For an ideal gas, $\rho = \large\frac{PM}{RT}$.

Here, $T$ is a constant which imples that Pressure must be increasing so as to increase $\rho$.

Therefore Option "(A) Pressure at B is lower than Pressure at A" is incorrect.

Since $P$ is increasing, $V$ decreases, which implies work done is negative.

Since $T$ is constant, $PV = $ constant and also $\Delta u = 0$.