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Sum of Coefficients of All Terms

If m is any p...

Question

If m is any positive integer then the last two digits in the expression ${(81)}^{m}$ ${(121)}^{m} - 1$ are

A

2

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B

12

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C

21

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D

0

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Solution

The correct option is D 0
$(81)^{m} (121)^{m} - 1 = (81 \times 121)^{m} - 1$

The given expression is always divisible by $(81 \times 121 - 1) = 9800$ only if the last two digits of the given equation are 00

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