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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 August 2021, Shift 2, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

An angle of intersection of the curves, x2a2+y2b2=1\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{b}^2} = 1 and x2+y2=abx^2+y^2 = \mathrm{ab}, a>b\mathrm{a} > \mathrm{b}, is :
  1. (1)tan⁡−1(a−bab)\tan^{-1}\left(\frac{\mathrm{a-b}}{\sqrt{\mathrm{ab}}}\right)Official answer
  2. (2)tan⁡−1(a+bab)\tan^{-1}\left(\frac{\mathrm{a+b}}{\sqrt{\mathrm{ab}}}\right)
  3. (3)tan⁡−1(a−b2ab)\tan^{-1}\left(\frac{\mathrm{a-b}}{2\sqrt{\mathrm{ab}}}\right)
  4. (4)tan⁡−1(2ab)\tan^{-1}\left(2\sqrt{\mathrm{ab}}\right)

Official answer

Option 1

NTA final key.

Same idea in other shifts

Asked 2× in all
  1. 4 Aug 2021, Shift 1 · Q75If the ellipse x216+y2b2=1\frac{x^2}{16}+\frac{y^2}{b^2}=1 and the circle x2+y2=4bx^2+y^2=4b intersect at an angle π3\frac{\pi}{3}, then a value of 'b' isHardSingle 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.