JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 3 September 2020, Shift 2, Maths Q57

Question 57 of 75 in this shift, Maths question 7 of 25.

\lim_{x \to a} \frac{(a + 2x)^{\frac{1}{3}} - (3x)^{\frac{1}{3}}}{(3a + x)^{\frac{1}{3}} - (4x)^{\frac{1}{3}}}

(a \neq 0)

is equal to :

(1) $\left(\frac{2}{3}\right)^{\frac{4}{3}}$
(2) $\left(\frac{2}{9}\right)\left(\frac{2}{3}\right)^{\frac{1}{3}}$
(3) $\left(\frac{2}{9}\right)^{\frac{4}{3}}$
(4) $\left(\frac{2}{3}\right)\left(\frac{2}{9}\right)^{\frac{1}{3}}$ Official answer

Official answer

Option 4

NTA final key (Sep 2020).

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Fractional Power Substitution

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.