AP EAMCET · Maths · Binomial Theorem
Thecoefficientof \(x^3\) in the expansion of \((1-2 x)^{\frac{1}{2}}(1+3 x)^{\frac{1}{3}}\) is
- A \(-\frac{20}{3}\)
- B \(\frac{20}{3}\)
- C \(\frac{17}{3}\)
- D \(-\frac{17}{3}\)
Answer & Solution
Correct Answer
(A) \(-\frac{20}{3}\)
Step-by-step Solution
Detailed explanation
\((1-2 x)^{1 / 2}(1+3 x)^{-1 / 3}\) \(=\left(1+\frac{1}{2}(-2 x)+\frac{1}{2} \frac{\left(\frac{1}{2}-1\right)}{2-1}(-2 x)^2+\frac{\frac{1}{2}\left(\frac{1}{2}-1\right)\left(\frac{1}{2}-2\right)}{3.2 .1}(-2 x)^3+\ldots\right)\)…
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