Option 1 states that there has been a rise in the cost inflation index over the year 2012-13. This statement is correct. The cost inflation index is updated every year by the CBDT, and it reflects the changes in inflation over time. As inflation increases, the cost inflation index also rises.

Option 2 states that the cost inflation index helps in reducing the inflationary gains, thereby reducing the long-term capital gains tax payout for a taxpayer. This statement is also correct. The cost inflation index is used to adjust the purchase price of an asset for inflation when calculating long-term capital gains. By adjusting for inflation, the taxable amount of capital gains reduces, resulting in a lower tax liability for the taxpayer.

Therefore, both statements are correct. The cost inflation index has indeed risen over the year 2012-13, and it helps in reducing the inflationary gains and lowering the long-term capital gains tax payout for a taxpayer.