Q36 / 90 · JEE Main 2018 (16 Apr Online) · Mathematics

The number of numbers between $2, 000$ and $5, 000$ that can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) and are multiple of $3$ is

Solution

When a number is divisible by $3$ , then sum of digits of a number is also divisible by $3$ .

Number can be formed from $(0, 1, 2, 3)$ or $(0, 2, 3, 4)$ .

Number of $4$ digits number

$= 3 \times 3 \times 2 \times 1 + 3 \times 3 \times 2 \times 1$

$= 36$ .

Hence, the correct answer is option: 'A'.