Which of the following ion is necessary for the contraction of a muscle and nerve impulse transmission?

The correct option is D Ca${}^{++}$ and Na${}^{+}$ ions
The signal comes via the axon, which causes depolarisation and repolarisation of the nerve and Na${}^{+}$ is involved in the process. This signal travels deep into the muscles. This triggers the calcium, which is stored in the sarcoplasmic reticulum to be released and the calcium released, then causes muscle contraction.
So, the correct answer is option C.