How is the Professional Tax which I pay is used?

But there is another kind of tax that the state government charge is Professional Tax. How is this Professional Tax used?

The simple answer is to fund the activities of the state - money is fungible, so whatever money the state takes in with taxes it uses to pay for the things the state does - the source of the tax isn't relevant.

The slightly more complicated answer is that it depends on the state. Some states will specify that all taxes from some source (professional taxes, sales taxes, revenue from state-run lotteries, etc...) must only be spent on some program or another. Sometimes it even works out like that.

However given the nature of money, even when money raised by a specific tax is slated to be used only to pay for a certain program, that itself can change the way other money is allocated.

Take for instance the Florida State Lottery. The state told the voters that all the profits from the lottery would go into the state public education system, and the voters approved the change to the law allowing a lottery. And yes, it did put money into the state public education system. But the state then reduced funding for state public education from other sources, i.e., property tax and sales tax. [source]

In this case, no matter what the state says, the simple answer is probably the best: to fund the activities of the state.