JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(x^{7}\) in the expression \((1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+\ldots+x^{10}\) is
- A \(120\)
- B \(330\)
- C \(210\)
- D \(420\)
Answer & Solution
Correct Answer
(B) \(330\)
Step-by-step Solution
Detailed explanation
Coefficient of \(x^{7}\) is \(^{10} \mathrm{C}_{7}+^{9} \mathrm{C}_{6}+^{5} \mathrm{C}_{5}+\ldots+^{4} \mathrm{C}_{1}+^{3} \mathrm{C}_{0}\) \(\underbrace{^{4} C_{0}+^{4} C_{1}}_{^{5} C_{1}}+^{5} C_{2}+\ldots+^{10} C_{7}=^{11} C_{7}=330\)
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