N

(C)

196 98 2 N and N 1 3 1 3

(D)

98 196 N and N 3 6

F4  2ˆi  ˆj  4kˆ

(C) 8.

9.

ln y  z plane

(D)

ln x  z plane

Along y-axis

Of these forces, the resultant of which of cannot be zero : (A) 2, 4, 7 (B) 10, 10, 12 (C) 10, 20, 40 (D) 10, 20, 25

 A  B   A  B

Paragraph for Q. 3-5

(A) (B)

can never be zero is always zero

a  ˆi  3 ˆj, b  2ˆi  4 ˆj, c  4ˆi  7 ˆj, d   6ˆi  ˆj .

(C)

can be zero if A and B are collinear

3.

4.

a b  c d 

(D)

(A)

5 ˆi  9 ˆj

(B)

5 ˆi  9 ˆj

(C)

5 ˆi  9 ˆj

(D)

5 ˆi  9 ˆj

(B) (D)

15 15

10.

a . b  c ? (A) (C)

21 5

VMC/Introduction to Vectors

51

None of these A unit vector in the direction of ˆi  ˆj is : (A)

ˆi  ˆj

(B)

1 ˆ ˆ i  j  2

(C)

ˆi  ˆj

(D)

Not defined

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : V&F 

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.  Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

The sum of these 3 vectors is : (A) 4i  4 j (B)

5i  2 j

(C)

4i  3 j

(D)

5i  8 j

Y

6 2

45

5

3i  4 j  5k  km

For Q. 3 - 6

10i  10 j  10k  km (C)

(B)

Y

c

b  4i  3 j

37

 k  km 

X

32

(B)

24

(C)

24

(D)

64

36k

(B)

2k

(C)

79k

(D)

36k

(B)

3i  2 j

(C)

2i  6 j

(D)

3i  7 j

(B)

79k

(C)

79k

(D)

36k

abc (A)

3i  5 j

a  c  b (A)

7.

 10  10  10 i j  2 2  2

a  b  c  (A)

6.

(D)

a  b . c  (A)

5.

3 7 i  6 j  k

10

a  i  7 j

4.

37 X 53

A helicopter is displaced by 10km during some interval of time. Its displacement vector could possibly be given by : (A)

3.

10

36 k

A large hemi sphere of radius 100m is fixed on the ground. A man weighing 700 N stands a at height of 50m above the ground. N and f represent the normal and frictional force acting on him. (A) N = 700 N, f = 0 Man (B) N = 350 N, f = 350 N (C)

N = 350 N, f = 350 3 N

(D)

N = 350 3 , f = 350 N

VMC/Introduction to Vectors

50m

52

HWT/Physics

Vidyamandir Classes 8.

Two blocks are kept on a smooth wedge which is fixed on a horizontal ground. Find m if the system is in equilibrium. 20 (A) m = 10 kg (B) m kg 3 (C)

9.

10.

m = 7 Kkg

(D)

20kg

30

(D)

200 N

30

T

The indicated tension if w = 100 N is (A) 50 N

(B)

60 N

(C)

(D)

50 3 N

VMC/Introduction to Vectors

60

m = 16.67 kg

In Q.8, the normal reaction on the pulley by the wedge is : (g = 10ms 2 ) (A) 173 N (B) 141 N (C) 100 N

80 N

M

53

w

HWT/Physics