If $I_n = \int_{\pi/4}^{\pi/2} \cot^n x \, dx$, then :

Option 1: $\frac{1}{I_2+I_4}, \frac{1}{I_3+I_5}, \frac{1}{I_4+I_6}$ are in A.P.

$\frac{1}{I_2+I_4}, \frac{1}{I_3+I_5}, \frac{1}{I_4+I_6}$ are in A.P.

$I_2+I_4, I_3+I_5, I_4+I_6$ are in A.P.

$\frac{1}{I_2+I_4}, \frac{1}{I_3+I_5}, \frac{1}{I_4+I_6}$ are in G.P.

$I_2+I_4, (I_3+I_5)^2, I_4+I_6$ are in G.P.

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

I_n = \int_{\pi/4}^{\pi/2} \cot^n x \, dx

, then :

(1) $\frac{1}{I_2+I_4}, \frac{1}{I_3+I_5}, \frac{1}{I_4+I_6}$ are in A.P.Official answer
(2) $I_2+I_4, I_3+I_5, I_4+I_6$ are in A.P.
(3) $\frac{1}{I_2+I_4}, \frac{1}{I_3+I_5}, \frac{1}{I_4+I_6}$ are in G.P.
(4) $I_2+I_4, (I_3+I_5)^2, I_4+I_6$ are in G.P.

Official answer

Option 1

NTA final key.

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

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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.