JEE Advance - Mathematics (2018 - Paper 1 Offline - No. 8)
The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is .................
Answer
625
Explanation
A number is divisible by 4 if last 2 digit number is divisible by 4.
$$ \therefore $$ Last two digit number divisible by 4 from (1, 2, 3, 4, 5) are 12, 24, 32, 44, 52
$$ \therefore $$ The number of 5 digit number which are divisible by 4, from the digit (1, 2, 3, 4, 5) and digit is repeated is 5 $$ \times $$ 5 $$ \times $$ 5 $$ \times $$ (5 $$ \times $$ 1) = 625
$$ \therefore $$ Last two digit number divisible by 4 from (1, 2, 3, 4, 5) are 12, 24, 32, 44, 52
$$ \therefore $$ The number of 5 digit number which are divisible by 4, from the digit (1, 2, 3, 4, 5) and digit is repeated is 5 $$ \times $$ 5 $$ \times $$ 5 $$ \times $$ (5 $$ \times $$ 1) = 625
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