Given below are two statements :
Statement-I : The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two non-ideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. 

In the light of the above statements, choose the correct answer from the options given below.

To analyze the correctness of the statements, let's consider two non-ideal batteries connected in parallel. Each battery has an emf ($E_1, E_2$) and an internal resistance ($r_1, r_2$).

Step 1: Equivalent EMF for Parallel Batteries

For two batteries with different emfs and internal resistances, the equivalent emf ($E_{\text{eq}}$) is given by:

$$E_{\text{eq}} = \frac{E_1/r_1 + E_2/r_2}{1/r_1 + 1/r_2}$$

Since this equation is a weighted average of $E_1$ and $E_2$, the equivalent emf lies between $E_1$ and $E_2$. This means:

$$E_{\text{eq}} \text{ is smaller than the larger emf and greater than the smaller emf.}$$

Thus, Statement-I is incorrect because it claims that $E_{\text{eq}}$ is smaller than either $E_1$ or $E_2$, which is not true.

Step 2: Equivalent Internal Resistance for Parallel Batteries

The equivalent internal resistance ($r_{\text{eq}}$) for two internal resistances in parallel is:

$$\frac{1}{r_{\text{eq}}} = \frac{1}{r_1} + \frac{1}{r_2}$$

Since the parallel combination of resistances always results in a smaller equivalent resistance than either of the individual resistances, we conclude:

$$r_{\text{eq}} < r_1 \quad \text{and} \quad r_{\text{eq}} < r_2$$

Thus, Statement-II is correct.