The number of integral values of $x$ satisfying $5x - 1 < (x + 1)^2 < 7x - 3$ is

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?

If $x \in R$ and $1 \leq \frac{3x^2-7x+8}{x^2+1} \leq 2$,then the minimum and maximum values of $x$ are respectively.

The marks scored by Mohan in two tests were $62$ and $48$. Find the minimum marks he should score in the third test to have an average of at least $60$ marks.

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between $8.2$ and $8.5$. If the first two pH readings are $8.48$ and $8.35$,then find the range of $pH$ value for the third reading that will result in the acidity level being normal.

The solution set of the constraints $|x-y| \leqslant 1, x, y \geqslant 0$ is