Lisp programming help!

Create a recursive function TYPECHECK that takes a list as its parameter and returns a list containing a list of the applicable types (in any order) for each item on the list.The types you should check for are: NIL, T, NUMBER, SYMBOL, LIST and STRING. Do error checking on the input.

I want to make it using basic functions like cond, cons, car, cdr.

[50]> (typecheck '(a b c))

((symbol t) (symbol t) (symbol t))

[51]> (typecheck ())

NIL

[52]> (typecheck '(1 "two" (3 4) ()))

((symbol t number) (string t) (list t) (symbol nil list))