If b n = ∫ 0 π 2 cos 2 n x sin x d x , n ∈ ℕ , then

1. $b_3-b_2,b_4-b_3,b_5-b_4$ are in an A.P. with common difference$-2$
2. $\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}$ are in an A.P. with common difference $2$
3. $b_3-b_2,b_4-b_3,b_5-b_4$ are in a G.P.
4. $\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}$ are in an A.P. with common difference $-2$

Solution

Asked in: JEE Main 2022 (25 Jun Shift 2)

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