Regular Expressions

Can someone check these for me...

Express each of these sets using a regular expression:

a)The set containing all strings with 0, 1, or 2 bits.
$ (\lambda\cup0\cup1\cup00\cup01\cup10\cup11) $

b)The set of strings of two 0's, followed by zero or more 1's, and ending with a 0
$ 001^*0 $

c)The set of strings with every 1 followed by two 0's.
$ (100)^* $

d)The set of strings ending in 00 and not containing 11. *NOT SURE
$ (00\cup100)^* $

e)The set of strings containing an even number of 1's. *NOT SURE
$ 0^*10^*(10^*)^* $