Question

two blocks are connected to each through a string that passes over a fixed pully such that the two blocks hang vertically. the two blocks must have same displacement, velocity and acceleration at all times. state true or false

Answer 1

If one block is pulled down at a distance x from it's original position, then the other one will also move upwards at a distance x. This is possible only because the pulley is fixed. So displacement is same. But acceleration and velocity won't be same at all times because the blocks won't always move with the same speed. It will depend on the weight of pulley.
So the answer will be false. Displacement, velocity and acceleration will not be same 'at all times'.
Hope you understand.