(A) According to the equation of continuity, $A_1 V_1 = A_2 V_2$, where $A$ is the cross-sectional area and $V$ is the velocity of the fluid.
In the narrow part of the pipe (venturimeter), the cross-sectional area $A_2$ is smaller than the area $A_1$ of the wider part.
Therefore, the velocity of the fluid $V_2$ in the narrow part must be greater than the velocity $V_1$ in the wider part $(V_2 > V_1)$.
According to Bernoulli's principle, for a horizontal flow of an incompressible, non-viscous fluid, the sum of pressure energy and kinetic energy per unit volume remains constant. This implies that where the velocity of the fluid is higher, the pressure must be lower.
Since $V_2 > V_1$, the pressure $P_2$ at the narrow section must be less than the pressure $P_1$ at the wider section $(P_2 < P_1)$.
Pressure is related to the height of the liquid column $(h)$ in the vertical tubes by the relation $P = \rho gh$. Thus, a lower pressure corresponds to a lower liquid level.
Consequently, the liquid level in the tube connected to the narrow part must be lower than the level in the tube connected to the wider part.
Comparing this with the figures, figure $(a)$ shows a higher level in the narrow part, which contradicts Bernoulli's principle. Therefore, figure $(a)$ is incorrect.