JEE Main 2024 Mathematics question

Mathematics Definite Integration JEE Main 2024

The value of k ∈ ℕ for which the integral , n ∈ ℕ, satisfies 147 I₂₀ = 148 I₂₁ is:

(A)10
(B)8
(C)14
(D)7Correct

Answer: (D)

Solution

Integration by parts gives Iₙ = (nk/(nk + 1))Iₙ₋₁, so I₂₁ = (21k/(21k + 1))I₂₀. Then 147(21k + 1) = 148 × 21k ⇒ 21k = 147 and k = 7.

Question ID VK-012358