The number of real solution(s) of the equation $x^2+3 x+2=\min \{|x-3|,|x+2|\}$ is:

The number of real roots of the equation ${e^{\sin x}} - {e^{ - \sin x}} - 4$ $ = 0$ are

If $72^x \cdot 48^y=6^{x y}$, where $x$ and $y$ are non-zero rational numbers, then $x+y$ equals

In the equation ${x^3} + 3Hx + G = 0$, if $G$ and $H$ are real and ${G^2} + 4{H^3} > 0,$ then the roots are

In a cubic equation coefficient of $x^2$ is zero and remaining coefficient are real has one root $\alpha = 3 + 4\, i$ and remaining roots are $\beta$ and $\gamma$ then $\alpha \beta \gamma$ is :-

The number of non-negative integer solutions of the equations $6 x+4 y+z=200$ and $x+y+z=100$ is