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Fill in each blank with an appropriate word:
He drew a beautiful diagram ____ the board.

Answer
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Hint: Try to verbally say the sentence out loud which will help you find the right answer. The placement of these places should also help you to find the right answer.

Complete answer:
 A preposition is a word governing, and usually preceding, a noun or pronoun and expressing a relation to another word or element in the clause.
For example, in the sentence ‘The cat is under the table’, the preposition ‘under’ tells us the exact location of the noun ‘the cat’.
Prepositions are words that are used to show positions, locations, direction, and time. They are usually in front of nouns and gerunds. Example - In the sentence ‘There is a lamp on the table’, the word ‘on’ describes the location of the lamp. So, it is a preposition. There are many verb + preposition combinations in English, which are easy to learn, like ‘go up’. Prepositions indicate relationships between other words in a sentence. They can be extremely important parts of a sentence, as they can give you important insight into the meaning of the sentence.
For example, in the sentence ‘We saw a movie at the theatre’, we understand where the movie was seen. It clearly conveys that the movie was not seen at any other location. This is an example of a preposition of location. There are many more kinds of prepositions.
Depending on which preposition is used after a verb, the meaning of the sentence can completely change. The preposition used makes a big difference. For example, ‘turn back’ and ‘turn off’ have two completely different meanings, even though the root verb is the same.

In the given sentence, we need the phrase to mean ‘the diagram existed on the surface of the board’. The word ‘on’ refers to ‘forming a distinctive or marked part of the surface of’.
So, the required preposition is ‘on’. The correct way to write the given sentence is in the following way-
He drew a beautiful diagram on the board.

Note:
Try to understand the meaning of the given sentence completely, and go through the given options one by one. It will help you to choose the required option accordingly.