The sum of integral values of $a$ such that the equation $||x\ -2|\ -|3\ -x||\ =\ 2\ -a$ has a solution
$1$
$2$
$3$
$4$
If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are
The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$
The roots of the equation $4{x^4} - 24{x^3} + 57{x^2} + 18x - 45 = 0$, If one of them is $3 + i\sqrt 6 $, are
If $\alpha , \beta$ and $\gamma$ are the roots of ${x^3} + 8 = 0$, then the equation whose roots are ${\alpha ^2},{\beta ^2}$ and ${\gamma ^2}$ is
Exact set of values of $a$ for which ${x^3}(x + 1) = 2(x + a)(x + 2a)$ is having four real solutions is