JEE Main 2022 Mathematics question
Let A be a matrix of order , whose entries are from the set {0, 1, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is .
Answer: 180
Solution
The sum of the entries must be a prime p with 2 < p < 8, i.e. 3, 5 or 7. Counting ordered arrangements of four entries (with the entry set that includes 2, as in the
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