If $a, b, c, d$ are four distinct numbers chosen from the set $\{1,2,3, \ldots, 9\}$, then the minimum value of $\frac{a}{b}+\frac{c}{d}$ is
$\frac{3}{8}$
$\frac{1}{3}$
$\frac{13}{36}$
$\frac{25}{72}$
If $x$ is real, then the value of ${x^2} - 6x + 13$ will not be less than
The number of real roots of the equation ${e^{\sin x}} - {e^{ - \sin x}} - 4$ $ = 0$ are
If $x$ is real and satisfies $x + 2 > \sqrt {x + 4} ,$ then
The solution of the equation $2{x^2} + 3x - 9 \le 0$ is given by
If $\alpha ,\beta $ and $\gamma $ are the roots of ${x^3} + px + q = 0$, then the value of ${\alpha ^3} + {\beta ^3} + {\gamma ^3}$ is equal to