JEE Main 2019MathematicsBinomial TheoremMediumMCQ

JEE Main 2019 — Binomial Theorem Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

If the coefficients of x2 and x3, are both zero, in the expansion of the expression 1+ax+bx21-3x15, in powers of x , then the ordered pair a,b is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A28,315

Step-by-step explanation

1+ax+bx21-3x15=1+ax+bx2C015-15C1 3x + 15C2 3x2-15C33x3+…-15C153x15

∴  Coefficient of x2 is:  b.15C0-3.a15C1+32..15C2=0

(Given)
⇒b-45a+945=0......i

Coefficient of x3 is:

-b.3.15C1+9a.15C2-27.15C3=0

⇒ -45b+9a×152×141-27×153×142×131=0

⇒ -b+21a-273=0

⇒ b-21a+273=0    .......ii

From i and ii

a=28 and b=315

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About this question

This is a previous-year question from JEE Main 2019, 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.