The correct answer is option 'C' - After the 1967 elections.

Explanation:
Coalition politics refers to the formation of alliances or partnerships between multiple political parties in order to gain a majority and form a government. In India, coalition politics at the federal level began after the 1967 elections.

1. Background:
- After India's independence in 1947, the Indian National Congress (INC) dominated the political landscape and formed the government at the federal level.
- However, the political scenario started changing in the 1960s due to various factors such as regional aspirations, dissatisfaction with the Congress party's policies, and emergence of regional political parties.

2. 1967 Elections:
- The 1967 elections were a turning point in Indian politics as the Congress party witnessed a decline in its popularity and lost its majority in several states.
- This led to the emergence of regional parties that gained significant support and representation in the state legislatures.

3. Coalition Governments:
- The results of the 1967 elections led to the formation of coalition governments in some states, where regional parties formed alliances with each other or with national parties to govern.
- This marked the beginning of coalition politics at the state level.

4. Impact at the Federal Level:
- The success of regional parties in state elections gave them confidence and strength to contest the federal elections as well.
- After the 1967 elections, regional parties started playing a crucial role in national politics and became important players in the formation of governments at the federal level.

5. Formation of Janata Party:
- The 1977 elections witnessed the defeat of the Congress party and the formation of the Janata Party, an alliance of various non-Congress parties.
- This was a significant development in Indian politics as it marked the first non-Congress government at the federal level, formed through a coalition.

6. Conclusion:
- The beginning of coalition politics at the federal level in India can be traced back to the aftermath of the 1967 elections when regional parties gained prominence and started forming alliances to form governments.
- The trend of coalition governments continued to grow in subsequent years, leading to a shift from single-party dominance to a more diverse and multi-party political landscape in India.