AP EAMCET · Maths · Binomial Theorem
The coefficients of \(x^{50}\) in \((1+x)^{101}\) \(\left(1-x+x^2\right)^{100}\) is......
- A 1
- B -1
- C 0
- D 2
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
Given expression is \(\begin{aligned} & (1+x)^{101}\left(1-x+x^2\right)^{100} \\ & =(1+x)\left[(1+x)\left(1-x+x^2\right)\right]^{100} \\ & =(1+x)\left(1+x^3\right)^{100} \end{aligned}\) So, coefficient of \(x^{50}\) in \((1+x)^{101}\left(1-x+x^2\right)^{100}\) \(=\) coefficient…
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