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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

If the solution curve of the differential equation dydx=x+y−2x−y\frac{dy}{dx}=\frac{x+y-2}{x-y} passes through the points (2,1)(2, 1) and (k+1,2)(k+1, 2), k>0k>0, then
  1. (1)2tan⁡−1(1k)=log⁡e(k2+1)2\tan^{-1}\left(\frac{1}{k}\right)=\log_e\left(k^2+1\right)Official answer
  2. (2)tan⁡−1(1k)=log⁡e(k2+1)\tan^{-1}\left(\frac{1}{k}\right)=\log_e\left(k^2+1\right)
  3. (3)2tan⁡−1(1k+1)=log⁡e(k2+2k+2)2\tan^{-1}\left(\frac{1}{k+1}\right)=\log_e\left(k^2+2k+2\right)
  4. (4)2tan⁡−1(1k)=log⁡e(k2+1k2)2\tan^{-1}\left(\frac{1}{k}\right)=\log_e\left(\frac{k^2+1}{k^2}\right)

Official answer

Option 1

NTA final key.

Same idea in other shifts

Asked 2× in all
  1. 25 Jul 2022, Shift 1 · Q11The general solution of the differential equation (x−y2) dx+y(5x+y2) dy=0(x-y^2)\,dx+y(5x+y^2)\,dy=0 is :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.