The rate of decomposition is slower if :

The correct answer is Option (4) → The detritus is rich in lignin and chitin

Option (1) Availability of large amount of oxygen — Incorrect. Decomposition is largely an oxygen-requiring process, so plenty of oxygen speeds it up.

Option (2) Warm and moist environment — Incorrect. Warm and moist conditions favour decomposition; cold and dryness slow it.

Option (3) The detritus is rich in nitrogen and sugars — Incorrect. NCERT says detritus rich in nitrogen and water-soluble substances like sugars is broken down quickly. So this makes decomposition faster, not slower.

Option (4) The detritus is rich in lignin and chitin — Correct. Lignin (in wood) and chitin are tough and hard for decomposers to break down.

NCERT Extract:
Decomposition – “… Decomposition is largely an oxygen-requiring process. The rate of decomposition is controlled by chemical composition of detritus and climatic factors. In a particular climatic condition, decomposition rate is slower if detritus is rich in lignin and chitin, and quicker, if detritus is rich in nitrogen and water-soluble substances like sugars.”