JEE Main 2021MathematicsLimitsMediumMCQ

JEE Main 2021 — Limits Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

If limx→∞x2-x+1-ax=b, then the ordered pair (a, b) is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A1,-12

Step-by-step explanation

Given that:limx→∞ x2−x+1−ax=b

⇒limx→∞ x2−x+1−ax×x2−x+1+axx2−x+1+ax=b

⇒limx→∞ x2−x+1−(ax)2x2−x+1+ax=b

⇒ Limit exist only If a2=1, because x2 must not be there in the numerator 

∴a=1,−1

⇒limx→∞ −x+1x2−x+1+ax=b

⇒limx→∞ −1+1x1−1x+1x2+a=b

⇒−11+a=b

Here, a≠−1

So a=1

b=−12

(a,b)≡1,−12

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About this question

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