JEE Mains · Maths · STD 11 - 7. binomial theoram
The Coefficient of \(x ^{-6}\), in the expansion of \(\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9\), is \(........\).
- A \(5041\)
- B \(5042\)
- C \(5043\)
- D \(5040\)
Answer & Solution
Correct Answer
(D) \(5040\)
Step-by-step Solution
Detailed explanation
\(\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9\) Now, \(T _{ r +1}={ }^9 C _{ r } \cdot\left(\frac{4 x }{5}\right)^{9- r }\left(\frac{5}{2 x ^2}\right)^{ r }\) \(={ }^9 C _{ r } \cdot\left(\frac{4}{5}\right)^{9- r }\left(\frac{5}{2}\right)^{ r } \cdot x ^{9-3 r }\) Coefficient…
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