Which of the following is incorrectly matched?

$A$ and $C$ are concentric conducting spherical shells of radii $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric layer of inner radius $a$,outer radius $b$,and dielectric constant $k$. If sphere $A$ is given a charge $Q$,the potential at the outer surface of the dielectric (at radius $b$) is:

One litre of oxygen at a pressure of $1 ~atm$ and two litres of nitrogen at a pressure of $0.5 ~atm$ are introduced into a vessel of volume $1 ~L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

$A$ sulphide ore is first converted into its oxide before reduction. This is done because

The value of the series $x \log _e a + \frac{x^3}{3!} (\log _e a)^3 + \frac{x^5}{5!} (\log _e a)^5 + \dots$ is

If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2 + cx$ on the interval $x \in [-1, 1]$ at the point $x = \frac{1}{2}$,then $(2b + c)$ is equal to: