The sum of the coefficients of ${\mathrm{x}}^{32}$ and ${\mathrm{x}}^{-17}$ in ${\left({\mathrm{x}}^4-\frac{1}{{\mathrm{x}}^3}\right)}^{15}$ is

For the coefficient of ${\mathrm{x}}^{32}; \mathrm{r}=\frac{15\times 4-32}{7}=\frac{28}{7}=4$

$\therefore$ Coefficient of ${\mathrm{x}}^{32}$ is ${(-1{)}^4}^{15}{\mathrm{C}}_4{=}^{15}{\mathrm{C}}_4$

For the coefficient of ${\mathrm{x}}^{-17};\mathrm{r}=\frac{15\times 4+17}{7}=\frac{77}{7}=11$

Coefficient of ${\mathrm{x}}^{-17}$ is ${ }^{15}{\mathrm{C}}_{11}(-1{)}^{11}={-}^{15}{\mathrm{C}}_4$

$\therefore$Sum of the coefficients of ${\mathrm{x}}^{32}$ and ${\mathrm{x}}^{-17}$ is ${ }^{15}{\mathrm{C}}_4{-}^{15}{\mathrm{C}}_4=0$.