JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

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 greatest integer

\leq t

. Then, in the open interval

(-1, 1)

, the number of points where

fog

is discontinuous 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
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
16 Mar 2021, Shift 2 · Q85Let $f:\mathbf R\to\mathbf R$ 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…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.