JEE Main 2022MathematicsBinomial TheoremMediumNumerical

JEE Main 2022 — Binomial Theorem Question with Solution

JEE Main 2022 (27 Jun Shift 1)

Question

If the coefficient of x10 in the binomial expansion of x514+5x1360 is 5kl, where l,k∈N and l is coprime to 5, then k is equal to ______.

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Tr+1=Cr60x51460-r5x13r

For x10, 60-r2-r3=10⇒  r=24

Hence coefficient of x10 will be C246053

Now, exponent of 5 in C2460 will be the power of 5 in 60!24!36! i.e. 51454·58=52

i.e. k=5

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About this question

This is a previous-year question from JEE Main 2022, covering the Binomial Theorem 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.