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

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. \(75^{\circ}\)

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. \(2\sqrt{10}~\text{unit}\)

In a uniform circular motion, if the speed of the particle is \(2\) m/s and radius of the circle is \(2\) m, then the values of centripetal and tangential acceleration are, respectively:
1. \(2~\text{m/s}^2,~2~\text{m/s}^2\)
2. \(2~\text{m/s}^2,~1~\text{m/s}^2\)
3. \(0,~2~\text{m/s}^2\)
4. \(2~\text{m/s}^2,~0\)

The position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:
1. \(2~\text{m/s}^2\)
2. \(3~\text{m/s}^2\)
3. \(4~\text{m/s}^2\)
4. zero

Coordinates of a particle as a function of time \(t\) are \(x= 2t\),
\(y =4t\). It can be inferred that the path of the particle will be:

Which of the following statement/s is/are incorrect regarding the motion in a plane?

A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s² along the north. The velocity of the body just after \(4\) s will be?

A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:
1. \(t=6\) s
2. \(t=7\) s
3. \(t=8\) s
4. \(t=14\) s