Warming of Hyundai Verna Engine

"...after this duration I saw some vapours are coming from engine .I switched off engine. What could be happened."

Can you account for your pet cat? If you don't have a cat, can you account for the pet cat belonging (maybe should be 'that belonged') to your neighbor?

"some vapours" is not a very good description of the condition.

Can you duplicate the vapours and take a picture for us.

If your vehicle battery is running down in only two or three weeks of sitting then I suspect you have an electrical problem. It could be as simple as your battery is tired and needs to be replaced, to a myriad of other possible drains on the battery.

You might investigate the possibility of a solar panel car charger. The first iterations of these devices were horrible. They would not sense battery voltage or anything to do a proper charge. Some ironically overcharged a battery, which reduced the lifetime of the battery instead of extending it.

As for your vapors, I suspect that this is condensation (dew) on the outside of your exhaust manifold that is steaming off. You might also have a small coolant leak. If a coolant leak is not corrected, you could loose the engine.

I recommend you finding somebody (mechanic, handy friend) to look at your vehicle instead of asking a group of distant strangers that cannot see the vehicle.

I'm no expert, but -

Unless you live in a climate that is extremely hot or extremely cold, your battery should be fine sitting for a few weeks at a time without being charged. Instead of sitting with the engine revved at 2000 rpm, drive the car for 5 or ten minutes to keep the battery charged, oil flowing, the transmission turning, the air conditioner running, and the tires rolling.

You don't describe these vapors, but any condensation on the engine, road film, spilled oil, and so forth, can create vapors. When you are driving your car you don't see these vapors as they are blown off by the air moving over the engine.

You don't say if it's diesel or petrol, if the smoke is white or black, how many miles on the engine and age....It could be any number of problems, or no problem at all....some vapors could be quite ordinary, but excessive smoke probably signals a problem...Is there an odor associated with the vapors? Does the vapor(smoke) linger in the air? or evaporate? Is the car using oil at an increasing rate? Has gas mileage changed? Is there a rat's nest in the air filter? Put a white tissue over the tail pipe to see if there is any residue from the smoke, or any odor....What is the temperature outside? Is the engine overheating, is the reservoir full?,, How many miles do you drive it a month?

There are lots of countries in which cars use to have alarms and / or tracking systems. If this is the case, there you have the cause of your problem. There are a lot of battery tenders (some are meant to be fixed under the hood) that will solve your problem: every time you leave for some days, just plug it in....

Is it not starting when you come back after 2 weeks? It should.

If not, charge it before you leave, then disconnect the black lead. Reconnect when you get back.

If it starts, you have a current leakage in the circuit somewhere. If not, battery may be on the way out.

But if thats the only problem you get, just charge it when you get home - save the money, take Verna out to dinner.

Every time you use your method of charging your depleted battery, you overload the alternator and its voltage regulator. Before long, the alternator will manifest problems; not least of which is its failure to charge your battery as the car runs. Buy or borrow a charger and consider the good answers posted as well.