Which of the following is an amphoteric hydroxide?

$(a)$ Show that for every natural number $n$ relatively prime to $10$,there exists a natural number $m$ consisting only of digits $1$ such that $n$ divides $m$.
$(b)$ Hence or otherwise,show that every positive rational number can be expressed in the form $\frac{a}{10^b(10^c-1)}$ for some natural numbers $a, b, c$.

$\frac{1}{2 \cdot 3} + \frac{1}{4 \cdot 5} + \frac{1}{6 \cdot 7} + \frac{1}{8 \cdot 9} + \dots$ is equal to

Cardiac output is determined by which of the following?

$A$ long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of windings of $N$ turns each. If it carries a current $i$,the magnetic field at its centre will be

$64$ small drops of mercury,each of radius $r$ and charge $q$,coalesce to form a big drop. The ratio of the surface charge density of each small drop to that of the big drop is: