The set of all values of $x$ which satisfy both the inequations $x^2-1 \leq 0$ and $x^2-x-2 \geq 0$ simultaneously is

If $(2k-1)x^2 - 2(3k-2)x + 4k > 0$ for every $x \in R$,then the sum of all possible integral values of $k$ is

The solution set of the inequation $\sqrt{x^2+6x+5} > (8-x)$ 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

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

The integer $k$,for which the inequality $x^{2}-2(3k-1)x+8k^{2}-7>0$ is valid for every $x \in \mathbb{R}$,is