An antipode or contrary is contrary in meaning to another word. Example- Superior is an antipode of inferior. 
The word ‘ base ’ has been deduced from the Medieval Latin word- Bassus, which means short. 
We know the meaning of the word ‘ base ’. Now, let’s look at its operation 
illustration- My neighbor is considered to be immoral and baser as she works late at night. Then, we can understand that X’s neighbor ‘ Y ’ is considered to be dishonorable or ignoble because she works late at night. 
Let’s Explains the meaning of the given options- 
Option a- ‘ Noble ’ refers to a person who's honorable and holds great moral values and principles. illustration- The lords attended our ball last night. ‘ Noble ’ is the contrary in meaning to base. Hence, it's the correct option. 
Option b- ‘ Happy ’ refers to the quality of being cheerful or pleased by commodity or someone. illustration- She was really happy to see me. ‘ Happy ’ has different in its meaning to base. Hence, it's an Wrong option for the question given. 
Option c- ‘ valorous ’ refers to the quality of being bold and stalwart. illustration- The valorous knight saved the townies. ‘ valorous ’ is different in meaning to base. Hence, it's an incorrect option. 
Option d- ‘ Precisely ’ refers to perform an action cautiously to avoid any detriment. illustration- I precisely hulled the chili. ‘ Precisely ’ is different in meaning to base. Hence, it's an incorrect option. 
The correct answer is Option ‘ a ’.