As you want here I am giving below IRDA Approved General Insurance Companies list on your demand :

List of Non-Life Insurance Companies in India
1. Agriculture Insurance Co. of India Ltd.
2. Apollo Munich Health Insurance Co. Ltd.
3. Bajaj Allianz General Insurance Co. Ltd.
4. Bharti Axa General Insurance Co. Ltd.
5. Cholamandalam MS General Insurance Co. Ltd.
6. Cigna TTK Health Insurance Co. Ltd.
7. Export Credit Guarantee Corporation of India Ltd.
8. Future Generali India Insurance Co. Ltd.
9. HDFC ERGO General Insurance Co. Ltd.
10. ICICI Lombard General Insurance Co. Ltd.
11. IFFCO Tokio General Insurance Co. Ltd.
12. L&T General Insurance Co. Ltd.
13. Liberty Videocon General Insurance Co. Ltd.
14. Magma HDI General Insurance Co. Ltd.
15. Max Bupa Health Insurance Co. Ltd.
16. National Insurance Co. Ltd.
17. The New India Assurance Co. Ltd.
18. The Oriental Insurance Co. Ltd.
19. Raheja QBE General Insurance Co. Ltd.
20. Reliance General Insurance Co. Ltd.
21. Religare Health Insurance Co. Ltd.
22. Royal Sundaram Alliance Insurance Co. Ltd.
23. SBI General Insurance Co. Ltd.
24. Shriram General Insurance Co. Ltd.
25. Star Health and Allied Insurance Co. Ltd.
26. Tata AIG General Insurance Co. Ltd.
27. United India Insurance Co. Ltd.
28. Universal Sompo General Insurance Co. Ltd.
29. Kotak Mahindra General Insurance Co. Ltd.
30. Aditya Birla Health Insurance Co. Ltd.

List of Life Insurance Companies in India
1. Aegon Life Insurance Co. Ltd.
2. Aviva Life Insurance Co. India Ltd.
3. Bajaj Allianz Life Insurance Co. Ltd.
4. Bharti AXA Life Insurance Co. Ltd.
5. Birla Sun Life Insurance Co. Ltd.
6. Canara HSBC Oriental Bank of Commerce Life Insurance Co. Ltd.
7. DHFL Pramerica Life Insurance Co. Ltd.
8.
Edelweiss Tokio Life Insurance Co. Ltd
9. Exide Life Insurance Co. Ltd.
10. Future Generali India Life Insurance Co. Ltd.
11. HDFC Standard Life Insurance Co. Ltd.
12. ICICI Prudential Life Insurance Co. Ltd.
13. IDBI Federal Life Insurance Co. Ltd.
14.
IndiaFirst Life Insurance Co. Ltd
15. Kotak Mahindra Old Mutual Life Insurance Ltd.
16. Life Insurance Corporation of India
17. Max Life Insurance Co. Ltd.
18. PNB MetLife India Insurance Co. Ltd.
19. Reliance Life Insurance Co. Ltd.
20. Sahara India Life Insurance Co. Ltd.
21. SBI Life Insurance Co. Ltd.
22. Shriram Life Insurance Co. Ltd.
23 Star Union Dai-Ichi Life Insurance Co. Ltd.
24. Tata AIA Life Insurance Co. Ltd.