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JEE Main 2-April-2025 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 2-April-2025 Paper - Shift 14 Marks
MCQ
The largest $n \in N$ such that $3^n$ divides 50 ! is:
  • A
    21
  • ✓
    22
  • C
    20
  • D
    23
✓

Answer

Correct option: B.
22
(B) 22
Explanation: $2^\alpha \cdot 3^\beta \cdot 5^\gamma$
$\begin{array}{l}B=\left[\frac{50}{3}\right]+\left[\frac{50}{3^2}\right]+\left[\frac{50}{3^3}\right]+\left[\frac{50}{3^4}\right] \\
=16+5+1 \\
=2\end{array}$
Maximum value of n is 22

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