JEE Main 2021MathematicsPermutation CombinationHardNumerical

JEE Main 2021 — Permutation Combination Question with Solution

JEE Main 2021 (25 Feb Shift 2)

Question

The total number of two digit numbers 'n', such that 3n+7n is a multiple of 10 , is ___ .

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Show full solutionCorrect answer: 45
Correct answer
45

Step-by-step explanation

∵7n=(10-3)n=10k+(-3)n

7n+3n=10k+(-3)n+3n

10k+-3n+3n=10k if n=odd10k+2.3n if n=even

Let n=2t; t∈N

∴3n=32t=(10-1)t

=10p+(-1)t

.=10p±1

∴ if n= even then 7n+3n will not be multiply of 10

So if n is odd then only 7n+3n will be multiply of 10

∴n=11,13,15,……….,99

∴ Number of odd two digit numbers =45

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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.