JEE Main 2022MathematicsBinomial TheoremHardNumerical

JEE Main 2022 — Binomial Theorem Question with Solution

JEE Main 2022 (26 Jun Shift 2)

Question

If C040+C141+C242+⋯+C2060=mn×C2060 where m & n are co-prime, then m+n is equal to

Enter your answer

Show full solutionCorrect answer: 102
Correct answer
102

Step-by-step explanation

We know Cr-1n+Crn=Crn+1

Also C040=C041

So C041+C141+C242+….C2060

=C142+C242+C343....C2060 =C243+C343+…C2060

=C1960+C2060=C2061

Given C2061=mnC2060

⇒C4161=6141C4060

⇒6141C2060=mnC2060 

⇒6141=mn ⇒m+n=102

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 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.