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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let g(x)g(x) be a linear funchion and f(x)={g(x),x≤0(1+x2+x)1x,x>0f(x)=\begin{cases}g(x), & x\leq0\\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}}, & x>0\end{cases} is continuous at x=0x=0. If f′(1)=f(−1)f'(1)=f(-1), then the value g(3)g(3) is
  1. (1)13log⁡e(49e1/3)\frac{1}{3}\log_e\left(\frac{4}{9e^{1/3}}\right)
  2. (2)log⁡e(49e1/3)\log_e\left(\frac{4}{9e^{1/3}}\right)Official answer
  3. (3)13log⁡e(49)+1\frac{1}{3}\log_e\left(\frac{4}{9}\right)+1
  4. (4)log⁡e(49)−1\log_e\left(\frac{4}{9}\right)-1

Official answer

Option 2

NTA final key.

Chapter
Continuity and Differentiability
Topic
Continuity and Differentiability
Idea tested
Continuity of f(x)^g(x)

Same topic in other shifts

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  3. 4 Apr 2026, Shift 2 · Q22Let f(x)={ex−1,x<0x2−5x+6,x≥0f(x)=\begin{cases}e^{x-1}, & x<0\\ x^2-5x+6, & x\ge0\end{cases} and g(x)=f(∣x∣)+∣f(x)∣g(x)=f(|x|)+|f(x)|. If the number of points where gg is not…MediumNumerical value
  4. 5 Apr 2026, Shift 1 · Q19Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a differentiable function such that f(x+y3)=f(x)+f(y)3f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3} for all…MediumSingle correct
  5. 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
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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 42 of the 174 JEE Main shifts held from 2017 to 2026.