JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum_{\mathrm{r}=0}^{10}\left(\frac{10^{\mathrm{r}+1}-1}{10^{\mathrm{r}}}\right) \cdot{ }^{11} \mathrm{C}_{\mathrm{r}+1}=\frac{\alpha^{11}-11^{11}}{10^{10}}\), then \(\alpha\) is equal to :
- A \(15\)
- B \(11\)
- C \(24\)
- D \(20\)
Answer & Solution
Correct Answer
(D) \(20\)
Step-by-step Solution
Detailed explanation
\(\sum_{\mathrm{r}=0}^{10}\left(\frac{1 \mathrm{r}^{\mathrm{r}-1}-1}{10^{\mathrm{r}}}\right){ }^{11} \mathrm{C}_{\mathrm{r}+1} \) \( =\sum_{\mathrm{r}=0}^{10}\left(10-\frac{1}{10^{\mathrm{r}}}\right)^{11} \mathrm{C}_{\mathrm{r}+1} \)…
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