Should these be placed in refrigerator: tomatoes, and banana?
You generally do not want to refrigerate tomatoes; they will will get mealy in texture, which can be unpleasant.

Bananas are more complicated.  Once you refrigerate them, ripening will stop, and it will not recommence when they are brought back to room temperature.  So you never want to refrigerate unripe bananas.

Ripe bananas can be refrigerated to make them last a few days longer, but the skins may darken, which some people find unacceptable.