Whether to study abroad for your bachelors or masters depends on your finances, goals, and readiness, and for many Indian students, doing the masters abroad is the more practical choice.
Studying a masters abroad is often the more popular and cost-effective route. You complete a cheaper bachelors in India, then go abroad for a focused one to two year masters, which costs less overall and comes when you are more mature and clear about your direction.
Studying the bachelors abroad gives a longer international experience and can lead to stronger settlement options in some countries, but it is far more expensive and a bigger commitment at a younger age.
Think about cost, since a full bachelors abroad is a large expense, your career goals, and whether you are ready to live independently abroad for several years right after Class 12.
There is no single right answer, only the one that fits your situation, budget, and plans.
Example: A student did an affordable bachelors in India, then a focused masters abroad, which gave her international exposure and better job prospects at a fraction of the cost of a full degree abroad.
One practical tip: For most students, a bachelors in India followed by a masters abroad gives the best balance of cost and opportunity, unless you have a strong reason and the funds for the full bachelors abroad.