Σ_{ k =0}^{20}left({ }^{20} C _{ k }right)^{2} बराबर है

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7.Binomial Theorem

hard

$\sum_{ k =0}^{20}\left({ }^{20} C _{ k }\right)^{2}$ बराबर है

A

${ }^{40} \mathrm{C}_{21}$

B

${ }^{40} \mathrm{C}_{19}$

C

${ }^{40} \mathrm{C}_{20}$

D

${ }^{41} \mathrm{C}_{20}$

(JEE MAIN-2021)

Solution

$\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}$

sum of suffix is const. so summation will be ${ }^{40} \mathrm{C}_{20}$

Standard 11

Mathematics

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