Mathematics · 2025
JEE Main · 2 April 2025, Shift 1 · Q6
The largest n ∈ N such that 3^n divides 50! is:
The largest $\displaystyle \mathrm{n} \in \mathbf{N}$ such that $\displaystyle 3^{\mathrm{n}}$ divides $\displaystyle 50$ ! is :
Official answer
From NTA’s final answer key for this paper.
(2)
$\displaystyle 22$
More from Permutations and Combinations
- The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is ____.2025
- The number of strictly increasing functions f from the set \{1, 2, 3, 4, 5, 6\} to the set \{1, 2, 3,...., 9\} such that f(i) ≠ i for 1 ≤ i ≤ 6, is…2026
- Let S be the set of the first 11 natural numbers. Then the number of elements in A={B ⊆ S: n(B) ≥ 2 and the product of all elements of B is even } is…2026
- Let A={(a, b, c): a, b, c are non-negative integers and a+b+2 c=22}. Then n( A) is equal to:2026
- A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10^th floor. The number of…2026
- There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of…2025
- The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank…2026
- Let S={1,2,3,4,5,6,7,8,9}. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is…2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.