Frequency Modulation with same carrier and message signal of same frequency but different amplitude
Frequency deviation is proportional to the amplitude of the modulating signal. So the deviation produced by your 10 V signal will be twice that produced by the 5 V signal.

does that mean maximum frequency deviation of a carrier is
proportional to the maximum value of amplitude of message signals the
carrier can carry whatever maybe the frequency of message signals?

A practical system will have a maximum permitted frequency deviation and a maximum permitted frequency for the modulating (message) signal. Within those limits then yes.