JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 26 February 2021, Shift 2, Maths Q79

Question 79 of 90 in this shift, Maths question 19 of 30, Section A.

A natural number has prime factorization given by

n=2^x 3^y 5^z

, where

y

and

z

are such that

y+z=5

and

y^{-1}+z^{-1}=\frac{5}{6}

y>z

. Then the number of odd divisors of n, including 1, is :

(1) $6$
(2) $11$
(3) $12$ Official answer
(4) $6x$

Official answer

Option 3

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Number of Divisors with Specific Properties

Same topic in other shifts

All Permutations and Combinations questions

2 Apr 2026, Shift 1 · Q6The number of seven-digit numbers, that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once,…MediumSingle correct
2 Apr 2026, Shift 2 · Q7Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$ -side regular polygon. If $p_{n+1} - p_n = 66$ ,…EasySingle correct
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 108 of the 174 JEE Main shifts held from 2017 to 2026.