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Friday, 9 October

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:R→Rf:\mathbf R\to\mathbf R and g:R→Rg:\mathbf R\to\mathbf R be defined as f(x)={x+a,x<0∣x−1∣,x≥0f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases} and g(x)={x+1,x<0(x−1)2+b,x≥0g(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∘f)(x)(g\circ f)(x) is continuous for all x∈Rx\in\mathbf R, then a+ba+b is equal to ________.

Official answer

1

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 3× in all
  1. 6 Apr 2026, Shift 2 · Q25Let f(x)={x3+8;x<0,x2−4;x≥0,f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases} and g(x)={(x−8)1/3;x<0,(x+4)1/2;x≥0.g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}…HardNumerical value
  2. 6 Apr 2024, Shift 2 · Q10Suppose for a differentiable function hh, h(0)=0h(0)=0, h(1)=1h(1)=1 and h′(0)=h′(1)=2h'(0)=h'(1)=2. If g(x)=h(ex)eh(x)g(x)=h(e^x)e^{h(x)}, then g′(0)g'(0) is equal to :MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.