Let the coefficient of xʳ in the expansion of (x + 3)ⁿ⁻¹ + (x + 3)ⁿ⁻²(x + 2) + (x + 3)ⁿ⁻³(x + 2)² + ..........

Question

Let the coefficient of xʳ in the expansion of (x + 3)ⁿ⁻¹ + (x + 3)ⁿ⁻²(x + 2) + (x + 3)ⁿ⁻³(x + 2)² + ....... (x + 2)ⁿ⁻¹ be αᵣ. If _ r=0 ^n _r = ^n - ^n, β, γ ∈ ℕ, then the value of β² + γ² equals ________.

Accepted Answer

25

JEE Main 2024 Mathematics question

Solution

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