Concept:
Mutation breeding is a plant breeding method in which mutations are artificially induced using physical or chemical mutagens. Gamma irradiation is one of the commonly used physical mutagens.
Step 1: Understand mutation breeding.
In mutation breeding, seeds or plant parts are exposed to mutagens such as:
\[
\text{Gamma rays}
\]
\[
\text{X-rays}
\]
\[
\text{Chemical mutagens}
\]
These mutagens create genetic changes, and useful mutants are selected for crop improvement.
Step 2: Identify the crop mentioned.
The crop mentioned in the question is:
\[
\text{Papaya}
\]
The question asks about a dwarf mutant of papaya having about \(1\) meter plant height.
Step 3: Identify the correct variety.
Pusa Nanha is a dwarf mutant variety of papaya. It was evolved through mutation breeding using gamma irradiation.
Step 4: Eliminate other options.
Pusa Majesty, Pusa Dwarf, and Arka Surya are not the correct answers for the dwarf mutant papaya developed through gamma irradiation.
\[
\therefore \text{Correct Answer is (A)}
\]