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Q.

The last two digits of the number 3⁴⁰⁰ are

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a

81

b

43

c

29

d

01

answer is D.

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Detailed Solution

$\begin{array}{l} 3^{400} = 81^{100} = (1 + 80)^{100} \\ =^{100} C_{0} +^{100} C_{1} 80 + \dots +^{100} C_{100} 80^{100} \end{array}$

Thus, the last two digits are 01 .

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