$A$ triangle is formed by the $X$-axis,$Y$-axis,and the line $3x + 4y = 60$. The number of points $P(a, b)$ which lie strictly inside the triangle,where $a$ is an integer and $b$ is a multiple of $a$,is $...........$

Solve the following inequality: $\frac{|x-1|}{x+2} < 1$.

$A$ solution of $8 \%$ boric acid is to be diluted by adding a $2 \%$ boric acid solution to it. The resulting mixture is to be more than $4 \%$ but less than $6 \%$ boric acid. If we have $640$ litres of the $8 \%$ solution,how many litres of the $2 \%$ solution will have to be added?

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{x + 2}{x - 1} < 4$ is

The number of points $P(x, y)$ with natural numbers as coordinates that lie inside the quadrilateral formed by the lines $2x + y = 2$,$x = 0$,$y = 0$,and $x + y = 5$ is

The constraints $x+y \leq 4$,$3x+3y \geq 18$,$x \geq 0$,$y \geq 0$ define: