What will be tax implications if a stock is bought in Dec'14 and sold in April'15? Will the investor need to pay short term capital gains tax?

There are two ways to do this

1. Pay the tax based on the closing price of stock as on March 31st 2015. So this closing price acts as a reference when filing your returns for 2015/16. So if you bought a stock at Rs 100 in dec, it was Rs 130 on March 31st, pay taxes on this Rs 30. 

Next year if you sold the stock at 150, declare the remaining Rs 20 as profits (starting point is 130). Next year if you sold at 120, declare the Rs 10 as loss. This loss can be adjusted with any other short term gain you make. If you haven't made any gain, you can carry forward the loss. 

So if you are following this way of filing, you need to pay your STCG for 2014/15

2. The other way is to declare only the exited trades. Since you sold in April 2015, declare the entire STCG when you file your returns for 2015/16. 

Do consult a CA, you can also check this post on all taxation queries: http://zerodha.com/z-connect/traders-zone/taxation-for-traders/taxation-simplified