JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\left({ }^{30} C _1\right)^2+2\left({ }^{30} C _2\right)^2+3\left({ }^{30} C _3\right)^2+\ldots \ldots+30\left({ }^{30} C _{30}\right)^2=\) \(\frac{\alpha 60 !}{(30 !)^2}\), then \(\alpha\) is equal to
- A \(30\)
- B \(60\)
- C \(15\)
- D \(10\)
Answer & Solution
Correct Answer
(C) \(15\)
Step-by-step Solution
Detailed explanation
\(S =0 .\left({ }^{30} C _0\right)^2+1 \cdot\left(\cdot{ }^{30} C _1\right)^2+2 \cdot\left({ }^{30} C _2\right)^2+\ldots \ldots+30 \cdot\left({ }^{30} C _{30}\right)^2\) \( S =30 \cdot(^{30} C _0)^2+29 \cdot{ }^{30} C _1)^2+28 \cdot{ }^{30} C _2)^2\)…
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