JEE Main 2023MathematicsBinomial TheoremMediumMCQ

JEE Main 2023 — Binomial Theorem Question with Solution

JEE Main 2023 (24 Jan Shift 2)

Question

If C1302+2C2302+3C3302..........30C30302=α60!30!2, then α is equal to 

Choose an option

Show full solutionCorrect option: C
Correct answer
C15

Step-by-step explanation

Let,

S=0C1302+1C1302+2C2302+3C3302..........30C30302

Now rewriting the above expression we get,

S=30C30302+29C29302+28C28302+27C27302..........+0C0302

Now adding both the equation we get,

2S=30C1302+C1302+C2302+C3302..........C30302

⇒S=15C302×30

⇒S=15C3060=15×60!30!2

Now comparing with S=α60!30!2,

We get α=15

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About this question

This is a previous-year question from JEE Main 2023, 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.