If I n = ∫ (π)/4 ^((π)/2) cot ⁿx dx, then:

(A) 1/(I₂ + I₄),1/(I₃ + I₅),1/(I₄ + I₆) are in A.P.

(B) I₂ + I₄, I₃ + I₅, I₄ + I₆ are in A.P.

(C) 1/(I₂ + I₄),1/(I₃ + I₅),1/(I₄ + I₆) are in G.P.

(D) I₂ + I₄, (I₃ + I₅)², I₄ + I₆ are in G.P.

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 25 Feb, Evening shift · Q3396

JEE Main 202125 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

{I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx}

, then :

JEE Main 2021 · 25 Feb, Evening shift · Q3396

JEE Main 202125 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

{I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx}

, then :