JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 2, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4}

is finite, then

(a+b)

is equal to :

(1) $\frac{1}{2}$ Official answer
(2) $0$
(3) $\frac{3}{4}$
(4) $-1$

Official answer

Option 1

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Determining Unknown Constants from Finite Limits

Same idea in other shifts

Asked 4× in all

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
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
25 Jul 2022, Shift 1 · Q5If $\lim_{n\to\infty}\left(\sqrt{n^2-n-1}+n\alpha+\beta\right)=0$ , then $8(\alpha+\beta)$ 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 42 of the 174 JEE Main shifts held from 2017 to 2026.