A rope is tied on a crate and makes a. 60 deg b. 30 deg with the ground .On what angle be able to move the crate with less force?

This is trickier than it looks.

Required force F in rope is given by:

(M*g - F sinA)*mu_s = F cos A

F*(cos A + mu_s* sinA) = M*g

For values of the static friction coefficient (mu_s) that are less than 1, F will be less for A = 30 degrees.