Learn

Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let ∫0x1−(y′(t))2 dt=∫0xy(t) dt, 0≤x≤3, y≥0, y(0)=0\int_0^x\sqrt{1-(y'(t))^2}\,dt=\int_0^x y(t)\,dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0. Then at x=2x=2, y′′+y+1y''+y+1 is equal to
  1. (1)11Official answer
  2. (2)1/21/2
  3. (3)2\sqrt{2}
  4. (4)22

Official answer

Option 1

NTA final key.

Chapter
Differential Equations
Topic
Leibniz Rule
Idea tested
Solving Integral Equations

Same idea in other shifts

Asked 4× in all
  1. 4 Apr 2026, Shift 2 · Q25Let ff be a twice differentiable function such that f(x)=∫0xtan⁡(t−x) dt−∫0xf(t)tan⁡t dtf(x)=\int_0^x\tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt,…HardNumerical value
  2. 5 Apr 2026, Shift 2 · Q19Let f:[1,∞)→Rf:[1,\infty)\to\mathbf{R} be a differentiable function defined as f(x)=∫1xf(t) dt+(1−x)(log⁡ex−1)+ef(x)=\int_1^x f(t)\,dt+(1-x)(\log_e x-1)+e. Then the value of…HardSingle correct
  3. 2 Apr 2025, Shift 2 · Q20Let f:[1,∞)→[2,∞)f : [1, \infty) \to [2, \infty) be a differentiable function. If 10∫1xf(t) dt=5xf(x)−x5−910\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9 for all…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 42 of the 174 JEE Main shifts held from 2017 to 2026.