Puzzle - Help the captain

In the year 2050 Captain Morgan and his crew are stuck midway development/testing for the next huge OSv5.1 release for their spaceship Jatayu.

The problem they are stuck at is:

To verify correctness of the results returned from a black box calculator
Procedure the crew follows:

1. Answer close to 40 questions [Please note: The questionnaire can have drop down menus, radio buttons, and relationships within questions (some questions will be displayed if a specific question is answered)]
The captain of the ship has signed an NDA and cannot share the questions
2. The answers are fed into a Black Box (Calculator)
3. The results are displayed on the screen

Assistance offered:
Black illusionists have agreed to verify if the values fed into their Black Box are correct or not. But they will check only 25 combinations (we supply inputs to each question and the actual results). They will annihilate us if we exceed the magic figure of 25.

Strategies suggested by Problem Squealers in the crew team:

1. Pick 25 random values returned by answering the questions to the Black illusionists and verify the results.
2. Discuss with the merchants and prioritize the most common 25 scenarios with realistic answers to the questions, and then have them verified by the Black illusionists.
3. Invest time to mechanize all possible combinations. Run the automation suite. Choose 25 weird values and get them verified by the Black illusionists.
4. Broadcast the risks to the Kingdom and follow idea 2.

Captain Morgan, though happy, is not assured with ideas from his crew. He now invites citizens of Planet Earth for help.

Can you help Captain Morgan?

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