JEE Main 2017MathematicsDefinite IntegrationHardMCQ

JEE Main 2017 — Definite Integration Question with Solution

JEE Main 2017 (09 Apr Online)

Question

If limn→∞⁡1a+2a+…+nan+1a-1na+1+na+2+…+na+n=160  for some positive real number a, then a is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C7

Step-by-step explanation

limn→∞na(∑r=1n(rn)a)(n+1)a−1.n2(a+1+1n2)=160

⇒limn→∞na∑r=1rnana+11+1na-1a+1+1n2=160

⇒limn→∞1n∑r=1n(rn)a(1+1n)a-1a+1+1n2=160

⇒∫01xadx(a+12)=160

⇒ 1a+1a+12=160

⇒ a+1 2a+1=120

⇒2a2+3a-119=0

⇒2a2+17a-14a-119=0

⇒ a-7 2a+17=0

a=7, -172.

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About this question

This is a previous-year question from JEE Main 2017, 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.