CAT 2023 Slot 2 Solved Paper

Since there are two distinct factors other than 1, and itself, which implies the total number of factors of N is 4.
It can be done in two ways.
First case: $\mathit{N}={\mathit{p}}^3$ (where $\mathrm{p}$ is a prime number)
Second case: $\mathit{N}={\mathit{p}}_1\times {\mathit{p}}_2$ (Where ${\mathit{p}}_1,{\mathit{p}}_2$ are the prime numbers)
From case 1 , we can see that the numbers which is a cube of prime and less than 50 are 8 , and 27 (2 numbers). $\left(3*7\right),\left(3*11\right),\left(3*13\right),\left(5*7\right)\{(13$ numbers $\left)\right\}$
Hence, the total number of numbers having two distinct factors is $\left(13+2\right)=15$.