TS EAMCET · Maths · Binomial Theorem
The coefficient of \(x^{50}\) in the expansion of \((1+x)^{101}\left(1-x+x^2\right)^{100}\) is
- A \(0\)
- B \(-1\)
- C \(50\)
- D \(100\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & (1+x)^{101}\left(1-x+x^2\right)^{100} \\ & =(1+x)\left[(1+x)\left(1-x+x^2\right)\right]^{100} \\ & =(1+x)\left(1+x^3\right)^{100}=1\left(1+x^3\right)^{100}+x\left(1+x^3\right)^{100} \\ & \begin{aligned} \therefore \text { Coefficient of } x^{50} \\ =\left\{1…
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