JEE Main 2026 — Permutation Combination Question with Solution
JEE Main 2026 (21 January Shift 1)
Question
Let . If the number of elements in S such that is a multiple of 5 is and the number of elements () in such that is a square of a prime number is q, then is equal to .
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Show full solutionCorrect answer: 1333
Correct answer
1333
Step-by-step explanation
For :
and
So
This equals 0 only when n is odd.
Number of odd n in {1,...,50} = 25, and m can be any of 50 values.
For = square of prime, possible values are 4, 9, 25, 49.
: 3 pairs
: 8 pairs
: 24 pairs
: 48 pairs
and
So
This equals 0 only when n is odd.
Number of odd n in {1,...,50} = 25, and m can be any of 50 values.
For = square of prime, possible values are 4, 9, 25, 49.
: 3 pairs
: 8 pairs
: 24 pairs
: 48 pairs
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