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

If $[x]$ denotes the greatest integer not exceeding $x$,then the values of $x$ satisfying $[x]^2-7[x]+12 \leq 0$ are

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

Statement $(I)$: The set of solutions of $|x|^2 - 4|x| + 3 < 0$ is the interval $(-3, 3)$.
Statement $(II)$: If $x < 3$ or $x > 5$, then $x^2 - 8x + 15 > 0$.
Which of the above statements is (are) true?

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 $........$.

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