Question

The coefficient of $x^{50}$ in $(1+x{)}^{101}{\left(1-x+x^2\right)}^{100}$ is

• A. 0
• B. 41
• C. 50
• D. 1

Answer 1

Answer: (A)

Here $(1+x{)}^{101}{\left(1-x+x^2\right)}^{100}=(1+x)(1+x{)}^{100}{\left(1-x+x^2\right)}^{100}$
$=(1+x){\left(1+x^3\right)}^{100}$
$={\left(1+x^3\right)}^{100}+x{\left(1+x^3\right)}^{100}$
$\therefore$ coefficient of $x^{50}=0+0=0$