JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2025, Shift 2, Maths Q16

Question 16 of 75 in this shift, Maths question 16 of 25, Section A.

Let

f

be a differentiable function on

\mathbf{R}

such that

f(2)=1

f'(2)=4

. Let

\lim_{x\to0}\left(f(2+x)\right)^{3/x}=e^{\alpha}

. Then the number of times the curve

y=4x^3-4x^2-4(\alpha-7)x-\alpha

meets x-axis is :

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

Official answer

Option 3

NTA final key.

Chapter: Continuity and Differentiability
Topic: Maxima and Minima
Idea tested: Analyzing Polynomial Roots via Extrema

Same topic in other shifts

All Maxima and Minima questions

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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.