Yes, You are allowed to Trade in either equity as well as mutual funds.
Because this is a Government regulated things as well as Government itself Promote to invest Indian Investor ( whether Govt employee, Pvt employee, House wives or unemployed) by giving Tax benefits by investing in specified Products.
In equity Investment it include high risk and high return by Investing in RGESS ( Rajiv Gandhi equity savings scheme) you can get Tax benefit upto 50,000
Similarily by Investing in mutual funds ( ELSS) schemes also you can get benefit for tax deduction.
It does not reduce your Tax payment from your Income as well as it will help in future savings as well as growth of your money.
Because by keeping money at your savings bank or Fixed deposit you get around 4-8% interest maximum, where as by investing in equity or mutual funds for long run you can earn 10-12% average some time it can give you 20-30% return also. But do not try to make a habit of regular trading because it will distract you from your official work.