The correct order of ionic radii of $Ce, La, Pm$ and $Yb$ in $+3$ oxidation state is

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively. Their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $r_2/r_1 = ?$

The monomers of $Buna-S$ rubber are

If $N$ denotes the set of all positive integers and if $f: N \rightarrow N$ is defined by $f(n) =$ the sum of positive divisors of $n$,then $f(2^k \cdot 3)$,where $k$ is a positive integer,is

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to