Concept:
Living organisms are divided into prokaryotic and eukaryotic organisms based on cellular organization.
Prokaryotic organisms lack a true nucleus and membrane-bound organelles.
Eukaryotic organisms possess a true nucleus and organized membrane-bound cell structures.
To solve this question, we must identify which organism belongs to eukaryotes.
Step 1: Understand characteristics of prokaryotes.
Prokaryotes possess
No true nucleus
No membrane-bound organelles
Circular DNA
Simple cell organization
Examples include bacteria, cyanobacteria and mycoplasma.
Step 2: Check bacteria and blue green algae.
Bacteria are classical prokaryotic organisms.
Blue green algae are cyanobacteria.
Cyanobacteria also lack true nucleus.
Thus both are prokaryotes.
Step 3: Check mycoplasma.
Mycoplasma are smallest living cells.
They lack cell wall but are still prokaryotic organisms.
Hence they are prokaryotes.
Step 4: Check fungi.
Fungi possess
True nucleus
Membrane-bound organelles
Complex cell organization
Thus fungi are eukaryotic organisms.
Hence fungi are not prokaryotes.
Therefore answer is
\[
\boxed{\text{Option (1)}}
\]