JEE Main 2015MathematicsBinomial TheoremMediumMCQ

JEE Main 2015 — Binomial Theorem Question with Solution

JEE Main 2015 (11 Apr Online)

Question

The term independent of x in the binomial expansion of 1-1x+3x5 2x2-1x8 is

Choose an option

Show full solutionCorrect option: D
Correct answer
D400

Step-by-step explanation

The term independent of x will come from

1-1x+3x52x2-1x8

General term of  2x2-1x8 is C 8 r ( − 1 x ) r  2x28-r= C 8 r 2 8−r (−1) r x 16−3r

From expansion

12x2-1x8-1x2x2-1x8+3x52x2-1x8

12x2-1x8→ no constant term

-1x2x2-1x8→ for constant term

 r=5  ⇒ − C 8 3 2 3 (−1) 5 =+448

3x52x2-1x8→ for constant term

r=7⇒ C 38 7 2 1 (−1) 7 =48

Hence, term independent from x=448-48=400
 

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About this question

This is a previous-year question from JEE Main 2015, 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.