JEE Mains · Maths · STD 11 - 7. binomial theoram
\(\sum_{\mathrm{k}=0}^{20}\left({ }^{20} \mathrm{C}_{\mathrm{k}}\right)^{2}\) is equal to :
- A \({ }^{40} \mathrm{C}_{21}\)
- B \({ }^{40} \mathrm{C}_{19}\)
- C \({ }^{40} \mathrm{C}_{20}\)
- D \({ }^{41} \mathrm{C}_{20}\)
Answer & Solution
Correct Answer
(C) \({ }^{40} \mathrm{C}_{20}\)
Step-by-step Solution
Detailed explanation
\(\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}\) sum of suffix is const. so summation will be \({ }^{40} \mathrm{C}_{20}\)
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