Let $n = 3^{100}$ , then for $n$

unit's digit is

1

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ten's digit is

0

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unit's digit is

7

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ten's digit is

2

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Solution

The correct options are
A unit's digit is $1$
B ten's digit is $0$
n=Given, $3^{100}$
$= 9^{50}$
$= (10 - 1)^{50}$
$= (1 - 10)^{50}$
$= 1 + 10 k$ where K is a positive integer.
Hence units digit of $3^{100}$ is 1.
Now
$1 + 10 k$
$= 1 - 10^{50} C_{1} +^{50} C_{2} 10^{2} -^{50} C_{3} 10^{3} . . .^{50} C_{50} 10^{50}$
$= 1 - 10 (50) + 100 u$ where u is a positive integer.
$= 100 u - 500 + 1$
$= 100 (u - 5) + 1$
Hence ten's digit is 0.

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Let n=3100, then for n

Let $n = 3^{100}$ , then for $n$