JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum_{\mathrm{r}=1}^9\left(\frac{\mathrm{r}+3}{2^{\mathrm{r}}}\right) .{ }^9 \mathrm{C}_{\mathrm{r}}=\alpha\left(\frac{3}{2}\right)^9-\beta, \quad \alpha, \beta \in \mathrm{N}, \quad\) then \((\alpha+\beta)^2\) is equal to
- A \(27\)
- B \(9\)
- C \(81\)
- D \(18\)
Answer & Solution
Correct Answer
(C) \(81\)
Step-by-step Solution
Detailed explanation
\(\sum_{\mathrm{r}=1}^9\left(\frac{\mathrm{r}+3}{2^{\mathrm{r}}}\right) \cdot{ }^9 \mathrm{C}_{\mathrm{r}}=\alpha\left(\frac{3}{2}\right)^9-\beta, \alpha, \beta \in \mathrm{N}\) Now,…
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