If $x=2+\sqrt{3},$ then the value of $\sqrt{x}+\frac{1}{\sqrt{x}}$ is:

The speed of a boat in still water and the speed of the current is in ratio $5:1$. If the difference between distances covered by the boat in going $2 \mathrm{hours}$ upstream and $2 \mathrm{hours}$  downstream is $8 \mathrm{km}$.

I. Quantity I - Speed of boat in still water

II. Quantity II -A cyclist goes $30 \mathrm{km}$ in $3 \mathrm{hours}$ 

Find the relation between these two quantities.

If $x$ is a natural number.

If $x^2+ax+16$ is a perfect square number, then which number is $a$?

If $x$ is a natural number.

If $x^2+ax+b$ is a perfect square, prove that $a^2=4b$.