Check the question's exact requirements one by one: the mission must be an ISRO mission, it must be the first of its kind, and it must study X-ray, optical and UV sources together.
Since only one option clears every requirement, the correct option is Astrosat.
Another way to work through this is by sorting the four names into the category of space activity they belong to, since the question is really pointing at one specific category, multi-wavelength astronomy.
Since the question is about a multi-band astronomy observatory, and only one of the four names falls into that category, the correct answer is Astrosat.
Check each site against the one fact the question hinges on: was it capable of launching a satellite into orbit in 1981?
The correct option is Kourou, French Guiana.
Split the four choices into two groups, Indian sites and foreign sites, and see which group actually matches the story behind APPLE's launch.
APPLE was launched in 1981, before India had its own orbital rocket, so ISRO had to rely on a foreign launch provider. That places the answer in the "foreign site" group, which has only one member.
The correct answer is Kourou, French Guiana.
The question needs a probe that was "successfully sent" to another planet, so check whether each one actually got there.
The correct option is Mariner 10.
Group these four spacecraft by outcome rather than by name, since the question is really testing which one succeeded.
Three of the four names belong to missions that never left Earth orbit or never flew, leaving one clear survivor.
The correct answer is Mariner 10.
The question specifies two facts, the year 1974 and that this was a test rather than a missile. Check each option against both.
The correct option is Smiling Buddha.
Sort the four names into two buckets, missile programmes and nuclear tests, and then narrow down by year.
Removing the missile bucket leaves two nuclear tests, and only the 1974 one matches the year given in the question.
The correct answer is Smiling Buddha.
NaviC was designed as a regional system, so first rule out any figure that suggests global reach, then match the exact design number.
The correct option is 1,500 km.
Line the four numbers up and sort them by whether they overshoot or undershoot NaviC's actual design radius.
Only one figure lines up exactly with the real specification instead of over or under it.
The correct answer is 1,500 km.