A) \[\frac{1}{3}\]
B) \[-\frac{1}{3}\]
C) \[\frac{2}{3}\]
D) \[\frac{3}{2}\]
E) \[0\]
Correct Answer: D
Solution :
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 \[={{\left( 1-\frac{1}{3} \right)}^{199}}\times {{\left( 1+\frac{1}{2} \right)}^{200}}\] \[(\because put\,x=1)\] \[={{\left( \frac{2}{3} \right)}^{199}}\times {{\left( \frac{3}{2} \right)}^{200}}\] \[={{\left( \frac{3}{2} \right)}^{(200-199)}}=\frac{3}{2}\]
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