AP EAMCET · Maths · Binomial Theorem
The numerically greatest term in the binomial expansion of \((2 a-3 b)^{19}\) when \(a=\frac{1}{4}\) and \(b=\frac{2}{3}\) is
- A \({ }^{19} C_5 \cdot 2^{11}\)
- B \({ }^{19} C_3 \cdot \frac{1}{2^{11}}\)
- C \({ }^{19} \mathrm{C}_4 \cdot \frac{1}{2^{13}}\)
- D \({ }^{19} \mathrm{C}_3 \cdot 2^{13}\)
Answer & Solution
Correct Answer
(D) \({ }^{19} \mathrm{C}_3 \cdot 2^{13}\)
Step-by-step Solution
Detailed explanation
We have, \((2 a-3 b)^{19}=2^{19} \cdot a^{19}\left(1-\frac{3 b}{2 a}\right)^{19}\) Ne know that, the \(r^{\text {th }}\) term of greatest term of \[ \begin{aligned} (1+x)^n & =\left[\frac{(n+1)|x|}{1+|x|}\right] \\ n & =19, x=-\frac{3 b}{2 a} \end{aligned} \] Here,…
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