JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Permutations and Combinations

For a 4-digit number between 1000 and 3000, the first digit must be 1 or 2. For divisibility by 4, the last two digits must form a number divisible by 4. Case I: First digit is 1. Possible last two digits from $\{2,3,4,5,6\}$ divisible by 4: 24, 32, 36, 52, 56, 64 (6 choices). For each, the second digit can be any of the 3 remaining digits, giving $6\times 3=18$ numbers. Case II: First digit is 2. Possible last two digits from $\{1,3,4,5,6\}$ divisible by 4: 16, 36, 56, 64 (4 choices). For each, the second digit can be any of the 3 remaining digits, giving $4\times 3=12$ numbers. Total: $18+12=30$.