The common bottle cork is a product of .......... .

Ethyl chloride reacts with sodium ethoxide to form a compound $A$. Which of the following reactions also yields $A$?

Identify the incorrect statements from the following.
$I$. Tin in $+2$ state acts as reducing agent while lead in $+4$ state acts as strong oxidising agent.
$II$. Silicon exists as $[SiF_6]^{2-}$ form,but $[SiCl_6]^{2-}$ does not.
$III$. The hybridisation of carbon in fullerene is $sp^3$.
$IV$. Among $Ge, Sn$ and $Pb$,the lowest melting point is for $Sn$.

An oscillator is nothing but an amplifier with

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):

If $\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)$ is finite,then the values of $a, b$ are respectively :