What are the investment opportunities in mutual funds to earn a monthly income of INR 40 K by one-time investing INR 20 lacs?

Your asking rate is too high! INR 40k a month is 4,80,000 a year which is 24% of your invested amount.

You can try two approaches:

1. Increase your investment amount so that a good dividend rate can provide you with cash flows.
2. You haven’t mentioned your time horizon (i.e. when the income is needed). Keep your base of Rs 20 lakhs invested for the long term (above 7 years) so that it compounds well. You can then start withdrawing from it to meet your income needs.