Given below are two statements:

Assertion (A):	The graph between \(P\) and \(Q\) is a straight line when \(\frac{P}{Q}\) is constant.
Reason (R):	The straight-line graph means that \(P\) is proportional to \(Q\) or \(P\) is equal to a constant multiplied by \(Q\).

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False

Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is 

(1) 45°

(2) 120°

(3) 150°

(4) 60°

Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is F/3. The angle between the two forces is 

(1) ${\cos }^{-1}\left(-\frac{{\displaystyle 17}}{{\displaystyle 18}}\right)$

(2) ${\cos }^{-1}\left(-\frac{{\displaystyle 1}}{{\displaystyle 3}}\right)$

(3) ${\cos }^{-1}\left(\frac{{\displaystyle 2}}{{\displaystyle 3}}\right)$

(4) ${\cos }^{-1}\left(\frac{8}{9}\right)$

Two forces are such that the sum of their magnitudes is \(18~\text{N}\) and their resultant is perpendicular to the smaller force and the magnitude of the resultant is \(12~\text{N}\). Then the magnitudes of the forces will be:
1. \(12~\text{N}, 6~\text{N}\)
2. \(13~\text{N}, 5~\text{N}\)
3. \(10~\text{N}, 8~\text{N}\)
4. \(16~\text{N}, 2~\text{N}\)

If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is 

(1) $5\sqrt{2},\pi /3$

(2) $5\sqrt{2},\pi /4$

(3) $-5\sqrt{2},\pi /3$

(4) $-5\sqrt{2},\pi /4$

Two forces A and B have a resultant $R_1$. If B is doubled, the new resultant $R_2$ is perpendicular to A. Then

1. $R_1=A$

2. $R_1=B$

3. $R_2=A$

4. $R_2=B$

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

 $1.$ $0^0$
$2.$ ${90}^0$
$3.$ ${45}^0$
$4.$ ${180}^0$

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

Given that \(\overrightarrow {C}= \overrightarrow {A}+\overrightarrow {B}\)$\mathrm{and}$\(\overrightarrow {C}\) makes an angle $\mathrm{}$\(\alpha\) with \(\overrightarrow {A}\) and \(\beta\) with \(\overrightarrow {B}\). Which of the following options is correct?
1. \(\alpha \) cannot be less than \(\beta\)
2. \(\alpha <\beta, ~\text{if}~A<B\)
3. \(\alpha <\beta, ~\text{if}~A>B\)
4. \(\alpha <\beta, ~\text{if}~A=B\)

Component of $3\hat{i}+4\hat{j}$ perpendicular to $\hat{i}+\hat{j}$ and in the same plane as that of $3\hat{i}+4\hat{j}$ is:

1. $\frac{1}{2}(\hat{j}-\hat{i})$

2. $\frac{3}{2}(\hat{j}-\hat{i})$

3. $\frac{5}{2}(\hat{j}-\hat{i})$

4. $\frac{7}{2}(\hat{j}-\hat{i})$