If the expression $\left( {mx - 1 + \frac{1}{x}} \right)$ is always non-negative, then the minimum value of m must be
$ - \frac{1}{2}$
$0$
$\frac{1}{4}$
$\frac{1}{2}$
The number of solutions, of the equation $\mathrm{e}^{\sin x}-2 e^{-\sin x}=2$ is
If $x$ is real, then the maximum and minimum values of expression $\frac{{{x^2} + 14x + 9}}{{{x^2} + 2x + 3}}$ will be
The real roots of the equation ${x^2} + 5|x| + \,\,4 = 0$ are
If $72^x \cdot 48^y=6^{x y}$, where $x$ and $y$ are non-zero rational numbers, then $x+y$ equals
The least integral value $\alpha $ of $x$ such that $\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0$ , satisfies