A force of 20 N acts on a particle along a direction, making an angle of 60° with the vertical. The component of the force along the vertical direction will be

1. 2 N

2. 5 N

3. 10 N

4. 20 N

Subtopic:  Resolution of Vectors |
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If A and B are two vectors inclined to each other at an angle θ, then the component of A perpendicular to B and lying in the plane containing A and B will be:

1.  A.BB2B

2.  A - A.BB2B

3.  A - B

4.  A + B

Subtopic:  Scalar Product |
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If A  B and A × B = A · B, then 

1.  A  B

2.  A  B

3.  A is antiparallel to B

4.  A is inclined to B at an angle of 45°

Subtopic:  Vector Product |
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Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:

1. North-East

2. North-West

3. South-West

4. South-East

Subtopic:  Resultant of Vectors |
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Given are two vectors,  A= (2i^ - 5j^ + 2k^) and B = (4i^ - 10j^ + ck^). What should be the value of c so that vector A and B would become parallel to each other?

1.  1

2.  2

3.  3

4.  4

Subtopic:  Vector Product |
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If A×B=C+D, then which of the following statement is correct?

1. B must be perpendicular to C

2. A must be perpendicular to C

3. Component of C along A = Component of D along A

4. Component of C along A = - (Component of D along A

Subtopic:  Vector Product |
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What is the maximum value of 5sinθ – 12cosθ?

1.  12

2.  17

3.  7

4.  13

Subtopic:  Trigonometry |
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A block of weight W is supported by two strings inclined at 60° and 30° to the vertical. The tensions in the strings are T1 and T2 as shown. If these tensions are to be determined in terms of W using the triangle law of forces, which of these triangles should you draw? (block is in equilibrium) :-

                                 

1.            2.  

3.            4.  

Subtopic:  Resultant of Vectors |
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The magnitude of the resultant of two vectors of magnitude 3 units and 4 units is 1 unit. What is the value of their dot product?

1.  –12 units

2.  –7 units

3.  –1 unit

4.  0

Subtopic:  Scalar Product |
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The value of 1x+1dx is:

1.  ln (x + 1) + C

2.  x+1-2+C

3.  1x-12+C

4.   ln (x – 1) + C

Subtopic:  Integration |
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