If the roots of ${x^2} + x + a = 0$exceed $a$, then
$2 < a < 3$
$a > 3$
$ - 3 < a < 3$
$a < - 2$
The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{{x + 2}}{{x - 1}} < 4,$ is
The number of integers $k$ for which the equation $x^3-27 x+k=0$ has at least two distinct integer roots is
The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations $x+y^2=x^2+y=12$ is
The number of pairs of reals $(x, y)$ such that $x=x^2+y^2$ and $y=2 x y$ is
If $x$ be real, the least value of ${x^2} - 6x + 10$ is