Permutation and Combination: The largest ninmathbfN such that 3^n divides 50! is : | JEE Main 2025 | Yukti Vault

Yukti Vault

JEE Main 2025 (Online) 2nd April Morning ShiftQuestion 1

The largest $n\in\mathbf{N}$ such that $3^{n}$ divides $50!$ is :

Permutation and Combination

$23$$22$✓ Correct answer$21$$20$

Solution

Exponent of 3 in $50!$: $\lfloor50/3\rfloor+\lfloor50/9\rfloor+\lfloor50/27\rfloor=16+5+1=22$. Option B.

More from Permutation and Combination

An n -digit number is a positive number with exactly n digits. Nine hundred distinct n -digit numbers are to…
All words, with or without meaning, are made using all the letters of the word MONDAY. These words are…
Six cards and six envelopes are numbered 1,2,3,4,5,6 and cards are to be placed in envelopes so that each…
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the…
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in…
The number of permutations, of the digits 1,2,3,ldots,7 without repetition, which neither contain the string…
If ^n-1C_r= (k^2-3 )^nC_r+1 , then kin
A committee of 12 is to be formed from 9 women and 8 men. In how many ways can this be done if at least five…