JEE Main 2021 · MathsNumerical answerNumerical valueEasyCalculation

JEE Main 3 August 2021, Shift 1, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

f(x)

be a differentiable function such that

f(9) = 9

and

f\,'(9) = 4

, then

\lim_{x \to 9} \frac{\sqrt{f(x)} - 3}{\sqrt{x} - 3}

is ________.

Official answer

NTA final key.

Chapter: Continuity and Differentiability
Topic: L'Hopital's Rule
Idea tested: Recognizing the Derivative Definition

Same topic in other shifts

All L'Hopital's Rule questions

2 Apr 2026, Shift 1 · Q16If $\lim_{x\to2}\frac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)}=m$ , then $a+b+m$ is equal to :HardSingle correct
5 Apr 2026, Shift 1 · Q17The product of all possible values of $\alpha$ , for which…HardSingle correct
5 Apr 2026, Shift 2 · Q17Let $f(x)=\lim_{y\to 0}\frac{(1-\cos(xy))\tan(xy)}{y^3}$ . Then the number of solutions of the equation $f(x)=\sin x$ , $x \in \mathbf{R}$ …MediumSingle correct
6 Apr 2026, Shift 1 · Q17The value of $\lim_{x\to 0}\left(\frac{x^2\sin^2 x}{x^2-\sin^2 x}\right)$ is:MediumSingle correct
2 Apr 2025, Shift 1 · Q7For $\alpha, \beta, \gamma\in\mathbf{R}$ , if $\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3$ , then…MediumSingle correct
2 Apr 2025, Shift 2 · Q17If $\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4}$ is finite, then $(a+b)$ is equal to :MediumSingle 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.