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} $
$=\left(\frac{3}{2}\right)^{(200-199)}=\frac{3}{2}$