If $f(x)=\begin{cases}\dfrac{\sin(a+2)x+\sin x}{x} & ;\,x 0\end{cases}$ is continuous at $x=0$, then a + 2b is equal to :

JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 January 2020, Shift 1, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25, Section A.

f(x)=\begin{cases}\dfrac{\sin(a+2)x+\sin x}{x} & ;\,x<0\\[1ex] \mathrm{b} & ;\,x=0\\[1ex] \dfrac{(x+3x^2)^{1/3}-x^{1/3}}{x^{4/3}} & ;\,x>0\end{cases}

is continuous at

x=0

, then a + 2b is equal to :

(1) $-1$
(2)0Official answer
(3)1
(4) $-2$

Official answer

Option 2

NTA final key (Jan 2020).

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity at a Point

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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.