Although, I am not an Indian I can share my story. I am from Bangladesh. Since Bangladesh and India are neighbors we may share some common patterns.
The Education SystemIn Bangladesh the education system was point based. That means if a student get 100 in math and 50 in English, the average would be 75 points. 75% average means the student obtained "star points". But you can easily see the flaw in this.
This problem is now fixed. All our education system now has either a 5 point or 4 point GPA system, in which all subjects matter.
Moreover, until a student is in college his extra curricular activities don't count. So almost everyone are encouraged to do well in math, biology etc. But no focus is given to anything else. For this reason, the number of diversified Bangladeshi is a bit difficult to find.
The Cultural BiasSince Bangladesh is a very densely populated country, the competition in every aspect of life is very tough. Arguably, the competition to get into a primary school is tougher than the competition to get into an elite college in the US. So what people do to get their kids into a good school? They train their child for one to two years before the test exam.
Moreover, if you want to be successful in Bangladesh, both socially and economically, be an Engineer or a Doctor. If you are anything else, you are pretty much doomed.
The Abundance of Technical Institute and Future GoalI found that the policy maker in India has been trying to improve the Engineering core for long time now. Which is evident in number of
Engineering schools in India.
However, this point is just my speculation about Indian policy and does not apply to Bangladesh. Bangladesh realized this only recently and trying to increase the number of universities. But, it's already late.
There could be other reasons. Moreover, some of the reasons I mentioned about Bangladesh, may not apply to India. In any case, I think it will provide some help to understand why some of the countries are doing better than other. (I am not implying that Bangladesh is doing better than some other countries though.
)