http://oeis.org/A046747
@Mk Utkarsh
yeah i checked that but i didn't find any method or may be i overlooked it.
let X(n) be number of singular matrices of Number of singular $N \times N$ rational (0,1) matrices.
let Y(n) be number of binary matrices of order $N \times N$ whose determinant is exactly zero.
$Y(n) =$$\large 2^{(n^2)} - n! * \binom{2^n -1}{n} + n! * X(n)$
I don't think it is required to to remember all these things for GATE.
actually i thought it also have some trivial method as odd/even #determinant matrices has but someone on SO mentioned it as somehow tough job so yeah may be it wont be asked.