Forces of 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

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. $\frac{7}{2}(\hat{j}-\hat{i})$

Given that $\overrightarrow{\mathrm{C} }= \overrightarrow{A } + \overrightarrow{B } \mathrm{and} \overrightarrow{\mathrm{C} }$ makes an angle $\mathrm{\alpha } \mathrm{with} \overrightarrow{\mathrm{A}} \mathrm{and} \mathrm{\beta } \mathrm{with} \overrightarrow{\mathrm{B}}$. Which of the following options is correct?

1.  $\mathrm{\alpha } \mathrm{cannot} \mathrm{be} \mathrm{less} \mathrm{then} \mathrm{\beta }$

2.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}<\mathrm{B}$

3.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}>\mathrm{B}$

4.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}=\mathrm{B}$

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

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. $R_2=B$

Choose any one of the following four responses:

1. If both assertion and reason are true and the reason is the correct explanation of the assertion.

2. If both assertion and 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 both are false.

Assertion: The graph between P and Q is a straight line when P/Q is constant.

Reason: The straight-line graph means that P proportional to Q or P is equal to constant multiplied by Q.

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 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12 N. Then the magnitudes of the forces are 

1. 12 N, 6 N

2. 13 N, 5N

3. 10 N, 8 N

4. 16 N, 2 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) $-5\sqrt{2},\pi /4$