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

The region represented by the inequation $x-y \leq -1, x-y \geq 0, x \geq 0, y \geq 0$ is $.....$

$A$ 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 values of $x$ for which the inequality $\frac{8x^2+16x-51}{(2x-3)(x+4)} > 3$ holds,are

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

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?