Two bodies are projected with the same velocity. If one is projected at an angle of 30° and the other at an angle of 60° to the horizontal, the ratio of the maximum heights reached is 

(1) 3 : 1

(2) 1 : 3

(3) 1 : 2

(4) 2 : 1

If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where \(\theta\) is in radians and \(t\) in seconds, then the angular velocity of the particle after \(2\) sec from its start is:
1. \(8\) rad/sec
2. \(12\) rad/sec
3. \(24\) rad/sec
4. \(36\) rad/sec

A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is 

(1) ${25}^o{8}^{\text{'}}$

(2) ${33}^o{7}^{\text{'}}$

(3) ${42}^o{8}^{\text{'}}$

(4) ${53}^o{8}^{\text{'}}$