Solution:

Given, the probability of getting qualified in IIT-JEE = 1/5
And, the probability of getting qualified in AIEEE = 3/5

We need to find the probability that the student gets qualified for at least one of the two tests.

Method 1: Using Complementary Probability

The probability that the student does not get qualified in both the tests can be found using the multiplication rule of probability:
P(not getting qualified in IIT-JEE and AIEEE) = P(not getting qualified in IIT-JEE) × P(not getting qualified in AIEEE)
= (4/5) × (2/5)
= 8/25

Therefore, the probability that the student gets qualified for at least one of the two tests is:
P(getting qualified in at least one test) = 1 - P(not getting qualified in both tests)
= 1 - 8/25
= 17/25

Method 2: Using the Addition Rule of Probability

The probability that the student gets qualified in either IIT-JEE or AIEEE or both can be found using the addition rule of probability:
P(getting qualified in IIT-JEE or AIEEE or both) = P(getting qualified in IIT-JEE) + P(getting qualified in AIEEE) - P(getting qualified in both)
= (1/5) + (3/5) - [(1/5) × (3/5)]
= 4/5

Therefore, the probability that the student gets qualified for at least one of the two tests is:
P(getting qualified in at least one test) = 4/5

Conclusion:

Hence, the probability that the student gets qualified for at least one of the two tests is either 17/25 or 4/5 depending on the method used.

P(atleast 1)
= 1 - P(none)
= 1 - [P( not JEE) × P( not AIEEE)]
= 1 - (4/5 × 2/5)
= 1 - 8/25
= 17/25