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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

Let y=y(x)y=y(x) be the solution of the differential equation cos⁡x(3sin⁡x+cos⁡x+3)dy=(1+ysin⁡x(3sin⁡x+cos⁡x+3))dx\cos x(3\sin x+\cos x+3)dy=(1+y\sin x(3\sin x+\cos x+3))dx, 0≤x≤π20\leq x\leq\frac{\pi}{2}, y(0)=0y(0)=0. Then, y(π3)y\left(\frac{\pi}{3}\right) is equal to :
  1. (1)2log⁡e(33−84)2\log_e\left(\frac{3\sqrt{3}-8}{4}\right)
  2. (2)2log⁡e(3+72)2\log_e\left(\frac{\sqrt{3}+7}{2}\right)
  3. (3)2log⁡e(23+96)2\log_e\left(\frac{2\sqrt{3}+9}{6}\right)
  4. (4)2log⁡e(23+1011)2\log_e\left(\frac{2\sqrt{3}+10}{11}\right)Official answer

Official answer

Option 4

NTA final key.

Chapter
Differential Equations
Topic
Linear Differential Equations
Idea tested
Integrating Factor Calculation

Same idea in other shifts

Asked 22× in all
  1. 4 Apr 2026, Shift 2 · Q19Let y=y(x)y=y(x) be the solution of the differential equation:…HardSingle correct
  2. 3 Apr 2025, Shift 1 · Q20Let gg be a differentiable function such that ∫0xg(t) dt=x−∫0xt g(t) dt\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt, x≥0x \ge 0 and let y=y(x)y = y(x) satisfy the…HardSingle correct
  3. 4 Apr 2024, Shift 2 · Q12Let y=y(x)y=y(x) be the solution of the differential equation (x2+4)2dy+(2x3y+8xy−2)dx=0(x^2+4)^2dy+(2x^3y+8xy-2)dx=0. If y(0)=0y(0)=0, then y(2)y(2) is equal toHardSingle correct
  4. 5 Apr 2024, Shift 1 · Q12If y=y(x)y=y(x) is the solution of the differential equation dydx+2y=sin⁡(2x)\frac{dy}{dx}+2y=\sin(2x), y(0)=34y(0)=\frac34, then y(π8)y\left(\frac{\pi}{8}\right)…MediumSingle correct
  5. 5 Apr 2024, Shift 1 · Q26Let ff be a differentiable function in the interval (0,∞)(0,\infty) such that f(1)=1f(1)=1 and lim⁡t→xt2f(x)−x2f(t)t−x=1\lim_{t\to x}\frac{t^2f(x)-x^2f(t)}{t-x}=1 for…HardNumerical value
  6. 6 Apr 2024, Shift 1 · Q13Let y=y(x)y=y(x) be the solution of the differential equation (1+x2)dydx+y=etan⁡−1x(1+x^2)\frac{dy}{dx}+y=e^{\tan^{-1}x}, y(1)=0y(1)=0. Then y(0)y(0) isMediumSingle correct
  7. 1 Feb 2024, Shift 1 · Q28If x=x(t)x=x(t) is the solution of the differential equation (t+1)dx=(2x+(t+1)4)dt(t+1)dx=(2x+(t+1)^4)dt, x(0)=2x(0)=2, then, x(1)x(1) equals __________.MediumNumerical value
  8. 30 Jan 2024, Shift 1 · Q26Let y=y(x)y=y(x) be the solution of the differential equation (1−x2)dy=[xy+(x3+2)3(1−x2)]dx(1-x^2)dy=\left[xy+(x^3+2)\sqrt{3(1-x^2)}\right]dx, −1<x<1-1<x<1, y(0)=0y(0)=0. If…MediumNumerical value

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.