The number of real values of $x$ for which the equality $\left| {\,3{x^2} + 12x + 6\,} \right| = 5x + 16$ holds good is
$4$
$3$
$2$
$1$
The integer $'k'$, for which the inequality $x^{2}-2(3 k-1) x+8 k^{2}-7>0$ is valid for every $x$ in $R ,$ is
If $\alpha , \beta , \gamma$ are roots of equation $x^3 + qx -r = 0$ then the equation, whose roots are
$\left( {\beta \gamma + \frac{1}{\alpha }} \right),\,\left( {\gamma \alpha + \frac{1}{\beta }} \right),\,\left( {\alpha \beta + \frac{1}{\gamma }} \right)$
The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$
If $x$ be real, the least value of ${x^2} - 6x + 10$ is
A real root of the equation ${\log _4}\{ {\log _2}(\sqrt {x + 8} - \sqrt x )\} = 0$ is