If the quadratic equation $ax^2+bx+c=0$ $(a>0)$ has two roots $\alpha$ and $\beta$ such that $\alpha < -2$ and $\beta > 2$, then which of the following is true?

$f(x)=ax^2-bx-a$ is a quadratic expression. If $K$ is the least real number such that $f(x) \leq K, \forall x \in R$,then

If the maximum value of $2x - 7 - ax^2$ cannot exceed $20$,then the minimum value of $a$ is

If both the roots of the equation $x^2-4ax+1-3a+4a^2=0$ exceed $1$,then $a$ lies in the interval

Consider the quadratic equation $(c - 5)x^2 - 2cx + (c - 4) = 0$,where $c \ne 5$. Let $S$ be the set of all integral values of $c$ for which one root of the equation lies in the interval $(0, 2)$ and the other root lies in the interval $(2, 3)$. Then the number of elements in $S$ is

If both the roots of the equation $x^2 - 6ax + 2 - 2a + 9a^2 = 0$ exceed $3$,then