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

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

The solution set of $x^{2} \leq 4$ is......

Let $f(x) = x^2 + 4x + 1$. Then

If $a$ and $b$ are the roots of the equation $x^2-7x-1=0$,then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to $........$.

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