Cryogenic engines find applications in
A. Rocket-technology
B. Frost-free refrigerators
C. Submarine propulsion
D. Researches in superconductivity

Hint: Cryogenics is the study of the properties and characteristics of substances at very low temperatures. Cryogenic engines are engines in which the fuel used is gases that are compressed and liquefied at very low temperatures.

Complete step by step answer:
As explained in the hint, cryogenics is the study of the behavior, properties, material characteristics and the production of different substances at very low temperatures (close to and below $\left( -{{150}^{0}}C \right)$).
Cryogenics find their applications in making rocket engines. In such cryogenic rocket engines, gases are liquefied and compressed by putting them under pressure and cooling to very low temperatures. Therefore, the fuel takes up a much lesser space and becomes easier to store and handle and also reduces losses that may occur due to inefficient burning of the fuel and leakage.
Cryogenic rocket engines have been in use since decades and the most notable use was in their introduction by NASA to be used in rockets that first reached the moon.
Hence, cryogenic engines find their applications in rocket technology.
Hence, the correct answer is A) rocket technology.

Note:
Students might think that cryogenic engines are involved in research in superconductivity. However, the superconductivity phenomenon of diamagnetic materials is observed at much lower temperatures close to and below $-{{250}^{0}}C$. However, cryogenic engines are not designed to operate at such low temperatures. So, students should not get confused with these two concepts.