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Question

Write last two digits of the number 3400

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Solution

3400=(9)200

=(101)200

=200C0(10)200+200C1(10)199(1)1+....200C198(10)2(1)198+200C199(10)1(1)199+200C200(1)200

100[(10)198+200C1(10)197(1)1+....+200C198(1)198]+200(10)1(1)199+200C200(1)200

=100[(10)198200C1(10)197+....+200C1982(10)]+1

=100 (a natural number)+1

Hence, last two digits of the number 3400 is 01


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