Question : What will be the remainder when $7^{42}$ is divided by 48?
Option 1: 2
Option 2: 3
Option 3: 1
Option 4: 0
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Correct Answer: 1
Solution : Given: $7^{42}$ = $(7^{2})^{21}$ = $(49)^{21}$ = $(48+1)^{21}$ So the remainder is 1. Hence, the correct answer is 1.
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Question : When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:
Option 1: 3
Option 2: 2
Question : When a number is divided by 45, the remainder is 21. What will be the remainder when the number is divided by 15?
Option 1: 6
Option 2: 5
Option 3: 3
Question : M is the largest 4-digit number which, when divided by 4, 5, 6, and 7, leaves the remainder as 2, 3, 4, and 5, respectively. What will be the remainder when M is divided by 9?
Option 2: 1
Option 4: 6
Question : A number when divided by 7 leaves a remainder of 4. If the square of the same number is divided by 7, then what is the remainder?
Option 3: 4
Option 4: 2
Question : A number, when divided by 6, leaves a remainder of 3. When the square of the same number is divided by 6, the remainder is:
Option 1: 0
Option 4: 3
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