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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

If bn=∫0π2cos⁡2nxsin⁡x dxb_n = \int_0^{\frac{\pi}{2}} \frac{\cos^2 nx}{\sin x}\,dx, n∈Nn \in \mathbb{N}, then
  1. (1)b3−b2, b4−b3, b5−b4b_3 - b_2,\ b_4 - b_3,\ b_5 - b_4 are in an A.P. with common difference −2-2
  2. (2)1b3−b2, 1b4−b3, 1b5−b4\frac{1}{b_3 - b_2},\ \frac{1}{b_4 - b_3},\ \frac{1}{b_5 - b_4} are in an A.P. with common difference 2
  3. (3)b3−b2, b4−b3, b5−b4b_3 - b_2,\ b_4 - b_3,\ b_5 - b_4 are in a G.P.
  4. (4)1b3−b2, 1b4−b3, 1b5−b4\frac{1}{b_3 - b_2},\ \frac{1}{b_4 - b_3},\ \frac{1}{b_5 - b_4} are in an A.P. with common difference −2-2Official answer

Official answer

Option 4

NTA final key.

Chapter
Integrals
Topic
Definite Integral Properties
Idea tested
Reduction Formulae in Definite Integrals

Same idea in other shifts

Asked 6× in all
  1. 6 Apr 2024, Shift 1 · Q25Let rk=∫01(1−x7)kdx∫01(1−x7)k+1dxr_k=\frac{\int_0^1\left(1-x^7\right)^k dx}{\int_0^1\left(1-x^7\right)^{k+1}dx}, k∈Nk \in \mathbb{N}. Then the value of…HardNumerical value
  2. 8 Apr 2024, Shift 1 · Q11The value of k∈Nk\in\mathbb{N} for which the integral In=∫01(1−xk)ndxI_n=\int_0^1(1-x^k)^n dx, n∈Nn\in\mathbb{N}, satisfies 147I20=148I21147I_{20}=148I_{21} isHardSingle correct
  3. 1 Feb 2024, Shift 2 · Q10If ∫0π3cos⁡4x dx=aπ+b3\int_0^{\frac{\pi}{3}}\cos^4x\,dx=a\pi+b\sqrt{3}, where aa and bb are rational numbers, then 9a+8b9a+8b is equal to :MediumSingle correct
  4. 13 Apr 2023, Shift 2 · Q10The value of…HardSingle correct
  5. 25 Feb 2021, Shift 2 · Q64If In=∫π/4π/2cot⁡nx dxI_n = \int_{\pi/4}^{\pi/2} \cot^n x \, dx, 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.