Question

The number of dissimilar terms in the expansion of ${\left(1+x+x^3\right)}^{10}$ is

• A. 11
• B. 29
• C. 30
• D. 31

Answer 1

Answer: (C)

${\left(1+x+x^3\right)}^{10}={}^{10}{C}_0+{}^{10}{C}_1\left(x+x^3\right)+{}^{10}{C}_2{x}^2{\left(1+x^2\right)}^2+{}^{10}{C}_3{x}^3{\left(1+x^2\right)}^3+\dots \dots \dots ..{}^{10}{C}_9{x}^9{\left(1+x^2\right)}^9+{}^{10}{C}_{10}{x}^{10}{\left(1+x^2\right)}^{10}$

The expansion does not contain any term of $x^{29}$
$\therefore$ Number of different terms is 30