In the given figure

 

1.	Angle between \(\overrightarrow {A}\) and \(\overrightarrow {B}\) is  \(110^{\circ}\)
2.	Angle between \(\overrightarrow {C}\) and \(\overrightarrow {D}\) is  \(60^{\circ}\)
3.	Angle between \(\overrightarrow {B}\) and \(\overrightarrow {C}\) is  \(110^{\circ}\)
4.	Angle between \(\overrightarrow {B}\) and \(\overrightarrow {C}\) is  \(70^{\circ}\)

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)  $320<mspace\; width="1em"></mspace>\mathrm{m}$

(2)  $32<mspace\; width="1em"></mspace>\mathrm{m}$

(3)  $16/\sqrt{2}<mspace\; width="1em"></mspace>\mathrm{m}$

(4)  $16\sqrt{2}<mspace\; width="1em"></mspace>\mathrm{m}$

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is -

1. $120°$

2.  $150°$

3.  $135°$

4.  None of these

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

What is the resultant of three coplanar forces: $300<mspace\; width="1em"></mspace>\mathrm{N}$ at $0°$, $400<mspace\; width="1em"></mspace>\mathrm{N}$ at $30°$ and $400<mspace\; width="1em"></mspace>\mathrm{N}$ at $150°$?

1.  $500<mspace\; width="1em"></mspace>\mathrm{N}$

2.  $700<mspace\; width="1em"></mspace>\mathrm{N}$

3.  $1100<mspace\; width="1em"></mspace>\mathrm{N}$

4.  $300<mspace\; width="1em"></mspace>\mathrm{N}$

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)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(1/2\right)$

(B)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(-1/2\right)$

(C)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(-1/4\right)$

(D)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(1/4\right)$