TS EAMCET · Maths · Binomial Theorem
The numerically greatest term in the binomial expansion of \((2 x-3 y)^5\) when \(x=\frac{3}{2}\) and \(y=\frac{2}{3}\) is
- A 360
- B 1080
- C 720
- D 2160
Answer & Solution
Correct Answer
(B) 1080
Step-by-step Solution
Detailed explanation
\((2 x-3 y)^5\) Numerically greatest term \(=\frac{(n+1)|\alpha|}{|\alpha|+1}\) where \(\alpha=\frac{-3 y}{2 x}, n=5\) \[ \because \quad x=\frac{3}{2}, y=\frac{2}{3} \] \[ \therefore \frac{x}{y}=\frac{9}{4}, \alpha=\frac{-3}{2} \times \frac{4}{9}=\frac{-2}{3} \text {. } \]…
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