The correct answer is option B.
L ={ 01,10,….}
L^2=L.L={01,10,….}.{01,10,…..}
L^2={0101,0110,1001,1010,…….}
L^3=L^2.L={0101,0110,1001,1010…..}.{01,10,….}
L^3 ={010101,010110,100101,…..}
L*=L^0 U L^1 U L^2 U L^3….
so definitely the string 010101 will be there.
Now 0000 can never be generated as
for 0000 which has length 4 we have to concat with
- length 0 + length 4
- length 1+ length 3
- length 2+ length 2
now here in the language smallest string is length 2 which is “01” or “10” so by concatenate them we cant get “0000” and L itself does not contain “0000”.
option c the string “111101” is present in the language ,it has even length and odd no of zero . So it will be in L*.
Option D is also not in the L* as it can be generate by concate either
- zero length string + 3 length string
- 1 length string + 2 length
Now L does not not contain “010”
we cant have this as well.
so correct answer is B,C.