WBJEE · Maths · Binomial Theorem
The coefficient of \(x^{10}\) in the expansion of \(1+(1+x)+\dots+(1+x)^{20}\)
- A \({ }^{19} C_{9}\)
- B \({ }^{20} C_{10}\)
- C \({ }^{21} C_{11}\)
- D \({ }^{22} C_{12}\)
Answer & Solution
Correct Answer
(C) \({ }^{21} C_{11}\)
Step-by-step Solution
Detailed explanation
The given series is in GP. Hence, its sum \(S=\frac{1\left\{(1+x)^{20+1}-1\right\}}{(1+x)-1}=\frac{(1+x)^{21}-1}{x}\) Therefore, the required coefficient of \(x^{10}\) in the expansion of \((1+x)^{21}-1\) \(=\) Coefficient of \(x^{11}\) in the expansion of \[ ={ }^{21} C_{11} \]
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