1) Every student was selected for their/his placement training in the college.
2) Each girl was given a bunch of flowers which pleased her/them very much.
Could anyone clear my doubt which pronoun to be used here.
In both of your examples, according to technical English, the singular form should be used; however, in spoken English, either way is considered to be acceptable. In fact, using their/them may be more common than using the singular forms.