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ISI 2020 | PCB Mathematics | Question: 2

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ISI 2020 | PCB Mathematics | Question: 1
Let $\epsilon>0$. Prove that there exists $n_{0} \in \mathbb{N}$ such that $$ n \geq n_{0} \Rightarrow 2-\epsilon<\frac{2 n+1}{n+2}<2+\epsilon. $$
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ISI 2020 | PCB Mathematics | Question: 5.2
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ISI 2020 | PCB Mathematics | Question: 4
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ISI 2020 | PCB Mathematics | Question: 5.1
Prove that if $N$ and $K$ are normal subgroups of a group $G$ such that $N \cap K=\left\{e_{G}\right\}$, then $x y=y x, \forall x \in N, \forall y \in K$.