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Binomial Theorem question

2024 · 31 Jan · Shift 2 · Q58

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PYQ Library
JEE Main
Mathematics
Binomial Theorem
2024 · 31 Jan · Shift 2 · Q58

Binomial Theorem question

2024 · 31 Jan · Shift 2 · Q58

JEE MainMathematicsBinomial TheoremNumerical+4 / −1

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+\ldots \ldots \ldots .+(x+2)^{n-1}

be

\alpha_r

. If

\sum_{r=0}^n \alpha_r=\beta^n-\gamma^n, \beta, \gamma \in \mathbb{N}

, then the value of

\beta^2+\gamma^2

equals

\underline{\hspace{2cm}}

.

Numerical answer

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