JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q5

MathematicsSingle correct+4 / -1Question 5 of 90

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Answer and worked solution

Official answer: D

Divisible by 3. The six digits sum to 24, so the dropped digit is 3 or 6.

Even last digit. Without 3: digits 1,2,5,6,7, last digit 2 or 6: $2\cdot4!=48$ . Without 6: last digit 2: $4!=24$ .

Total 72.

(D)

Topics:Permutations

JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 5