The number of solution$(s)$ of the equation $2^x = x^2$ is

If $|x - 2| + |x - 3| = 7$, then $x =$

If the sum of all the roots of the equation $e^{2 x}-11 e^{x}-45 e^{-x}+\frac{81}{2}=0$ is $\log _{ e } P$, then $p$ is equal to

The sum of the cubes of all the roots of the equation $x^{4}-3 x^{3}-2 x^{2}+3 x+1=10$ is

If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are

The number of integers $a$ in the interval $[1,2014]$ for which the system of equations $x+y=a$, $\frac{x^2}{x-1}+\frac{y^2}{y-1}=4$ has finitely many solutions is