JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 September 2020, Shift 2, Maths Q62

Question 62 of 75 in this shift, Maths question 12 of 25.

Consider a region

R=\{(x,\ y)\in\mathbf{R}^2 : x^2\le y\le 2x\}

. If a line

y=\alpha

divides the area of region R into two equal parts, then which of the following is true ?

(1) $3\alpha^2-8\alpha+8=0$
(2) $\alpha^3-6\alpha^2+16=0$
(3) $3\alpha^2-8\alpha^{3/2}+8=0$ Official answer
(4) $\alpha^3-6\alpha^{3/2}-16=0$

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Application of Integrals
Topic: Area Under Curves
Idea tested: Bisection of Bounded Areas

Same idea in other shifts

Asked 3× in all

31 Aug 2021, Shift 2 · Q87If the line $y = \mathrm{m}x$ bisects the area enclosed by the lines $x = 0$ , $y = 0$ , $x = \frac{3}{2}$ and the curve $y = 1+4x-x^2$ ,…MediumNumerical value
8 Jan 2020, Shift 1 · Q61For $a>0$ , let the curves $C_1: y^2=ax$ and $C_2: x^2=ay$ intersect at origin O and a point P. Let the line $x=b$ ( $0<b<a$ ) intersect the…HardSingle 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.