This question requires matching chemical elements and compounds from List-I with their respective applications presented in List-II. Let's analyze each pair based on the provided correct matches:

Matching Magnesium Alloy Uses

(A) Magnesium based alloy with (I) Bullets

Magnesium-based alloys are lightweight and strong metals. While not the traditional material for standard bullets (which typically use lead and copper), specific alloys or magnesium compounds might be incorporated into specialized projectiles, such as incendiary ammunition, due to magnesium's flammability. Following the provided matching, we consider this connection.

Matching Lanthanoid Oxide Uses

(B) Lanthanoid oxide with (III) Television screen

Certain lanthanoid oxides, particularly europium oxide (Eu$_2$O$_3$) and terbium oxide (Tb$_2$O$_3$), are utilized as phosphors. These phosphors emit light when struck by electrons, playing a crucial role in the display technology of television screens (especially older cathode ray tube models) and other electronic displays to produce specific colors.

Matching Mixed Lanthanoid Oxides Uses

(C) Mixed oxides of Lanthanoids with (II) Petroleum cracking

Mixed oxides containing lanthanoids, especially cerium oxide (CeO$_2$), are widely employed as catalysts in the petroleum industry. They are essential components in the fluid catalytic cracking (FCC) process, which breaks down heavy crude oil fractions into more useful lighter products like gasoline.

Matching Misch Metal Uses

(D) Misch metal with (IV) Lanthanoid metal and iron

Misch metal is a specific type of alloy composed primarily of rare-earth elements, which are also known as lanthanoids. It typically contains around 50% cerium, along with lanthanum, neodymium, and other lanthanoids. It is commonly alloyed with iron (Fe) to produce pyrophoric materials used in lighter flints. Therefore, it represents a combination of 'Lanthanoid metal and iron'.

Summary of Correct Matches

Based on the analysis aligning with the provided correct answer:

• (A) Magnesium based alloy corresponds to (I) Bullets.
• (B) Lanthanoid oxide corresponds to (III) Television screen.
• (C) Mixed oxides of Lanthanoids correspond to (II) Petroleum cracking.
• (D) Misch metal corresponds to (IV) Lanthanoid metal and iron.

This confirms the matching set is (A)-(I), (B)-(III), (C)-(II), (D)-(IV).