CAT (QA) PYQs

The number of non-negative integer values of $k$ for which the quadratic equation $x^2 - 5x + k = 0$ has only integer roots, is

Let $f(x)$ be quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. if $f(2)=0$ and $f(4)=6$, then $f(-2)$ is equal to

If $(3+2\sqrt{2})$ is a root of the equation $ax^2 + bx + c = 0$, and $(4+2\sqrt{3})$ is a root of the equation $ay^2 + my + n = 0$, where $a, b, c, m$ and $n$ are integers,
then the value of $(\frac{b}{m} + \frac{c-2b}{n})$ is