Should I invest in buying home in Bangalore ?

I probably think you should consult a financial advisor. There's lot of personal financial advisory offering 1st financial plan for free. Like this one : https://1finance.co.in/request-a-callback

Returns that you will make in the form of rental yield will be less than 7% to 8% if we add the interest component of the EMI in the cost of Real estate that it will lesser than that.

There are a few types of mutual funds wherein with that Corpus you may earn at least 1L per month plus your corpus will grow at 12% if invested for more than 6 years.

When the amount is big always consult an advisor.

Try Pune because it’s a growing market for tech and GCC companies
I know a real estate advisor - 7887800557