JEE Main 2024MathematicsBinomial TheoremMediumMCQ

JEE Main 2024 — Binomial Theorem Question with Solution

JEE Main 2024 (31 Jan Shift 2)

Question

If for some m, n; 6Cm+26Cm+1+6Cm+2>8C3 and n−1P3:nP4=1:8, then nPm+1+n+1Cm is equal to

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Show full solutionCorrect option: D
Correct answer
D372

Step-by-step explanation

Given: 6Cm+26Cm+1+6Cm+2>8C3

⇒6Cm+6Cm+1+6Cm+1+6Cm+2>8C3

⇒7Cm+1+7Cm+2>8C3

⇒8Cm+2>8C3

⇒m=2

Also, n−1P3:nP4=1:8

⇒n−1n−2n−3nn−1n−2n−3=18

⇒n=8

⇒nPm+1+n+1Cm=8P3+9C2

⇒nPm+1+n+1Cm=8×7×6+9×82

⇒nPm+1+n+1Cm=372

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About this question

This is a previous-year question from JEE Main 2024, 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.