Determine the following:

a$)$ the time a $24-$hour clock reads $300$ hours before $15$:$00$

b$)-1033$ mod $11$

c$)415$ in octal converted to hexadecimal

d$)101110010$ in binary converted to octal

e$)$ least common multiple of $60$ and $165$

f$)$ greatest common denominator of $60$ and $165$