JEE Main 2016MathematicsBinomial TheoremHardMCQ

JEE Main 2016 — Binomial Theorem Question with Solution

JEE Main 2016 (10 Apr Online)

Question

If the coefficients of x-2 and x-4, in the expansion of x13+12x1318,x>0, are m and n respectively, then mn is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B182

Step-by-step explanation

We have, x13+12x1318,x>0

General term, Tr+1=18Crx1318-r12x13r=18Cr x6-2r312r
Now,6-2r3=-2⇒r=12 and, 6-2r3=-4⇒r=15
Hence, mn=Coefficient of x-2Coefficient of x-4=C1218212C1518215

=18!6!.12!18!3!.15!×23

=15×14×136×5×4×23

=182

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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.