First, let's understand what PMJDY and LIC are:

- PMJDY: Pradhan Mantri Jan Dhan Yojana (PMJDY) is a financial inclusion program launched by the Indian government in 2014. Its aim is to provide access to banking facilities to all households in the country, especially those from low-income groups.
- LIC: Life Insurance Corporation of India (LIC) is a state-owned insurance company in India. It offers various insurance products, including life insurance, to individuals.

Now, let's break down the question and the given options:

Question: PMJDY LIC Insurance of Rs.30,000/- is available for first-time accounts opened.
Options:
a) On 15th August 2014
b) On 26th January 2015
c) Between 15th August 2014 and 26th January 2015
d) None of the above

To find the correct answer, we need to determine the time period during which the PMJDY LIC Insurance of Rs.30,000/- is available for first-time accounts opened.

- Option a) On 15th August 2014: This option suggests that the insurance is available only for accounts opened on 15th August 2014. However, it may not consider accounts opened after this date.
- Option b) On 26th January 2015: This option suggests that the insurance is available only for accounts opened on 26th January 2015. Again, it may not consider accounts opened before this date.
- Option c) Between 15th August 2014 and 26th January 2015: This option suggests that the insurance is available for accounts opened between 15th August 2014 and 26th January 2015. This means that accounts opened on any date within this time period are eligible for the insurance.
- Option d) None of the above: This option suggests that the insurance is not available for any accounts opened within the given time period.

Based on the above analysis, the correct answer is option c) Between 15th August 2014 and 26th January 2015. This means that accounts opened between these two dates are eligible for the PMJDY LIC Insurance of Rs.30,000/-.