Q42 / 75 · JEE Main 2025 (2 Apr Shift 1) · Mathematics
The largest $\mathrm{n} \in \mathrm{N}$ such that $3^{\mathrm{n}}$ divides 50 ! is:
- A21
- Correct answerB22
- C20
- D23
Solution
$2^\alpha \cdot 3^\beta \cdot 5^\gamma$
$\mathrm{B}=\left[\frac{50}{3}\right]+\left[\frac{50}{3^2}\right]+\left[\frac{50}{3^3}\right]+\left[\frac{50}{3^4}\right]$
$=16+5+1$
$=2$
Maximum value of $n$ is 22
$\mathrm{B}=\left[\frac{50}{3}\right]+\left[\frac{50}{3^2}\right]+\left[\frac{50}{3^3}\right]+\left[\frac{50}{3^4}\right]$
$=16+5+1$
$=2$
Maximum value of $n$ is 22
Hence, the correct answer is option: 'B'.