The set of all values of $x$ for which the inequalities $x^2-7x+10 \geq 0$ and $2x+3-x^2 > 0$ hold simultaneously is

For what values of $x$ is $\frac{8x^2 + 16x - 51}{(2x - 3)(x + 4)} > 3$?

If $x^2+2px-2p+8>0$ for all real values of $x$,then the set of all possible values of $p$ is

The set of values of $x$ for which the inequalities $x^2-3x-10 < 0$ and $10x-x^2-16 > 0$ hold simultaneously is:

The common solution set of the inequations $x^2-4x \leq 12$ and $x^2-2x \geq 15$ taken together is

Assertion $(A)$: $3x^2 - 16x + 4 > -16$ is satisfied for some values of real $x$ in $(0, \frac{10}{3})$.
Reason $(R)$: $ax^2 + bx + c$ and $a$ will have the same sign for some values of $x \in \mathbb{R}$ when $b^2 - 4ac > 0$.
The correct option among the following is