What kind of measurement cannot be made after the battery of the multimeter is taken out?

The correct choice is that resistance cannot be measured after the battery of the multimeter has been removed. A multimeter requires a power source to function properly as it uses its internal battery to send a small current through the component being tested for resistance measurements. This allows the multimeter to determine the resistance based on the voltage drop across the component and the current flowing through it, according to Ohm's law (V = IR).

When the battery is removed, the multimeter loses the ability to provide that current necessary for resistance testing. Therefore, without the battery, the multimeter cannot perform resistance measurements.

In contrast, voltage can be measured directly from the circuit if it's energized, and for current measurement, the multimeter needs to be inserted into the circuit and still requires a power source to calculate. Power is derived from measurements of voltage and current, which also cannot be accurately assessed without a functioning multimeter.