JEE Main 2025 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 7 April 2025, Shift 1, Maths Q16

Question 16 of 75 in this shift, Maths question 16 of 25, Section A.

\lim_{x \to 0^+} \frac{\tan\left(5(x)^{\frac{1}{3}}\right) \log_e\left(1+3x^2\right)}{\left(\tan^{-1} 3\sqrt{x}\right)^2 \left(e^{5(x)^{\frac{4}{3}}} - 1\right)}

is equal to

(1) $1$
(2) $\frac{1}{3}$ Official answer
(3) $\frac{5}{3}$
(4) $\frac{1}{15}$

Official answer

Option 2

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Simplifying with Standard Limits Before L'Hopital

Same idea in other shifts

Asked 13× in all

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
7 Apr 2025, Shift 2 · Q23For $t>-1$ , let $\alpha_t$ and $\beta_t$ be the roots of the equation…HardNumerical value
5 Apr 2024, Shift 2 · Q23Let $a > 0$ be a root of the equation $2x^2+x-2=0$ . If…HardNumerical value
8 Apr 2024, Shift 2 · Q25If $\alpha = \lim_{x \to 0^+} \left(\frac{e^{\sqrt{\tan x}} - e^{\sqrt{x}}}{\sqrt{\tan x} - \sqrt{x}}\right)$ and…HardNumerical value
31 Jan 2024, Shift 1 · Q6 $\lim_{x\to0}\frac{e^{2|\sin x|}-2|\sin x|-1}{x^2}$ MediumSingle correct
8 Apr 2023, Shift 1 · Q10 $\lim_{x\to0}\left(\left(\frac{1-\cos^2(3x)}{\cos^3(4x)}\right)\left(\frac{\sin^3(4x)}{\left(\log_e(2x+1)\right)^5}\right)\right)$ is…MediumSingle correct
8 Apr 2023, Shift 2 · Q9If $\alpha > \beta > 0$ are the roots of the equation $ax^2 + bx + 1 = 0$ , and…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.