JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum\limits_{ k =1}^{31}\left({ }^{31} C _{ k }\right)\left({ }^{31} C _{ k -1}\right)-\sum\limits_{ k =1}^{30}\left({ }^{30} C _{ k }\right)\left({ }^{30} C _{ k -1}\right)=\frac{\alpha(60 !)}{(30 !)(31 !)}\) Where \(\alpha \in R\), then the value of \(16 \alpha\) is equal to
- A \(1411\)
- B \(1320\)
- C \(1615\)
- D \(1855\)
Answer & Solution
Correct Answer
(A) \(1411\)
Step-by-step Solution
Detailed explanation
\(\sum\limits_{ R =1}^{31}{ }^{31} C _{ R } \cdot{ }^{31} C _{ R -1}\) \(={ }^{31} C _{1} \cdot{ }^{31} C _{0}+{ }^{31} C _{2} \cdot{ }^{31} C _{1}+\ldots .+{ }^{31} C _{31} \cdot{ }^{31} C _{30}\)…
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