Predict which member of each pair has the higher boiling point and explain the reasons for your predictions.

$($a$)$ hexan$-1-$ol or $3,3-$dimethylbutan$-1-$ol

$($b$)$ hexan$-2-$one or hexan$-2-$ol

$($c$)$ hexan$-2-$ol or hexane$-1,5-$diol

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$($d$)$ pentan$-2-$ol or hexan$-2-$ol

Predict whether each of the following alcohols will have a high or low solubility in water.

$($a$)$

$($c$)$