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The greater of the two numbers  \small 100^{300} \text { and } 300 !  is .... 

Option: 1

300!


Option: 2

200!


Option: 3

Both of the above


Option: 4

None of the above


Answers (1)

best_answer

For n>6,

\left(\frac{n}{3}\right)^n<n !<\left(\frac{n}{2}\right)^n

\Rightarrow \quad\left(\frac{n}{3}\right)^n<n !

Putting n=300

\therefore(100)^{300}<300 \text { ! }
i.e.\ 300!

 

Posted by

himanshu.meshram

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