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Friday, 9 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 topic in other shifts

All Area Under Curves questions
  1. 2 Apr 2026, Shift 2 · Q24If the area of the region bounded by 16x2−9y2=14416x^2 - 9y^2 = 144 and 8x−3y=248x - 3y = 24 is AA, then 3(A+6log⁡e(3))3(A + 6\log_e(3)) is equal toHardNumerical value
  2. 4 Apr 2026, Shift 1 · Q18The area of the region {(x,y):y≤π−∣x∣, y≤∣xsin⁡x∣, y≥0}\{(x,y): y\le\pi-|x|,\ y\le|x\sin x|,\ y\ge0\} is:HardSingle correct
  3. 4 Apr 2026, Shift 2 · Q18The area of the region bounded by the curves x+3y2=0x+3y^2=0 and x+4y2=1x+4y^2=1 is equal to:EasySingle correct
  4. 5 Apr 2026, Shift 1 · Q16The area of the region R={(x,y):xy≤27, 1≤y≤x2}R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\} is equal to:MediumSingle correct
  5. 5 Apr 2026, Shift 2 · Q24Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function such that f(x)+3f(π2−x)=sin⁡xf(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x, x∈Rx \in \mathbf{R}. Let the maximum…HardNumerical value
  6. 6 Apr 2026, Shift 1 · Q19The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 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 42 of the 174 JEE Main shifts held from 2017 to 2026.