Question : What will be the remainder when $252^{126}+244^{152}$ is divided by 10?
Option 1: 4
Option 2: 6
Option 3: 0
Option 4: 8
Correct Answer: 0
Solution : To find the remainder when $252^{126}+244^{152}$ is divided by 10, we only need to consider the unit digit of each term in the sum. The unit digit of $252^{126}$ is the same as the unit digit of 2 126 . Divide 126 by 4 and get remainder = 2 So, the unit digit of $252^{126}$ is $2^2$ = 4 The unit digit of $244^{152}$ is the same as the unit digit of 4 152 . If the power of 4 is even, the unit digit is 6. So, the unit digit of $244^{152}$ is 6. The sum of the unit digits = 4 + 6 = 10 The remainder when $252^{126}+244^{152}$ is divided by 10 = Remainder when 10 is divided by 10 = 0 So, the remainder is 0. Hence, the correct answer is 0.
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