Concept:
Kingdom Monera includes all prokaryotic organisms. Bacteria exhibit remarkable diversity in nutrition and habitat.
They may be:
• Autotrophic
• Heterotrophic
• Photosynthetic
• Chemosynthetic
Therefore, not all bacteria have the same nutritional mode.
Step 1: Examine Option (A)
Many bacteria are heterotrophic, but several bacteria are autotrophic.
Examples:
• Cyanobacteria are photosynthetic autotrophs.
• Nitrifying bacteria are chemosynthetic autotrophs.
Hence, the statement that all bacteria are heterotrophs is false.
Step 2: Examine Option (B)
Cyanobacteria contain chlorophyll and perform photosynthesis.
Thus, this statement is true.
Step 3: Examine Option (C)
Anabaena is a filamentous cyanobacterium capable of nitrogen fixation.
Thus, this statement is true.
Step 4: Examine Option (D)
Methanogens are archaebacteria that inhabit anaerobic and extreme environments such as marshes and the rumen of cattle.
Hence, this statement is true.
\[
\boxed{\text{(A) All bacteria are heterotrophs}}
\]