1. If R and H are the horizontal range and maximum height attained by a projectile, than what is its speed of projection? Please explain .
2. A particle projected from ground at angle 45 degrees with horizontal from distance 'd1' from the foot of a pole and just after touching the top of pole it falls on ground at a distance 'd2' from pole on other side, then what is the height of pole?please explain.
3. A particle projected from ground moves at angle 45 degrees with horizontal one second after projection and speed is minimum two seconds after the projection.What is the angle of projection of particle?(neglect the effect of air resistance) please explain.
4.A particle is moving on a circular path with constant speed v. It moves between two points A and B, which subtends an angle 60 degree at the centre of the circle. What are the magnitude of change in its velocity and change in magnitude of its velocity during motion from A to B respectively? Please explain.

Here's a hint to get you started with (1): If you determine the values for H and R in terms of vertical and horizontal components of the initial velocity (i.e. v \sin \theta and v \cos \theta, respectively), you can then combine them using v^2 \sin^2 \theta + v^2 \cos ^2 \theta = v^2.

For (4) the first question it's simple vector subtraction, and the second should be obvious since you're told it's moving at constant velocity.

I suggest you show us what work you've accomplished on all 4 and we'll try to help you out where you get stuck.