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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

If the solution curve y=y(x)y=y(x) of the differential equation y2dx+(x2−xy+y2)dy=0y^2\mathrm{d}x+(x^2-xy+y^2)\mathrm{d}y=0, which passes through the point (1,1)(1,1) and intersects the line y=3xy=\sqrt{3}x at the point (α,3α)(\alpha,\sqrt{3}\alpha), then value of log⁡e(3α)\log_e(\sqrt{3}\alpha) is equal to :
  1. (1)π3\frac{\pi}{3}
  2. (2)π2\frac{\pi}{2}
  3. (3)π12\frac{\pi}{12}Official answer
  4. (4)π6\frac{\pi}{6}

Official answer

Option 3

NTA final key.

Chapter
Differential Equations
Topic
Homogeneous Equations
Idea tested
Alternative Substitution x = vy

Same idea in other shifts

Asked 2× in all
  1. 31 Jan 2024, Shift 1 · Q12The solution curve of the differential equation ydxdy=x(log⁡ex−log⁡ey+1), x>0, y>0y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0 passing through the point (e,1)(e,1) isMediumSingle 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.