In India, stamp duties on financial transactions are neither levied and collected by the state government, nor are they appropriated by the Union government.

Option 1 suggests that stamp duties on financial transactions are levied and collected by the State government. This is incorrect because it is actually the responsibility of the Stock exchange to collect the stamp duties and remit the collected amount to the respective state governments.

Option 2 states that stamp duties on financial transactions are appropriated by the Union government. Even this is not true, as the revenue from stamp duties is not directly appropriated by the Union. They are actually distributed between the Union and the State governments.

Therefore, neither option 1 nor 2 is correct. This makes option 4 - `Neither 1 nor 2` the correct choice.