If $x^2-4ax+5+a>0$ for all $x \in R$ whenever $a \in (\alpha, \beta)$,then $4\beta+\alpha=$

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

If $\alpha_1, \alpha_2$ and $\alpha_3$ are the roots of $x^3+3x+2=0$,then $\alpha_1^5+\alpha_2^5+\alpha_3^5=$

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 $3^x+3^{1-x}-4 < 0$ 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