Number of integral values of $m$ for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0$ for all $x \in \mathbb{R}$ is (where $\{.\}$ denotes the fractional part function).

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

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

If $x^2+2px-2p+8>0$ for all real values of $x$,then the set of all possible values of $p$ 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 set $\{x \in R: 4+11x-3x^2>0\}$ is the interval