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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Let the solution curve y=y(x)y=y(x) of the differential equation [xx2−y2+eyx]xdydx=x+[xx2−y2+eyx]y\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right]x\frac{dy}{dx}=x+\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right]y pass through the points (1,0)(1, 0) and (2α,α)(2\alpha, \alpha), α>0\alpha>0. Then α\alpha is equal to
  1. (1)12exp⁡(π6+e−1)\frac{1}{2}\exp\left(\frac{\pi}{6}+\sqrt{e}-1\right)Official answer
  2. (2)12exp⁡(π3+e−1)\frac{1}{2}\exp\left(\frac{\pi}{3}+e-1\right)
  3. (3)exp⁡(π6+e+1)\exp\left(\frac{\pi}{6}+\sqrt{e}+1\right)
  4. (4)2exp⁡(π3+e−1)2\exp\left(\frac{\pi}{3}+\sqrt{e}-1\right)

Official answer

Option 1

NTA final key.

Chapter
Differential Equations
Topic
Homogeneous Equations
Idea tested
Substitution y = vx

Same idea in other shifts

Asked 10× in all
  1. 5 Apr 2026, Shift 1 · Q25Let y=y(x)y = y(x) be the solution of the differential equation…HardNumerical value
  2. 9 Apr 2024, Shift 1 · Q10The solution of the differential equation (x2+y2)dx−5xy dy=0(x^2+y^2)dx-5xy\,dy=0, y(1)=0y(1)=0, is :MediumSingle correct
  3. 10 Apr 2023, Shift 1 · Q10The slope of tangent at any point (x,y)(x,y) on a curve y=y(x)y=y(x) is x2+y22xy\frac{x^2+y^2}{2xy}, x>0x>0. If y(2)=0y(2)=0, then a value of y(8)y(8) isMediumSingle correct
  4. 25 Jul 2022, Shift 2 · Q25Let y=y(x)y=y(x) be the solution of the differential equation dydx=4y3+2yx23xy2+x3, y(1)=1\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3},\ y(1)=1. If for some…MediumNumerical value
  5. 28 Jul 2022, Shift 1 · Q1Let the solution curve of the differential equation x dy=(x2+y2+y)dx, x>0x\,dy=\left(\sqrt{x^2+y^2}+y\right)dx,\ x>0, intersect the line x=1x=1 at y=0y=0 and…MediumSingle correct
  6. 29 Jun 2022, Shift 1 · Q2Let the solution curve of the differential equation xdydx−y=y2+16x2x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}, y(1)=3y(1) = 3 be y=y(x)y = y(x). Then y(2)y(2) is…MediumSingle correct
  7. 18 Mar 2021, Shift 2 · Q86Let y=y(x)y=y(x) be the solution of the differential equation x dy−y dx=(x2−y2) dxx\,dy-y\,dx=\sqrt{(x^2-y^2)}\,dx, x≥1x\ge1, with y(1)=0y(1)=0. If the area bounded…HardNumerical value
  8. 9 Jan 2020, Shift 2 · Q64If dydx=xyx2+y2\frac{dy}{dx}=\frac{xy}{x^2+y^2}; y(1)=1y(1)=1; then a value of xx satisfying y(x)=ey(x)=e 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 108 of the 174 JEE Main shifts held from 2017 to 2026.