Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

Let number be
1000x+100x+10y+y
It would be 11(100x+y).
So right now number is a multiple of 11, So to be a perfect square it should be a multiple of 11^2
So, 11^2 * 2^6 =7744.

(When exponents of the factors of the number are even then it is a perfect square)

Sir, How to solve such questions?

Answer is 7744
Only one possibility