If $\frac{2x}{2x^2 + 5x + 2} > \frac{1}{x + 1}$,then

If $\theta$ is an acute angle and $\sin\theta = \frac{p - 6}{8 - p}$, then $p$ must satisfy:

If $\frac{x^{2}-1}{x^{2}+1} \geq 0,$ then $x \in$

The longest side of a triangle is $3$ times the shortest side and the third side is $2 \, cm$ shorter than the longest side. If the perimeter of the triangle is at least $61 \, cm$,find the minimum length of the shortest side. (in $, cm$)

The solution set for the system of linear inequations $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,and $y \geq 0$ is represented graphically. Which of the following figures represents the correct solution set?

Ravi obtained $70$ and $75$ marks in the first two unit tests. Find the minimum marks he should get in the third test to have an average of at least $60$ marks.