The number of elements in the set $S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \leq 0 \text{ and } x^2 - 3x > 0\}$ is

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

The value of the greatest integer $k$ satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in \mathbb{N}$ is

In drilling the world's deepest hole,it was found that the temperature $T$ in degrees Celsius,$x \text{ km}$ below the earth's surface,is given by $T = 30 + 25(x - 3)$,where $3 \leq x \leq 15$. At what depth will the temperature be between $155^{\circ}C$ and $205^{\circ}C$?

The cost and revenue functions of a product are given by $C(x) = 20x + 4000$ and $R(x) = 60x + 2000$ respectively,where $x$ is the number of items produced and sold. The value of $x$ to earn profit is

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