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Question

For all nN,24n15n1 is divisibl;e by

A
225
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B
125
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C
325
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D
None of these
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Solution

The correct option is D 225
We have 24n=(24)n=(16)n=(1+15)n
24n=1+nC1×15+nC2×152+nC3×153+...24n115n=152[nC2+nC3×15+...]
=225K, where K is an integer.
Hence 24n115n is divisible by 225.

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