TS EAMCET · Maths · Binomial Theorem
The coefficient of \(x^3\) in the expansion of \(\left(1-\frac{3}{4} x\right)^{\frac{1}{2}}\) is
- A \(\frac{27}{1024}\)
- B \(\frac{-27}{1024}\)
- C \(\frac{81}{1024}\)
- D \(\frac{-81}{1024}\)
Answer & Solution
Correct Answer
(B) \(\frac{-27}{1024}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(1-\frac{3}{4} x\right)^{\frac{1}{2}}=1+\frac{1}{2}\left(-\frac{3}{4} x\right)+\frac{\frac{1}{2}\left(-\frac{1}{2}\right)}{2 !}\left(-\frac{3}{4} x\right)^2 \\ & +\frac{\frac{1}{2} \times\left(-\frac{1}{2}\right) \times\left(-\frac{3}{2}\right)}{3…
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