JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let

f:\mathbf{R}\to\mathbf{R}

be a polynomial function of degree four having extreme values at

x=4

and

x=5

. If

\lim_{x\to 0}\frac{f(x)}{x^2}=5

, then

f(2)

is equal to :

(1)8
(2)10Official answer
(3)12
(4)14

Official answer

Option 2

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Determining Coefficients from Extrema

Same idea in other shifts

Asked 5× in all

31 Aug 2021, Shift 2 · Q85Let $f(x)$ be a cubic polynomial with $f(1) = -10$ , $f(-1) = 6$ , and has a local minima at $x = 1$ , and $f'(x)$ has a local minima at…MediumNumerical value
18 Mar 2021, Shift 2 · Q85Let $P(x)$ be a real polynomial of degree 3 which vanishes at $x=-3$ . Let $P(x)$ have local minima at $x=1$ , local maxima at $x=-1$ and…MediumNumerical value
8 Jan 2020, Shift 2 · Q73Let $f(x)$ be a polynomial of degree 3 such that $f(-1) = 10$ , $f(1) = -6$ , $f(x)$ has a critical point at $x = -1$ and $f'(x)$ has a…MediumNumerical value
2 Sep 2020, Shift 1 · Q61If $p(x)$ be a polynomial of degree three that has a local maximum value 8 at $x=1$ and a local minimum value 4 at $x=2$ ; then $p(0)$ is…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.