CAT 2019 Shift 2 Paper

$2^4\times 3^5\times {10}^4=2^8\times 3^5\times 5^4$
For perfect squares, we have to take only even powers of the prime factors of the number.
The number of ways 2's can be used is 5 i.e. $2^{\circ },2^2,2^4,2^6,2^8$
The number of ways 3 's can be used is 3 i.e. $3^0,3^2,3^4$
The number of ways $5^{\prime }$ s can be used is 3 i.e. $5^0,5^2,5^4$
Therefore, the total number of factors which are perfect squares $=5\times 3\times 3=45$
But this also includes the number $1.$ Hence excluding $1,$ the required number is $45-1=44.$