In the sentence :
My brother Arvind plays tennis.
'My' is possessive pronoun or possessive adjective

its possessive pronoun

DEAR FRIEND,
MY IS A POSSESSIVE PRONOUN.
BECAUSE ADJECTIVES ARE DESCRIBING WORDS,BUT MY DOESN'T DESCRIBE ANY WORD THERE SO OBVIOUSLY IT'S NOT AN ADJECTIVE.
PRONOUN'S ARE USED INSTEAD OF NOUNS(NAMING WORDS)MY IS USED AS TOLD SO IT'S OF COURSE A PRONOUN

IT IS A POSSESSIVE PRONOUN BECAUSE:-
POSSESSIVE PRONOUNS ARE WORDS WHICH ARE DESCRIBES THAT'S A PERSON IS POSSESSING SOMETHING.
HERE THE WORD 'MY' IS POSSESSING THE WORD 'BROTHER'
SO IT'S POSSESSIVE PRONOUN.

ASK MORE!!!

'My' in the above sentence i.e. My brother Arvind plays Tennis is a possessive adjective because the word My came before a noun i.e. Brother.
If we need to know whether the pronouns are possessive pronouns or possessive adjectives then we should always remember that A noun never comes immediately after a possessive pronoun and in a possessive adjective it always comes before a noun.
For example :1. Possessive pronouns : That pen is yours.(Here the pronoun is not immediately followed by the noun.)
                      2. Possessive adjectives : That is my book. (Here the pronoun is coming before a noun.)                                                                                   HOPE IT HELPS!!!!!!!!!!!!!

( my ) is possessive adjective as it is placed before a noun and is also describing that the book is whose.
 

SORRY NIPUN FOR GIVING YOU THE WRONG ANSWER AND EXPLAINATION
 

it is a possessive adjective