Question

A SPRING IS CUT INTO TWO EQUAL HALVES.HOW IS THE SPRING CONSTANT EACH HALF IS AFFECTED?

Answer 1

Since f=-kx(restoring force), then k=f/x.

Now if you apply the same force to the half-length spring it only moves half as far. So if x is halved above, then k will double.
Basically there are now half as many coils to take up the force via displacement.
x is displacement from the mean position
as the displacemnt from mean positionx=(length of spring+distance u move it)