Question

The sum of the coefficients in the expansion of ${\left(x^2-\frac{1}{3}\right)}^{199}\times {\left(x^3+\frac{1}{2}\right)}^{200}$ is

• A. $\frac{1}{3}$
• B. $-\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$
• E. $0$

Answer 1

Answer: (D)

Given expression ${\left(x^2-\frac{1}{3}\right)}^{199}\times {\left(x^3+\frac{1}{2}\right)}^{200}$
The sum of the coefficients in the above expression
$={\left(1-\frac{1}{3}\right)}^{199}\times {\left(1+\frac{1}{2}\right)}^{200}$
$(\because$ put $x=1)$
$={\left(\frac{2}{3}\right)}^{199}\times {\left(\frac{3}{2}\right)}^{200}$
$={\left(\frac{3}{2}\right)}^{(200-199)}=\frac{3}{2}$