first things first, when buying a family car, one needs to check:
1. Original number plates and engine room plate (known as tikli) are present.
2. CPLC is clear, call and ask is the car clear? then ask whether the car has any history? was the car stolen at any point in time?
3. Return file is there are is complete, check it from start to finish for sales receipt, and check that each book is present or not including current book.
4. Check the amount of tax which is due, you dont want to buy a car which has 5 years of tax due on it.
after that comes the physical part, you can never know a car by checking it, taking a mechanic only unveils major issues but countless other issues can never be checked, they rise after a while only when you start using the car. but there are some major things to check, which may include:
1. the mileage, the lower the better. but in some cases it doesn't matter (like my 98 civic with 125,000 kms was much better than my 2005 civic with 90,000 kms)
2. color should be original (mechanic can never check this)
3. rev the engine upto at least 4000 rpm, if there are rattling sounds, it probably means the engine needs work. (mechanic can check this)
4. check the suspension, shock absorbers, brakes and tires (mechanic can check this)
5. check the AC, though real test of the AC will be when u take it out for a 30 minute drive in blunt sunlight. AC rectification can cost from a mere 3 thousand for over 20 thousand rupees.
6. check whether all electronics and stuff are working or not. if everything is working fine, the car was kept good, if it isn't, the car wasn't kept nicely, simple rule. ask the mechanic to check whether the radiator fans are running through thermostat or not, if they are direct, it tells a lot about how a car was kept.
dont hesitate to spend a little more if you find a reasonably maintained car. drive it, feel it, you'll understand for yourself. other than that, problems can arise in even brand new cars.