JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

Let

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

\int_{-1}^{1}P(x)\,dx=18

, then the sum of all the coefficients of the polynomial

P(x)

is equal to ___________.

Official answer

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

7 Apr 2025, Shift 2 · Q18Let $f:\mathbf{R}\to\mathbf{R}$ be a polynomial function of degree four having extreme values at $x=4$ and $x=5$ . If…MediumSingle correct
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
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.