JEE Main 2016MathematicsBinomial TheoremHardMCQ

JEE Main 2016 — Binomial Theorem Question with Solution

JEE Main 2016 (10 Apr Online)

Question

The sum ∑r=110r2+1×r!, is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B10 ×11! 

Step-by-step explanation

∑r=110r2+1r!
Let us express the rth term, as a difference involving consecutive factorials, Tr=r2+1+r-r r! =r2+r r!-r-1r!
Therefore,
⇒Tr=rr+1!-r-1r! 
Putting r=1,2,3,...,10 and adding, we get ∑r=110rr+1!-r-1r! =10×11!
∴∑r=110r2+1×r!=10×11!

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 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.