TS EAMCET · Maths · Binomial Theorem
The numerically greatest term in the expansion of \((3 x-16 y)^{15}\) when \(x=\frac{2}{3}\) and \(y=\frac{3}{2}\) is
- A 13th term
- B 14th term
- C 15th term
- D 16th term
Answer & Solution
Correct Answer
(C) 15th term
Step-by-step Solution
Detailed explanation
\((3 x-16 y)^{15}=(3 x)^{15}\left(1-\frac{16 y}{3 x}\right)^{15}=(3 x)^{15}(1+\alpha)^n\) Here \(n=15, \alpha=-\frac{16 y}{3 x}=\frac{-16 \times \frac{3}{2}}{3 \times \frac{2}{3}}=\frac{-24}{2}=-12\) \(\frac{(n+1)|\alpha|}{|\alpha|+1}=\frac{(15+1) \cdot 12}{12+1}=14.76\)…
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