If \( { }^{20} C_{1}+\left(2^{2}\right){ }^{20} C_{2}+\left(3^{2}\r...

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If \( { }^{20} C_{1}+\left(2^{2}\right){ }^{20} C_{2}+\left(3^{2}\right){ }^{20} C_{3}+\ldots . .+\left(20^{2}\right)^{20} C_{20}=A\left(2^{\beta}\right) \) then the ordered pair \( (A, \beta) \) is equal to
\( \mathrm{P} \)
(2019 Main, 12 April II)
WV
(a) \( (420,19) \)
(b) \( (420,18) \)
(c) \( (380,18) \)
(d) \( (380,19) \)
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