JEE Main 2025 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 2 April 2025, Shift 1, Maths Q6

Question 6 of 75 in this shift, Maths question 6 of 25, Section A.

The largest

n\in\mathbf{N}

such that

3^n

divides

50!

is :

(1)23
(2)22Official answer
(3)21
(4)20

Official answer

Option 2

NTA final key.

Chapter: Binomial Theorem
Topic: Permutations and Combinations
Idea tested: Exponent of Prime in n! (Legendre's Formula)

Same topic in other shifts

All Permutations and Combinations questions

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4 Apr 2026, Shift 1 · Q4The number of functions $f:\{1,2,3,4\}\to\{a,b,c\}$ , which are not onto, is:EasySingle correct
4 Apr 2026, Shift 1 · Q8The number of ways, of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:EasySingle correct
4 Apr 2026, Shift 2 · Q17Let $A=\{(a,b,c):a,b,c$ are non-negative integers and $a+b+2c=22\}$ . Then $n(A)$ is equal to:MediumSingle correct
5 Apr 2026, Shift 1 · Q21Let $A = \{1, 2, 3, 4, 5, 6\}$ . The number of one-one functions $f: A \to A$ such that $f(1) \geq 3$ , $f(3) \leq 4$ and $f(2) + f(3) = 5$ ,…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.