JEE Mains · Maths · STD 11 - 7. binomial theoram
Let the coefficients of three consecutive terms in the binomial expansion of \((1+2 x)^{ n }\) be in the ratio \(2: 5: 8\). Then the coefficient of the term, which is in the middle of these three terms, is \(...........\).
- A \(1020\)
- B \(9920\)
- C \(1120\)
- D \(1000\)
Answer & Solution
Correct Answer
(C) \(1120\)
Step-by-step Solution
Detailed explanation
\(\Rightarrow \frac{{ }^n C_{r-1}(2)^{r-1}}{{ }^{ n } C_r(2)^r}=\frac{2}{5}\) \(\Rightarrow \frac{\frac{n !}{(r-1) !(n-r+1) !}}{\frac{n !(2)}{r !(n-r) !}}=\frac{2}{5}\) \(\Rightarrow \frac{r}{n-r+1}=\frac{4}{5} \Rightarrow 5 r=4 n-4 r+4\)…
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