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Question

If 500!=2m× an integer, then


A

m=494

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B

m=496

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C

It is equivalent to no. ofnis 400!=2nxan integer

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D

m=500C2

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Solution

The correct option is A

m=494


Explanation for the correct option:

Given, 500!=2m× an integer

In general, k2 integers less than or equal tokare even, such that some are divisible by 4, some by 8and so on.

Therefore, we need to find the total by adding the values k2+k4+...

The highest power of 2 not greater than 500 is 28

Therefore,

5002+5004+5008+50016+50032+50064+5002×64+500256

250+125+62+31+15+7+3+1=494

Hence . correct option is (A).


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