JEE Main 2021MathematicsDefinite IntegrationEasyMCQ

JEE Main 2021 — Definite Integration Question with Solution

JEE Main 2021 (16 Mar Shift 2)

Question

Let Px=x2+bx+c be a quadratic polynomial with real coefficients such that ∫01Pxdx=1 and Px leaves remainder 5 when it is divided by x-2 Then the value of 9b+c is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C7

Step-by-step explanation

∫01x2+bx+cdx=1

13+b2+c=1  ⇒ b2+c=23

3b+6c=4 ...1

P2=5

4+2b+c=5

2b+c=1 ...2

From 1 & 2 

b=29 & c=59

9b+c=7

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About this question

This is a previous-year question from JEE Main 2021, covering the Definite Integration 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.