How does the price of a put option respond to the following changes, other things equal?

$($a$)$ Stock price increases.

$($b$)$ Exercise price is increased.

$($c$)$ Risk$-$free rate increases.

$($d$)$ Expiration date of the option is extended.

$($e$)$ Volatility of the stock price falls.

$($f$)$ Time passes.