JEE Mains · Maths · STD 11 - 7. binomial theoram
If some three consecutive in the binomial expansion of \({\left( {x + 1} \right)^n}\) in powers of \(x\) are in the ratio \(2 : 15 : 70\), then the average of these three coefficient is
- A \(964\)
- B \(625\)
- C \(227\)
- D \(232\)
Answer & Solution
Correct Answer
(D) \(232\)
Step-by-step Solution
Detailed explanation
Given: \(\frac{^{n} C_{r-1}}{^{n} C_{r}}=\frac{2}{15}\) \(\Rightarrow \frac{r}{n-r+1}=\frac{2}{15}\) \(\Rightarrow 15 r=2 n-2 r+2\) \(\Rightarrow 17 r=2 n+2.........(1)\) also given \(\frac{^{n} C_{r}}{^{n} C_{r+1}}=\frac{15}{70}\) \( \Rightarrow \frac{r+1}{n-r}=\frac{3}{14}\)…
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