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Q. $2^{n}>n^{2}$ when $n \in N$ such that

Principle of Mathematical Induction

Solution:

Let the given statement be $P (n)$, then
$P (1) \Rightarrow 2^1 > 1^2$ which is true
$P (2) \Rightarrow 2^2 > 2^2$ which is false
$P (3) \Rightarrow 2^3 > 3^2$ which is false
$P (4) \Rightarrow 2^4 > 4^2$ which is false
$P (5) \Rightarrow 2^5 > 5^2$ which is true
$P (6) \Rightarrow 2^6 > 6^2$ which is true
$\therefore P (n)$ is true when $n \ge 5$