JEE Mains · Maths · STD 11 - 7. binomial theoram
\({ }^{\text { } }\) If \(\alpha=1+\sum_{r=1}^6(-3)^{r-1} \quad{ }^{12} \mathrm{C}_{2 r-1}\), then the distance of the point \((12, \sqrt{3})\) from the line \(\alpha x-\sqrt{3} y+1=0\) is _________.
- A 10
- B 15
- C 5
- D 20
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\begin{aligned} & \alpha=1+\sum_{\mathrm{r}=1}^6(-1)^{\mathrm{r}-1}{ }^{12} \mathrm{C}_{2 \mathrm{r}-1} 3^{\mathrm{r}-1} \\ & \alpha=1+\sum_{\mathrm{r}=1}^6{ }^{12} \mathrm{C}_{2 \mathrm{r}-1} \frac{(\sqrt{3} \mathrm{i})^{2 \mathrm{t}-1}}{\sqrt{3} \mathrm{i}} \quad…
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