AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^5\) in the expansio of \((1+x)^{21}+(1+x)^{22}+\ldots+(1+x)^{30}\) is
- A \({ }^{31} \mathrm{C}_6-{ }^{21} \mathrm{C}_6\)
- B \({ }^{51} C_5\)
- C \({ }^9 \mathrm{C}_5\)
- D \({ }^{30} \mathrm{C}_5+{ }^{20} \mathrm{C}_5\)
Answer & Solution
Correct Answer
(A) \({ }^{31} \mathrm{C}_6-{ }^{21} \mathrm{C}_6\)
Step-by-step Solution
Detailed explanation
As we know, coefficient of \(x^r\) in the binomial expansion of \((1+x)^n\) is given by \({ }^n C_r\). So, coefficient of \(x^5\) in the binomial expansion of…
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