JEE Main 2016MathematicsBinomial TheoremHardMCQ

JEE Main 2016 — Binomial Theorem Question with Solution

JEE Main 2016 (09 Apr Online)

Question

The value of ∑r=115r215Cr15Cr−1 is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D680

Step-by-step explanation

Given ∑ r=1 15 r 2 ( 15 C r 15 C r−1 )

Here 15Cr15Cr-1=16-rr

∑ r=1 15 r 2 ( 15 C r 15 C r−1 ) =   ∑ r=1 15 r 2 16-rr

= ∑ r=1 15 r 16-r

=16  ∑ r=1 15 r -  ∑ r=1 15 r 2

=16 ×15 ×162-15 ×31 ×166

=8 ×15 ×16-5 ×8 ×31

=1920-1240=680

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About this question

This is a previous-year question from JEE Main 2016, 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.