JEE Main 2024MathematicsBinomial TheoremMediumMCQ

JEE Main 2024 — Binomial Theorem Question with Solution

JEE Main 2024 (27 Jan Shift 1)

Question

Crn-1=k2-8Cr+1n if and only if :

Choose an option

Show full solutionCorrect option: A
Correct answer
A22<k≤3

Step-by-step explanation

Given: Crn-1=k2-8Cr+1n   ...i

⇒r+1≥0,  r≥0⏟r≥0

⇒Crn-1Cr+1n=k2-8

⇒n-1!r!n-r-1!n!r+1!n-r-1!=k2-8

⇒r+1n=k2-8

⇒k2-8>0

⇒(k-22)(k+22)>0

⇒k∈(-∞,-22)∪(22,∞)   ...(ii)

Using equation i,

⇒n≥r+1

⇒r+1n≤1

⇒k2-8≤1

⇒k2-9≤0

⇒-3≤k≤3   ...(ii)

From equation ii and iii we get,

k∈[-3,-22)∪(22,3]

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Binomial Theorem chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.