Question

Identical charges q each are kept at the distance r from each other. Third charge q is placed on the line joining the two charges such that all the three charges are in eqilibrium. What is the magnitude and sign of the charge q?

Answer 1

If a third charge has to be placed in the line joining two identical charges
then third charge can be taken as positive or negative.

So both the signs are applicable.
Magnitude = any integer

Since there are two identical charges so the third charge must be kept at the center.