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 idea in other shifts

Asked 6× in all

26 Jul 2022, Shift 1 · Q24The number of distinct real roots of the equation $x^5(x^3 - x^2 - x + 1) + x\ (3x^3 - 4x^2 - 2x + 4) - 1 = 0$ is ___________.HardNumerical value
30 Jul 2022, Shift 2 · Q83The number of integral values of $b$ for which $2x^3 - 3x^2 - 12x + b = 0$ has three distinct real roots is ________.MediumNumerical value
27 Jun 2022, Shift 1 · Q6The number of distinct real roots of $x^4-4x+1=0$ is :MediumSingle correct
27 Aug 2021, Shift 1 · Q85The number of distinct real roots of the equation $3x^4+4x^3-12x^2+4=0$ is __________.MediumNumerical value
3 Sep 2020, Shift 2 · Q58Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1$ , 0, 1. If $T = \{x \in \mathbf{R} \mid f(x) = f(0)\}$ , then…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 108 of the 174 JEE Main shifts held from 2017 to 2026.