your mother cannot  open a demat account and do trading 

2) “No Government servant shall make, or permit any member of his family or any person acting on his behalf to make any investment which is likely to embarrass or influence him in the discharge of his official duties.”

3) As per the provisions of sub-rule (1) of Rule 16 of Central Civil Service (Conduct) Rules, 1964, Government Servants are not allowed to engage in speculation of any stocks, shares or other investments. As per Explanation to sub-rule (1), frequent purchase or sale or both, of shares, securities or other investments shall be deemed to be speculation. Further, 1st proviso to this sub-rule explicitly states that government servants can occasionally make investments through stock brokers or other persons duly authorised and licensed or who have obtained a certificate of registration under the relevant law,”

4) Any violation of the said service conduct rule would attract penalties – varying from withholding increment to termination from service depending on the gravity of the misconduct

There is no legal hindrance to trade in the name of mother. Mother is distinct entity from son, she is not bound by service rules governing son.  

you can make investments in shares through IPO or open market purchases 

Yes you can do it on your mother name 

.- As per Central Civil Services conduct rules, A government employee can invest in trading/shares, debentures and mutual funds, but cannot speculate in any form. 

- There is no limit on investing in mutual fund , but as per rule , all government employees need to send an intimation if total transactions in shares, securities, debentures, mutual funds scheme exceeds six months' basic pay during the calendar year.

- However , you can do trading in the name of family members . 

You can very well do the share market intraday transactions on your mother's name, there is no restriction on that.

The trading and the demat account has to be on your mother's name.

Yes you can proceed with the proposed investment on your mother's name.