JEE Main 2022MathematicsBinomial TheoremMediumMCQ

JEE Main 2022 — Binomial Theorem Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

If 12·310+122·39+…+1210·3=K210·310, then the remainder when K is divided by 6 is

Choose an option

Show full solutionCorrect option: D
Correct answer
D5

Step-by-step explanation

We know xn-yn=x-yxn-1+xn-2y+⋯xyn-2+yn-1

12·310+122·39+⋯·129·32+1210·3

=29+28·3+  ⋯  2·38+39210·316=310-210210·310

So, K=310-210
Since we need the remainder when K is divided by 6

so, 310=6q1+3 and 210=6q2+4
Now K will be of the form 6q1+3-6q2+4
=6q1-q2-1
Hence, when K is divided by 6, we get the remainder as 6-1=5

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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.