L(r1) = {0,01,011,0111......} , L(r2) = {1,01,001,0001......}
in question it is giving that L is any regular language obtained with quotient of L(r1) and L(r2)
then if you will consider right quotient ,
L = L(r1)/L(r2) = {0,01,011,0111.....}/{1,01,001,0001......}
now in L only those string will come which follow below property,
(from wikipedia)
means there is one x in L2 by which you can drive wx in L1.
-> Now in L2 first string is 1 and in L1 you can drive 0(from the string 01(w=0,x=1)), 01(from the string 011(w=01,x=1)), 011(from the string 0111(w=011,x=1))like wise go further...
-> Now in L2 second string is 01 and in L1 you can drive only $\epsilon$(from the string 01(w=$\epsilon$,x=01)) nothing else.
-> after second string in L2 third is 001. Now you can not drive any string from this. Same for others also
So finally L will contain strings like-
={$\epsilon$, 0,01,011,....} = $(\epsilon + 01^{*})$
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if you will consider left quotient ,
L = L(r1)\L(r2) = {0,01,011,0111.....}\{1,01,001,0001......}
= {$\epsilon$, 1,01,001,....} = $(\epsilon + 0^{*}1)$
now in L only those string will come which follow below property,
clearly answer is D)none.
For better understanding - https://math.stackexchange.com/questions/871662/finding-right-quotient-of-languages