Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined as $f(x)=\begin{cases}\frac{\sin(a+1)x+\sin 2x}{2x}, & \text{if } x 0\end{cases}$ If $f$ is continuous at $x=0$, then the value of $a+b$ is equal to :

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

Let

f:\mathbb{R}\to\mathbb{R}

be a function defined as

f(x)=\begin{cases}\frac{\sin(a+1)x+\sin 2x}{2x}, & \text{if } x<0\\ b, & \text{if } x=0\\ \frac{\sqrt{x+bx^3}-\sqrt{x}}{bx^{5/2}}, & \text{if } x>0\end{cases}

f

is continuous at

x=0

, then the value of

a+b

is equal to :

The figure, in words

Piecewise definition of f(x) shown with a large left brace and three cases (x<0, x=0, x>0).

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

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Finding Unknown Constants for Continuity

Same idea in other shifts

Asked 10× in all

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. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.