The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$
$x < - \,2$ or $x > 6$
$ - \,6 < x < 2$
$2 < x < 6$
$ - \,2 < x < 6$
The number of distinct real roots of the equation $x ^{7}-7 x -2=0$ is
Number of integers satisfying inequality, $\sqrt {{{\log }_3}(x) - 1} + \frac{{\frac{1}{2}{{\log }_3}\,{x^3}}}{{{{\log }_3}\,\frac{1}{3}}} + 2 > 0$ is
The number of integers $n$ for which $3 x^3-25 x+n=0$ has three real roots is
Let $\alpha ,\beta $ be the roots of ${x^2} + (3 - \lambda )x - \lambda = 0.$ The value of $\lambda $ for which ${\alpha ^2} + {\beta ^2}$ is minimum, is
If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-