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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 1 February 2024, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

Let α\alpha be a non-zero real number. Suppose f:R→Rf:\mathbf{R}\to\mathbf{R} is a differentiable function such that f(0)=2f(0)=2 and lim⁡x→−∞f(x)=1\lim_{x\to-\infty}f(x)=1. If f′(x)=αf(x)+3f'(x)=\alpha f(x)+3, for all x∈Rx\in\mathbf{R}, then f(−log⁡e2)f(-\log_e 2) is equal to ________.
  1. (1)33
  2. (2)55
  3. (3)77
  4. (4)99

Official answer

Dropped by NTA (marks given to all)

NTA final key: NTA final key: Drop (question dropped).

Chapter
Differential Equations
Topic
Linear Differential Equations
Idea tested
General Solution Formula

Same idea in other shifts

Asked 3× in all
  1. 7 Apr 2025, Shift 2 · Q19Let y=y(x)y=y(x) be the solution of the differential equation (x2+1)y′−2xy=(x4+2x2+1)cos⁡x(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x, y(0)=1y(0)=1. Then ∫−33y(x) dx\int_{-3}^{3}y(x)\,dx is :MediumSingle correct
  2. 5 Apr 2024, Shift 2 · Q26Let y=y(x)y = y(x) be the solution of the differential equation dydx+2x(1+x2)2 y=xe1(1+x2)\frac{dy}{dx} + \frac{2x}{(1+x^2)^2}\,y = x e^{\frac{1}{(1+x^2)}};…MediumNumerical value
  3. 25 Feb 2021, Shift 1 · Q69If a curve passes through the origin and the slope of the tangent to it at any point (x,y)(x, y) is x2−4x+y+8x−2\frac{x^2 - 4x + y + 8}{x - 2}, then…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.