# 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 are two vectors inclined to each other at an angle $\theta$, then the component of $\stackrel{\to }{\mathrm{A}}$ perpendicular to $\stackrel{\to }{\mathrm{B}}$ and lying in the plane containing  will be:

1.  $\frac{\stackrel{\to }{\mathrm{A}}\stackrel{\to }{\mathrm{.B}}}{{\mathrm{B}}^{2}}\stackrel{\to }{\mathrm{B}}$

2.

3.

4.

Subtopic:  Scalar Product |
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If  and  = , then

1.

2.

3.  $\stackrel{\to }{\mathrm{A}}$ is antiparallel to $\stackrel{\to }{\mathrm{B}}$

4.  $\stackrel{\to }{\mathrm{A}}$ is inclined to $\stackrel{\to }{\mathrm{B}}$ 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,   and . What should be the value of c so that vector  would become parallel to each other?

1.  1

2.  2

3.  3

4.  4

Subtopic:  Vector Product |
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If $\stackrel{\to }{A}×\stackrel{\to }{B}=\stackrel{\to }{C}+\stackrel{\to }{D}$, then which of the following statement is correct?

1. $\stackrel{\to }{B}$ must be perpendicular to $\stackrel{\to }{C}$

2. $\stackrel{\to }{A}$ must be perpendicular to $\stackrel{\to }{C}$

3. Component of $\stackrel{\to }{C}$ along $\stackrel{\to }{A}$ = Component of $\stackrel{\to }{D}$ along $\stackrel{\to }{A}$

4. Component of $\stackrel{\to }{C}$ along $\stackrel{\to }{A}$ = - (Component of $\stackrel{\to }{D}$ along $\stackrel{\to }{A}$

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 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 $\int \frac{1}{x+1}d\mathrm{x is:}$

1.  ln (x + 1) + C

2.  ${\left(x+1\right)}^{-2}+C$

3.  $\frac{1}{{\left(x-1\right)}^{2}}+C$

4.   ln (x – 1) + C

Subtopic:  Integration |
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