The remainder obtained when $51^{50}$ + $49^{50}$ is divided by 50 is

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Solution

The correct option is D
2

$51^{50} = (50 + 1)^{50}$

$49^{50} = (50 - 1)^{50}$

$51^{50} + 49^{50} = (50 + 1)^{50} + (50 - 1)^{50}$

= 50k + 2 (using binomial theorem)

So when this is divided by 50 the remainder is 2.

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