There are no Zero Risk mutual funds.
You want two things. Safety and the best returns in one package. Not possible.
Firstly, there are no funds that can be termed safest when investing in mutual funds. The risks can be high or low, but mutual funds without risk do not exist. You should understand this at the onset.
Risk is often misunderstood as well. For instance, "safe" investments such as bank deposits also carry the risk of a bank going under. Morever, there is the risk in terms of interest rates.
Equity funds have the potential to give you the highest returns, when compared to other mutual funds, over a long-term. However, they carry the maximum amount of risk as they invest in stocks. On the other hand, liquid funds are the safest amongst all mutual funds, but they invest in securities that mature within a day to three months and, therefore, yield very modest returns. Within equity funds, pure large-cap offerings are safer than funds which invest in mid- and small-cap stocks. Based on your risk appetite and the time frame of your investments, make your selection.
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Also, know how to buy mutual funds online:
Invest in DSP BlackRock Mutual Funds Online
Invest in Reliance Mutual Funds Online
Invest in HDFC Mutual Funds Online
Invest in Sundaram Mutual Funds Online
Invest in Birla Sunlife Mutual Funds Online
Invest in UTI Mutual Funds Online
Invest in SBI Mutual Funds Online
Invest in Edelweiss Mutual Funds Online
Invest in IDFC Mutual Funds Online