Random Puzzles 

Workings

Hint
This is a well known nursery rhyme.

Answer
HDD.

The initial letters from the nursery rhyme, Hickory Dickory Dock.
Hickory, dickory, dock,
The mouse ran up the clock,
The clock struck one,
The mouse ran down,
Hickory, dickory, dock.

Workings

Hint
Do leap years make a difference?

Answer
Hours in 10 years.

Reasoning
In a day, there are 60 x 60 x 24 seconds = 86,400 seconds.

In 10 years, there are 10 x 365 x 24 hours = 87,600 hours, which even without the leap years is already the larger number.

Workings

Hint
There are lots of vowels.

Answer
A.

This is the vowels AEIOU intermingled with the reverse UOIEA.

Workings

Hint
One of the words begins with the letter S.

Answers
-s-g- = usage --r-f = serif -zu-- = azure e--x- = epoxy -p--c = optic --ln- = kilns -w--m = swarm ---jo = banjo q---a = quota -v-k- = evoke i--h- = itchy -b-y- = obeys --dt- = width