Find the remainder when first 1000 digits of the number P are divided by 16?

A number when divided successively by 13 and 3 gives respective remainder 5 and 1. What will the remainder when the largest such two-digit number is divided by 19.

A 99-digit number is formed by writing the first 59 natural numbers one after the other as: 1234567891011121314...5859. Find the remainder obtained when the above number is divided by 16.

A number when divided by 16 leaves a remainder 4. When the square of the number is divided by 16, what will be the remainder?

A number when divided by 16 leaves remainder 8. What is the remainder when the same number is divided by 8?

When a number is divided by 192, the remainder is 54. If the same number is divided by 16, what will be the remainder?

A number leaves a remainder of 61 when divided by 136. Find the remainder when the number is divided by 34