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

The number of elements in the set $\{n \in \mathbb{Z} : |n^2 - 10n + 19| < 6\}$ is $...........$

The solution set contained in $R$ of the inequation $3^x+3^{1-x}-4 < 0$ is:

The longest side of a triangle is $3$ times the shortest side and the third side is $2 \, cm$ shorter than the longest side. If the perimeter of the triangle is at least $61 \, cm$,find the minimum length of the shortest side. (in $, cm$)

The set of all real values of $x$ satisfying the inequation $\frac{8x^2-14x-9}{3x^2-7x-6} > 2$ is

Find all pairs of consecutive even positive integers,both of which are larger than $5$,such that their sum is less than $23$.