Let $S$ be the set of all point $\left(\frac{a}{b},\frac{c}{d}\right)$ on the circle with radius $1$ centred at $\left(0,0\right)$ where $a$ and $b$ are relatively prime integers, $c$ and $d$ are relatively prime integers (that is $\mathrm{H}\mathrm{C}\mathrm{F}\mathrm{ }\left(a,b\right)=\mathrm{H}\mathrm{C}\mathrm{F} \left(c,d\right)=1$), and the integers $b$ and $d$ are even. Then the set $S$

Which among the following is not an irrational number?

Consider the following statements: For any integer $n,$ 

I.. $n^2+3$ is never divisible by $17$ .

II.. $n^2+4$ is never divisible by $17$. Then

How many numbers are there from $14$ to $159$ which are divisible by both $2$ and $8$?