Yes..that is acceptable.. to support further, you can show an affidavit on a stamp paper signed by your mother (no need to notorize this) stating she is giving you this money out of her own past savings..
sample affidavit format below (plz arrange properly in word file)
do note that any large transaction in your account within last six months..needs to be properly supported..if you have big salary..then salary slips..likewise..
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Sample Affidavit Format
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I, XXXX<mother's name>, s/o YYYYY, r/o <your complete address> do hereby state as under:
1. That I have gifted a sum of Rs. XXXXXX (Rupees XXXXXX Only) through cheque no ABCDEF dated YY/BB/2017 drawn on <bank name & address> to my brother/son <name>, r/o <address>.
2. That I have gifted the said amount out of my past savings.
3. That I am a regular Income Tax Assessee and my Income Tax Pan is <XXXXXX>.
I, <mother's name>, do hereby verify and confirm that contents of my above deposition are true and correct and nothing material has been concealed therefrom.
Place: <>
Dated: <>