Two bodies of masses 3kg and 5kg moving with velocities 2 m/s and V m/s respectively in opposite directions collide. If they move together after collision with velocity 3.5 m/s in the direction of the 5kg mass, find the value of V.
The equation of a circle is \(x^{2} + y^{2} - 8x + 9y + 15 = 0\). Find its radius.
A particle is acted upon by two forces 6N and 3N inclined at an angle of 120° to each other. Find the magnitude of the resultant force.
If \(s = 3i - j\) and \(t = 2i + 3j\), find \((t - 3s).(t + 3s)\).
If \(2\sin^{2}\theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find \(\theta\).
