The three vectors OA, OB and OC have the same magnitude R. Then the sum of these vectors have magnitude -

                       

1. $\mathrm{R}$

2. $\sqrt{2}\mathrm{R}$

3. $3\mathrm{R}$

4. $\left(1+\sqrt{2}\right)\mathrm{R}$

A truck travelling due north with 20m/s turns towards west and travels at the same speed. Then the change in velocity is -

(1)  40 m/s north-west

(2)  $20\sqrt{2}$ m/s north-west

(3)  40 m/s south-west

(4)  $20\sqrt{2}$ m/s south-west

A particle is moving in a circle of radius r centered at O with constant speed v. The change in velocity moving from A to B $\left(\angle \mathrm{AOB}=40°\right)$ is -

(A)  $2\mathrm{v} \cos 40°$

(B)  $2\mathrm{v} \sin 40°$

(C)  $2\mathrm{v} \cos 20°$

(D)  $2\mathrm{v} \sin 20°$

Two forces, ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ are acting on a body. One force is doubled of the other force and the resultant is equal to the greater force. Then the angle between the two forces is -

(A)  ${\cos }^{-1} \left(1/2\right)$

(B)  ${\cos }^{-1} \left(-1/2\right)$

(C)  ${\cos }^{-1} \left(-1/4\right)$

(D)  ${\cos }^{-1} \left(1/4\right)$

If the angle between vector a and b is an acute angle, then the difference a$-$b is -

(1)  the main diagonal of the parallelogram

(2)  the minor diagonal of the parallelogram

(3)  any of the above

(4)  none of the above

What displacement must be added to the displacement $25 \hat{\mathrm{i}}-6 \hat{\mathrm{j}} \mathrm{m}$  to give a displacement of $7.0 \mathrm{m}$ pointing in the x-direction?

(1)  $18 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}$

(2)  $32 \hat{\mathrm{i}}-13 \hat{\mathrm{j}}$

(3)  $-18 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}$

(4)  $-25 \hat{\mathrm{i}}+13 \hat{\mathrm{j}}$

The value of unit vector in the direction of vector $\mathrm{A}=5 \hat{\mathrm{i}}-12 \hat{\mathrm{j}}$, is -

1. $\hat{\mathrm{i}}$

2. $\hat{\mathrm{j}}$

3. $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)/13$

4. $\left(5\hat{\mathrm{i}}-12\hat{\mathrm{j}}\right)/13$

A child pulls a box with a force of \(200~\text{N}\) at an angle of $\mathrm{}$\(60^{\circ}\) above the horizontal. Then the horizontal and vertical components of the force will be:
              

1. \(100~\text{N}, ~175~\text{N}\)
2. \(86.6~\text{N}, ~100~\text{N}\)
3. \(100~\text{N}, ~86.6~\text{N}\)
4. \(100~\text{N}, ~0~\text{N}\)

A man rows a boat at a speed of $\mathrm{}$\(18~\text{km/hr}\) in the northwest direction. The shoreline makes an angle of $\mathrm{}$\(15^{\circ}\) south of west. The component of the velocity of the boat along the shoreline is:
1. \(9~\text{km/hr}\)
2. \(18\frac{\sqrt{3}}{2}~\text{km/hr}\)
3. \(18\cos 15^{\circ}~\text{km/hr}\)
4. \(18\cos 75^{\circ}~\text{km/hr}\)

A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is:

1. $5\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}\right)$

2. $5\left(4\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right)$

3. $0.6\hat{\mathrm{i}}+0.8\hat{\mathrm{j}}$

4. $6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$