JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 16 March 2021, Shift 2, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

Let

f:\mathbf R\to\mathbf R

and

g:\mathbf R\to\mathbf R

be defined as

f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases}

and

g(x)=\begin{cases}x+1, & x<0\\ (x-1)^2+b, & x\ge0\end{cases}

, where a, b are non-negative real numbers. If

(g\circ f)(x)

is continuous for all

x\in\mathbf R

, then

a+b

is equal to ________.

Official answer

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity and Differentiability of Composite Functions

Same idea in other shifts

Asked 7× in all

6 Apr 2026, Shift 2 · Q25Let $f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases}$ and $g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}$ …HardNumerical value
6 Apr 2024, Shift 2 · Q10Suppose for a differentiable function $h$ , $h(0)=0$ , $h(1)=1$ and $h'(0)=h'(1)=2$ . If $g(x)=h(e^x)e^{h(x)}$ , then $g'(0)$ is equal to :MediumSingle correct
11 Apr 2023, Shift 2 · Q10Let $f$ and $g$ be two functions defined by $f(x) = \begin{cases} x+1, & x<0 \\ |x-1|, & x \ge 0 \end{cases}$ and…MediumSingle correct
25 Jun 2022, Shift 2 · Q22Let $f(x) = \left[2x^2 + 1\right]$ and $g(x) = \begin{cases} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{cases}$ , where $[t]$ is the…HardNumerical value
26 Jun 2022, Shift 1 · Q7Let $f, g : \mathbf{R} \to \mathbf{R}$ be two real valued functions defined as…HardSingle correct
28 Jun 2022, Shift 2 · Q6Let $f, g : \mathbf{R} \to \mathbf{R}$ be functions defined by $f(x) = \begin{cases} [x] , & x < 0 \\ |1-x| , & x \geq 0 \end{cases}$ 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.