IPMAT Indore 2024 (SA) PYQs

If one of the factors of the number $3^{7} 2^{8} 17^{3}$ is randomly chosen, then the probability that the chosen factor will be a perfect square is

The number of positive integers that divide $(1890) \cdot (130) \cdot (170)$ and are not divisible by $45$ is ________

The maximum value of the natural number $n$ for which $21^n$ divides $50!$ is