Carnet de Passages en Douane is still required in 71 countries, which are parties to the Customs Convention on ATA Carnet. It is an internationally recognized Customs document entitling the holder to TEMPORARILY import a vehicle duty-free into countries, which normally require a deposit against import charges for such vehicles.
It is basically a promise, that you'll take your vehicle out of the country (you're visiting), when you leave.
Who can provide Carnet de Passage in India
The carnet, is not issued by a Government department in India (or elsewhere), rather by the Automobile Association of the country (or its affiliate and authorized member associations), which is an affiliated member of Alliance Internationale de Tourisme
The Federation of Automobile Associations of India is an affiliated member of the International federation and has the authority to provide Carnet de Passage through its member bodies, which cover different regions in India. You can approach any of these, based on where you stay in India:
You can also get a Carnet through FICCI in India, though the applicants through FICCI cover a wider range of categories, and you might be asked to contact an Automobile Association for your case, since their primary audience is business people.
You cannot get a Carnet from a Government department. More than that, the amount you have been asked for (INR 10000), is what any authorized agency in India will ask for. The fee structure for Carnet can be verified from this link. The fee you have to pay, depends on the value of your vehicle (or goods, you're trying to carry).
I will advise you to get a Carnet, before you start your travel, to avoid any hassles at the border customs office, especially knowing that Pakistan is not that friendly with India, as compared to Nepal and Bhutan, and so rules will be strictly followed and adhered to (along with checking all required documents).