gst input tax

No ITC on purchase of car is not allowed even if it is first hand

When you purchase anything, you are required to pay GST on it. Later, you can claim input tax credit on the GST paid on your purchases. This GST paid can be claimed as credit in the same way as inputs.

However, if you claim depreciation on the GST paid while purchasing the capital asset, you cannot claim input tax credit.

Also in case if you are using that car for personal use or for supply of exempt goods,then you can not claim ITC.

you must make sure that in case your car is covered under blocked credit u/s 17(5).
If it is the case then you can not claim ITC. However subject to some exceptions mentioned there.

yes if you can prove that it is used for transportation of goods........