$\text{(I)}{\text{CH}}_3-\underset{••}{\overset{••}{\text{O}}}-\stackrel{\oplus }{{\text{CH}}_2}{\text{is more stable than CH}}_3-\stackrel{\oplus }{{\text{CH}}_2}{\text{, }}_{}$becausse of $+\text{M}$-effect of ${\text{CH}}_3-\underset{••}{\overset{••}{\text{O}}}-$.
$\text{(II)}{\text{Me}}_3\stackrel{\oplus }{\text{C}}\text{H}is\; more\; stable\; than{CH}_3-{\text{CH}}_2-{\stackrel{\oplus }{\text{CH}}}_2,$  
because ${\text{Me}}_{\text{3}}{\text{C}}^{\oplus }$ have more 2-hydrogen atoms than ${\text{CH}}_3-{\text{CH}}_2-{\text{CH}}_2^{\oplus },$ so, it is more stable, due to greater hyperconjugation.

(III) The positive charge is delocalised in $\text{C}{\text{H}}_2=\text{C}\text{H}-\text{C}\stackrel{\oplus }{{\text{H}}_{\begin{array}{l}2\\ \end{array}}}$, so more stable than,${\text{CH}}_3-{\text{CH}}_2-{\text{CH}}_2^{\oplus }.$

$\text{(IV)}{CH}_2=\stackrel{\oplus }{\text{CH}}$ will be less stable than ${CH}_3-\stackrel{\oplus }{{\text{CH}}_2}$ as positive charge is less stable on double bonded 'C' than on single bonded 'C'.