Let $S$ be the set of positive integral values of $a$ for which $\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32} < 0, \forall x \in R$. Then,the number of elements in $S$ is:

For the inequality $2^{\log_{\sqrt{2}}(x - 1)} > x + 5$,the set of real values of $x$ is:

The set of all solutions of the inequation $x^2 - 2x + 5 \leq 0$ in $R$ is

Statement $(I)$: The set of solutions of $|x|^2 - 4|x| + 3 < 0$ is the interval $(-3, 3)$.
Statement $(II)$: If $x < 3$ or $x > 5$,then $x^2 - 8x + 15 > 0$.
Which of the above statements is (are) true?

If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$,then

The complete solution of the inequation $x^2 - 4x < 12$ is