JEE Mains · Maths · STD 11 - 7. binomial theoram
If the co-efficient of \(x^9\) in \(\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}\) and the co-efficient of \(x^{-9}\) in \(\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}\) are equal, then \((\alpha \beta)^2\) is equal to \(.............\).
- A \(2\)
- B \(4\)
- C \(1\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
Coefficient of \(x ^9\) in \(\left(\alpha x^3+\frac{1}{\beta x}\right)={ }^{11} C_6 \cdot \frac{\alpha^5}{\beta^6}\) \(\because\) Both are equal \(\therefore \frac{11}{C_6} \cdot \frac{\alpha^5}{\beta^6}=-\frac{11}{C_5} \cdot \frac{\alpha^6}{\beta^5}\)…
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