A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?

Which number amongst 2⁴⁰, 3²¹, 4¹⁸ and 8¹² is the smallest?

What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?