If the point $(a, a)$ is placed between the lines $|x + y| = 4$,then

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

Let $2\sin^2 x + 3\sin x - 2 > 0$ and $x^2 - x - 2 < 0$ ($x$ is measured in radians). Then $x$ lies in the interval

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180 \ cm$,then:

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to

In a manufacturing company,the cost and revenue functions of a product are given by $C(x) = 500 + \frac{5}{2}x$ and $R(x) = 3x$,where $x$ is the number of items produced and sold. How many items must be sold to realize no profit or loss? Is there any profit?