Two forces, 1 N and 2 N, act along with the lines x = 0 and y = 0. The equation of the line along which the resultant lies is given by:

1.  y - 2x = 0

2.  2y - x = 0

3.  y + x = 0

4.  y - x = 0

If the angle between the vector $\overrightarrow{A} and \overrightarrow{B}$ is  $\theta$, the value of the product $\left(\overrightarrow{B}\times \overrightarrow{A}\right).\overrightarrow{A}$ is equal to:

1. $B{A}^2 \cos \theta$

2. $B{A}^2 \sin \theta$

3. $B{A}^2 \sin \theta \cos \theta$

4. zero

Assertion: The graph between P and Q is a straight line when P/Q is constant.
Reason: The straight-line graph means that P is proportional to Q or P is equal to a constant multiplied by Q.

Which one, of the following statements, is correct?
1. If both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
2. If both the assertion and the reason are true but the reason is not the correct explanation of the assertion.
3. If the assertion is true but the reason is false.
4. If the assertion and reason are both false

Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N. Then the magnitudes of the forces will be:

1. 12 N, 6 N

2. 13 N, 5N

3. 10 N, 8 N

4. 16 N, 2 N

If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:

1. 90°

2. 45° 

3. 180° 

4. 0°

Six vectors $\overrightarrow{a} through \overrightarrow{f}$ have the directions as indicated in the figure. Which of the following statements may be true?

1. $\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{-f}$                       
2. $\overrightarrow{d}+\overrightarrow{c}=\overrightarrow{f}$
3. $\overrightarrow{d}+\overrightarrow{e}=\overrightarrow{f}$                       
4. $\overrightarrow{b}+\overrightarrow{e}=\overrightarrow{f}$

In the given figure

1.  Angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ is $110°$

2.  Angle between $\overrightarrow{\mathrm{C}}$ and $\overrightarrow{\mathrm{D}}$ is $60°$

3.  Angle between $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ is $110°$

4.  Angle between $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ is $70°$

A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

(1)  1 N

(2)  11 N

(3)  15 N

(4)  20 N

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

(1)  2, 4, 8

(2)  4, 8, 16

(3)  1, 2, 1

(4)  0.5, 1, 2

A blind person after walking 10 steps in one direction, each of length 80 cm, turns randomly to the left or to the right by $90°.$ After walking a total of 40 steps the maximum possible displacement of the person from his starting position could be -

(1)  $320 \mathrm{m}$

(2)  $32 \mathrm{m}$

(3)  $16/\sqrt{2} \mathrm{m}$

(4)  $16\sqrt{2} \mathrm{m}$