AP EAMCET · Maths · Binomial Theorem
If the coefficients of \(r\) th and \((r+1)\) th terms in the expansion of \((1+x)^{24}\) are in the ratio \(12: 13\), then \(r\) is the root of the quadratic equation
- A \(x^2-5 x+6=0\)
- B \(x^2-11 x+30=0\)
- C \(x^2-14 x+13=0\)
- D \(x^2-14 x+24=0\)
Answer & Solution
Correct Answer
(D) \(x^2-14 x+24=0\)
Step-by-step Solution
Detailed explanation
According to given information, \(\frac{{ }^{24} C_{r-1}}{{ }^{24} C_r}=\frac{12}{13}\) \(\begin{gathered} \Rightarrow \frac{\frac{24 !}{(r-1) !(25-r) !}}{\frac{24 !}{r !(24-r) !}}=\frac{12}{13} \\ \Rightarrow \frac{r}{25-r}=\frac{12}{13} \Rightarrow r=12 \end{gathered}\) and…
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