JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2024, Shift 1, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

If the function

f(x)=\frac{\sin3x+\alpha\sin x-\beta\cos3x}{x^3}

x\in\mathbb{R}

, is continuous at

x=0

, then

f(0)

is equal to :

(1) $2$
(2) $-2$
(3) $4$
(4) $-4$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Limits via Series Expansion for Continuity

Same idea in other shifts

Asked 4× in all

7 Apr 2025, Shift 2 · Q25If the function $f(x)=\frac{\tan(\tan x)-\sin(\sin x)}{\tan x-\sin x}$ is continuous at $x=0$ , then $f(0)$ is equal to ________.HardNumerical value
22 Jul 2021, Shift 2 · Q65Let $f:\mathbf{R}\to\mathbf{R}$ be defined as…HardSingle correct
17 Mar 2021, Shift 1 · Q84If the function $f(x)=\frac{\cos(\sin x)-\cos x}{x^{4}}$ is continuous at each point in its domain and $f(0)=\frac{1}{k}$ , then k is…MediumNumerical value

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.