$\overrightarrow{\mathrm{A} }\mathrm{and} \overrightarrow{\mathrm{B}}$ are two vectors given by $\overrightarrow{\mathrm{A}} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}} = \hat{\mathrm{i}} + \hat{\mathrm{j}}$. The magnitude of the component of $\overrightarrow{\mathrm{A}}$along $\overrightarrow{\mathrm{B}}$ is 

• $\frac{5}{\sqrt{2}}$

• $\frac{3}{\sqrt{2}}$

• $\frac{7}{\sqrt{2}}$

• $\frac{1}{\sqrt{2}}$

Given $\overrightarrow{\mathrm{C}} = \overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}} \mathrm{and} \overrightarrow{\mathrm{D}} = \overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{A}}$. What is the angle between $\overrightarrow{\mathrm{C}} \mathrm{and} \overrightarrow{\mathrm{D}}$ ?

• 30°

• 60°

• 90°

• 180°

The acceleration a (in ms^-2 ) of a body, starting from rest varies with time t (in s) following the equation a = 3 t + 4. The velocity of the body at time t = 2 s will be

• 10 ms^-1

• 18 ms^-1

• 14 ms^-1

• 26 ms^-1

Figure below shows the distance-time graph of the motion of a car. It follows from the graph that the car is

• at rest

• in uniform motion

• in non-uniform acceleration

• uniformly accelerated

Two particles have masses m and 4m and their kinetic energies are in the ratio 2 : 1. What is the ratio of their linear momenta ?

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{16}$

The force F acting on a particle moving in a straight line is shown below. What is the work done by the force on the particle in the 1st metre of the trajectory ?

• 5 J

• 10 J

• 15 J

• 2.5 J

If the kinetic energy of a body changes by 20 %, then its momentum would change by

• 20 %

• 24 %

• 9.5 %

• 44 %

A bullet is fired with a velocity u making an angle of 60° with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is

• u

• 0

• $\frac{\sqrt{3\mathrm{u}}}{2}$

• $\frac{\mathrm{u}}{2}$

A particle is projected at 60° to the horizontal with a kinetic energy KE. The kinetic energy at the highest point is

• KE

• zero

• $\frac{\mathrm{KE}}{4}$

• $\frac{\mathrm{KE}}{2}$

The work done in carrying a charge Q once around a circle of radius r about a charge q at the centre is

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0} \frac{1}{\mathrm{\pi r}}$

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0} \left(\frac{1}{2\mathrm{\pi r}}\right)$

• Zero