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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 January 2020, Shift 1, Maths Q61

Question 61 of 75 in this shift, Maths question 11 of 25, Section A.

For a>0a>0, let the curves C1:y2=axC_1: y^2=ax and C2:x2=ayC_2: x^2=ay intersect at origin O and a point P. Let the line x=bx=b (0<b<a0<b<a) intersect the chord OP and the xx-axis at points Q and R, respectively. If the line x=bx=b bisects the area bounded by the curves, C1C_1 and C2C_2, and the area of ΔOQR=12\Delta OQR=\frac{1}{2}, then 'a' satisfies the equation :
  1. (1)x6+6x3−4=0x^6+6x^3-4=0
  2. (2)x6−12x3+4=0x^6-12x^3+4=0Official answer
  3. (3)x6−12x3−4=0x^6-12x^3-4=0
  4. (4)x6−6x3+4=0x^6-6x^3+4=0

Official answer

Option 2

NTA final key (Jan 2020).

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

Same idea in other shifts

Asked 3× in all
  1. 31 Aug 2021, Shift 2 · Q87If the line y=mxy = \mathrm{m}x bisects the area enclosed by the lines x=0x = 0, y=0y = 0, x=32x = \frac{3}{2} and the curve y=1+4x−x2y = 1+4x-x^2,…MediumNumerical value
  2. 2 Sep 2020, Shift 2 · Q62Consider a region R={(x, y)∈R2:x2≤y≤2x}R=\{(x,\ y)\in\mathbf{R}^2 : x^2\le y\le 2x\}. If a line y=αy=\alpha divides the area of region R into two equal parts,…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.