To determine which Indian communication satellite, launched in the early 1980s, became the first fully operational satellite of the INSAT series and significantly strengthened India's telecommunication and broadcasting services, let's examine the options provided:

1. INSAT-1A - 10th April, 1982: INSAT-1A was the first satellite in the Indian National Satellite System (INSAT) series. However, it encountered a series of technical failures and was decommissioned earlier than expected.
2. INSAT-1B - 30th August, 1983: This satellite successfully became the first fully operational satellite of the INSAT series. It played a crucial role in enhancing India's telecommunication and broadcasting capabilities, marking a significant milestone in India's space and communication endeavors.
3. IRS-1A - 17th March, 1988: IRS-1A, or Indian Remote Sensing satellite, was launched to aid in resource monitoring and management. It is unrelated to telecommunication or broadcasting services.
4. APPLE - 19th June, 1981: APPLE (Ariane Passenger Payload Experiment) was India’s first three-axis stabilized geostationary experimental communication satellite. While it was pivotal for India's space research, it was not part of the operational INSAT series.

From the above, only INSAT-1B fits the description of significantly bolstering India's telecommunication and broadcasting sector as the first fully operational satellite in the INSAT series.

Therefore, the correct answer is:

INSAT-1B - 30th August, 1983

In conclusion, INSAT-1B's successful launch and operational capabilities were instrumental in developing India's communication infrastructure in the 1980s, paving the way for future advancements in the sector.