JEE Main 2021MathematicsPermutation CombinationHardMCQ

JEE Main 2021 — Permutation Combination Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

A natural number has prime factorization given by n=2x3y5z, where y and z are such that y+z=5 and y-1+z-1=56,y>z. Then the number of odd divisors of n, including 1, is:

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Show full solutionCorrect option: A
Correct answer
A12

Step-by-step explanation

y+z=5

1y+1z=56  y>z

⇒y=3,z=2

⇒n=2x.33.52=2.2.2…3.3.35.5

For calculating the odd divisor ofn=2x3y5z, x must be 0.

Hence, Number of odd divisors =3+1×2+1=4×3=12.

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About this question

This is a previous-year question from JEE Main 2021, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.