when a resistance of 2Ω is connected across the terminals of a cell, the current is 0.5 A, but when the resistance across the cell is 5 Ω, the current is 0.25 A. What is the EMF?

1.5 V

Explanation:

If V is the voltage of the cell and R is the internal resistance of the cell, then from Ohm's law:

V = 0.5 (R + 2)

V = 0.25 (R + 5)

V = 0.5 R + 1

V = 0.25 R + 1.25

Solve with substitution or elimination. I'll use elimination. Multiply the second equation by 2:

2V = 0.5 R + 2.5

Subtract the first equation:

V = 1.5

The voltage is 1.5 V.