Are the belief in creation and the theory of evolution mutually exclusive? Does holding of one necessarily mean not holding the other? If not please share some examples.
Not necessarily. There are christians on all parts of the spectrum. I see them as 2 main camps.
#1 mutation/natural selection exists but only to a point
There are many christians that will accept parts of the constructs of evolution such as natural selection via environmental pressure and/or artificial selection but quote the scripture "God made the beasts of the earth after their kind" to illustrate that one species can never turn into another. They say a dog will always be a dog no matter how much you breed it to have long hair or a squashed nose. The don't believe that new information or bio-mechanical function can arise from random mutations like gene repetition/deletion, copy errors, etc. They point out that creatures like dogs that are bred down certain paths have always lost information not gained. Now this group of Christians can either believe in an ancient universe or a 6-10k year one but all will state that life is about 6-10k years old. They also like to point out that that there as been no documented examples yet of NEW function arising from selection pressure.
#2 Everything happened according to science but God started/nurtured it
This is a belief held by many modern Christians. It combines predestination in varying degrees as a lens to view reality. The most 'hands-off' interpretation says that God stacked the deck a certain way (the weightings of various physical laws, vacuum energy etc) before he exploded the gigantic soup of particles and started off the universe down the track of star and then planet formation and eventually life. The other end of the predestination spectrum is that you and I were conceived of before the Word spoke the universe into existence. Every facet of chemical reactions, evolution, mutation was planned so as to produce you and everyone else so as to participate in eternity with our Creator.