7.Binomial Theorem
hard

$\sum_{\mathrm{k}=0}^{20}\left({ }^{20} \mathrm{C}_{\mathrm{k}}\right)^{2}$ is equal to :

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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