Let's identify the noble gases based on their uses described.
Noble gas 'X': Used as a diluent for oxygen in modern diving apparatus.
The air we breathe is mostly nitrogen. At high pressures experienced during deep-sea diving, nitrogen can dissolve in the blood. If a diver ascends too quickly, this dissolved nitrogen forms bubbles in the blood, causing a painful and dangerous condition called "the bends" or decompression sickness. To prevent this, a mixture of oxygen and helium is used. Helium is used because of its very low solubility in blood, even at high pressures.
So, 'X' is Helium (He).
Noble gas 'Y': Used to provide an inert atmosphere in high-temperature metallurgical processes.
Many metallurgical processes, like arc welding of metals, require an inert atmosphere to prevent the hot metal from reacting with oxygen or nitrogen from the air. Argon is commonly used for this purpose because it is chemically inert and is the most abundant and cheapest noble gas to produce (it makes up about 1% of the atmosphere).
So, 'Y' is Argon (Ar).
The question asks for 'Y' and 'X' respectively.
'Y' is Argon (Ar).
'X' is Helium (He).
Therefore, the correct pair is (Ar, He).