JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 27 August 2021, Shift 2, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

\lim_{x \to \infty} \left(\sqrt{x^2 - x + 1} - ax\right) = b

, then the ordered pair (a, b) is :

(1) $\left(-1, -\frac{1}{2}\right)$
(2) $\left(1, -\frac{1}{2}\right)$ Official answer
(3) $\left(1, \frac{1}{2}\right)$
(4) $\left(-1, \frac{1}{2}\right)$

Official answer

Option 2

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Conjugation vs L'Hopital for Radicals

Same idea in other shifts

Asked 4× in all

4 Apr 2024, Shift 1 · Q24If $\lim_{x\to1}\frac{(5x+1)^{1/3}-(x+5)^{1/3}}{(2x+3)^{1/2}-(x+4)^{1/2}}=\frac{m\sqrt{5}}{n(2n)^{2/3}}$ , where $\gcd(m, n)=1$ , then…HardNumerical value
27 Jan 2024, Shift 1 · Q9If $a=\lim_{x\to0}\dfrac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}$ and $b=\lim_{x\to0}\dfrac{\sin^2 x}{\sqrt{2}-\sqrt{1+\cos x}}$ , then the…MediumSingle correct
25 Jun 2022, Shift 2 · Q5…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.