Let the coefficient of x^r 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 \alpha_r. If \sum_{r=0}^{n} \alpha_r=\beta^n-\gamma^n, \beta, \gamma \in N, then the value of \beta^2+\gamma^2 equals [31-Jan-2024 Shift 2]

JEE Main 31-Jan-2024 Shift 2 Solved Paper

Section: Mathematics

Question : 24 of 90

Marks: +1, -0

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

αr=βn−γn,β,γ∈N, then the value of β2+γ2 equals

[31-Jan-2024 Shift 2]

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