Step 1: Context of the event
- In 1987, India signed the Indo-Sri Lanka Accord with Sri Lanka.
- Under this agreement, India agreed to deploy a peacekeeping force to help resolve the ethnic conflict between the Sri Lankan government and the Liberation Tigers of Tamil Eelam (LTTE).
Step 2: Indian Peace Keeping Force (IPKF)
- The force sent by India was known as the IPKF (Indian Peace Keeping Force).
- Its mission was to disarm militant groups, maintain peace, and support the political solution.
- However, the mission faced strong resistance from the LTTE, leading to prolonged conflict and casualties.
Step 3: Analyzing options
- Bhutan: India did not send a peacekeeping force here in 1987.
- Nepal: No such intervention occurred.
- Myanmar: Not related to Indian peacekeeping in 1987.
- Sri Lanka: Correct, India sent the IPKF here in 1987.
Step 4: Conclusion
Thus, the Indian Government sent its peacekeeping force to Sri Lanka in 1987.
\[
\boxed{\text{Correct Answer: (D) Sri Lanka}}
\]