Question

$\forall n\in N,n^4$ is less than

• A. ${10}^n$
• B. $4n$
• C. $4^n$
• D. ${10}^{10}$

Answer 1

The correct option is A ${10}^n$

Let $y=n^4$
put $n=10\Rightarrow y={10}^4=10000>4\times 10,4^4$
Hence option B and C discarded.
Now put $n={10}^3\Rightarrow y={10}^{12}>{10}^{10}$. thus option D is also incorrect.
Hence option 'A' is correct.