CAT (QA) PYQs

How many factors of $2^4 \times 3^5 \times 10^4$ are perfect squares which are greater than $1?$

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

The number of positive integers less than $50$, having exactly two distinct factors other than $1$ and itself, is