As per CCS (Conduct) Rules, 1964 or AIS (Conduct) Rules, a Central Government employee (including teachers) can very well invest (buy and sell) in equities and in mutual funds. However, regular intra-day trading of huge amount is generally discouraged (but not banned).
All the State Governments Rules are more or less the same. So, an employee of State Government (of Kerala/Karnataka) can also invest in shares/equities and in mutual funds. Kerala/Karnataka Civil Services (KCSR) Rules would also be similar as indicated above.
Come on, have a fight. Don't shoot and scoot.