The probability that a randomly chosen 2 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

JEE Main 2022 Mathematics question

The probability that a randomly chosen matrix with all the entries from the set of first 10 primes, is singular, is equal to :

(1)
(2)
(3)Correct
(4)

Answer: (3)

Solution

The matrix is singular when ad = bc. Since the entries are primes, unique factorisation gives {a, d} = {b, c} as multisets. Case I: all four entries equal, in 10 ways. Case II: exactly two distinct primes p and q are used, in one of the four patterns $ p &

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Question ID VK-035316