The sum of all real values of $x$ satisfying the equation ${\left( {{x^2} - 5x + 5} \right)^{{x^2} + 4x - 60}} = 1$ is ;

The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ 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 number of solutions of $\frac{{\log 5 + \log ({x^2} + 1)}}{{\log (x - 2)}} = 2$ is

If $x$ be real, then the minimum value of ${x^2} - 8x + 17$ is

Let $P(x) = x^3 - ax^2 + bx + c$ where $a, b, c \in R$ has integral roots such that $P(6) = 3$, then $' a '$ cannot be equal to