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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q75

Question 75 of 90 in this shift, Maths question 15 of 30, Section A.

Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as f(x)=e−xsin⁡xf(x)=e^{-x}\sin x. If F:[0,1]→RF:[0, 1]\to\mathbf{R} is a differentiable function such that F(x)=∫0xf(t) dtF(x)=\int_0^x f(t)\,dt, then the value of ∫01(F′(x)+f(x))exdx\int_0^1(F'(x)+f(x))e^x dx lies in the interval
  1. (1)[330360,331360]\left[\frac{330}{360}, \frac{331}{360}\right]Official answer
  2. (2)[327360,329360]\left[\frac{327}{360}, \frac{329}{360}\right]
  3. (3)[331360,334360]\left[\frac{331}{360}, \frac{334}{360}\right]
  4. (4)[335360,336360]\left[\frac{335}{360}, \frac{336}{360}\right]

Official answer

Option 1

NTA final key.

Chapter
Integrals
Topic
Definite Integral Properties
Idea tested
Bounding and Estimation Property

Same idea in other shifts

Asked 4× in all
  1. 27 Jul 2022, Shift 1 · Q8Let I=∫π/4π/3(8sin⁡x−sin⁡2xx)dxI = \int_{\pi/4}^{\pi/3} \left(\dfrac{8\sin x - \sin 2x}{x}\right) dx. ThenMediumSingle correct
  2. 18 Mar 2021, Shift 2 · Q71Let g(x)=∫0xf(t) dtg(x)=\int_0^x f(t)\,dt, where ff is continuous function in [0,3][0, 3] such that 13≤f(t)≤1\frac{1}{3}\le f(t)\le 1 for all t∈[0,1]t\in[0, 1] and…MediumSingle correct
  3. 8 Jan 2020, Shift 2 · Q61If I=∫12dx2x3−9x2+12x+4I = \int_1^2 \frac{dx}{\sqrt{2x^3 - 9x^2 + 12x + 4}}, 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.