Which of the following carbocations will be most stable?

State whether the following statements are True or False:
$(i)$ $CH_3-CH_2^+$ is more stable than $CH_3^+$
$(ii)$ $CH_3-CH_2^+$ is less stable than $CH_3^+$
$(iii)$ $(CH_3)_3C^+$ is less stable than $CH_3^+$
$(iv)$ $(CH_3)_3C^+$ is more stable than $CH_3^+$

Identify the correct order of stability for carbocations.

The correct order of stability is:

State True or False for the following statements:
$(i)$ $\mathop{C}\limits^{+}H_3$ and $CH_3\mathop{C}\limits^{+}H_2$ both are primary carbocations.
$(ii)$ $(CH_3)_3\mathop{C}\limits^{+}$ is a tertiary carbocation and all carbons are $sp^3$ hybridized.
$(iii)$ $\mathop{C}\limits^{+}H_3$ is trigonal planar.
$(iv)$ $CH_4$ is not trigonal planar.

Consider the following compounds:
$(I)$ $(CH_3)_3C-CH^{\bullet}-C_6H_5$
$(II)$ $(C_6H_5)_3C^{\bullet}$
$(III)$ $2$-methylbicyclo$[2.2.1]$hept$-2-$yl radical (as shown in the image)
Hyperconjugation occurs in: