JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L\), then \(L\) is equal to \(.....\)
- A \(222\)
- B \(221\)
- C \(223\)
- D \(224\)
Answer & Solution
Correct Answer
(B) \(221\)
Step-by-step Solution
Detailed explanation
\(\sum_{ K =1}^{10} K ^{2}\left({ }^{10} C _{ K }\right)^{2}\) \(\sum_{ K =1}^{10}\left( K ^{10} C _{ K }\right)^{2}=\sum_{ K =1}^{10}\left(10 \cdot{ }^{9} C _{ K -1}\right)^{2}\) \(=100 \sum_{ K =1}^{9} C _{ K -1} \cdot{ }^{9} C _{10- K }\)…
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