JEE Main 2021MathematicsPermutation CombinationMediumNumerical

JEE Main 2021 — Permutation Combination Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

Let n be a non-negative integer. Then the number of divisors of the form 4n+1 of the number 1010·1111·1313 is equal to _____.

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Show full solutionCorrect answer: 924
Correct answer
924

Step-by-step explanation

Let N=210×510×1111×1313

Now, power of 2 must be zero,

Power of 5 can be anything,

Power of 13 can be anything.

But, power of 11 should be even.

So, required number of divisors is

1×11×14×6=924.

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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.