Which is a common use? Which is grammatically right?
There is a river and a pond near my house.
There are a river and a pond near my house.
"There is" is much more common than "There are" in your sentences. The latter might be awkward to many native speakers. When you're making a list of things in a sentence including "there is/are", look at the noun that directly follows "There is/are".
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"There is" is much more common than "There are" in your sentences. The latter might be awkward to many native speakers. When you're making a list of things in a sentence including "there is/are", look at the noun that directly follows "There is/are". If the first noun or thing is singular, use "There is", but if it is plural, use "There are". In your sentences the singular form "there is" is m
When the verb is followed by a noun phrase coordination and the coordinate that is adjacent to the verb is singular, plural agreement tends to be unidiomatic, even though the coordination as a whole is plural. For this reason, many speakers prefer to use a singular verb.
Plural agreement, however, occurs readily in lists, for example: There are still Brown, Jones, Mason and Smi