If a particle is moving in a circular orbit with constant speed, then:

1.	its velocity is variable.
2.	its acceleration is variable.
3.	its angular momentum is constant.
4.	All of the above

In a uniform circular motion,

(1) Both velocity and acceleration are constant.

(2) Acceleration and speed are constant but velocity changes.

(3) Both acceleration and velocity change.

(4) Both acceleration and speed are constant.

The relative velocity of a car P with respect to Q is $20\sqrt{2}$ m/s North-East. The velocity of car Q is 40 m/s due to South. The velocity of car P is:

(1) 20 m/s East

(2) $20\sqrt{2}$ m/s South-East

(3) 20 m/s West

(4) $20\sqrt{2}$ m/s North-West

A projectile is projected with initial kinetic energy \(K\). If it has kinetic energy \(0.25K\) at its highest point, then the angle of projection is:
1. \(30^{\circ}\)
2. \(45^{\circ}\)
3. \(60^{\circ}\)
4. \(75^{\circ}\)

A body is projected from the ground at an angle of 30° with horizontal. The instantaneous velocity of the body becomes perpendicular to initial velocity during its motion:

(1) Once

(2) Twice

(3) Thrice

(4) Never

In the uniform circular motion, which of the following physical quantity remains constant?

(1) Angular velocity

(2) Angular momentum

(3) Angular speed

(4) All of these

A body is projected with velocity $\overrightarrow{\mathrm{v}}= \left(\mathrm{\alpha }\hat{\mathrm{i}} + \mathrm{\beta }\hat{\mathrm{j}}\right)$ m/s. The time of flight of body considering x as horizontal and y as the vertical axis and g is the acceleration due to gravity:

1.  $\frac{2\mathrm{\beta }}{\mathrm{g}}$

2.  $\frac{2\mathrm{\alpha }}{\mathrm{g}}$

3.  $\frac{2\mathrm{\alpha \beta }}{\mathrm{g}}$

4.  $\frac{2\mathrm{\alpha }}{\mathrm{g\beta }}$

Two balls are projected along the same initial line from a height h = 20 m. The direction of the projections is horizontal. If initial speeds are 20 m/s and 25 m/s, the maximum separation between the balls when they will hit the ground is

(1) 40 m

(2) 50 m

(3) 10 m

(4) 90 m

If the position of a particle varies according to the equations \(x= 3t^2\)${\mathrm{}}^{}$, \(y =2t\), and \(z= 4t+4\), then which of the following is incorrect?

If three coordinates of a particle change according to the equations \(x = 3 t^{2}, y = 2 t , z= 4\), then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. \(2\sqrt{11}~\text{unit}\)
2. \(\sqrt{34}~\text{unit}\)
3. \(40~\text{unit}\)
4. \(2\sqrt{10}~\text{unit}\)