what is the output carry of full adder?
AB+BCin+ACin .-------> (1)
What is the output of MUX?
A' . B' . I0 + A' . B . I1 + A . B' . I2 + A . B . I3 -------> (2)
compare two equations
I0 = 0 , I3=1 ,
(2) now look like as
A' . B . I1 + A . B' . I2 + A . B .
= A' . B . I1 + A . B' . I2 + A . B + A.B
= ( A.B + A' . B . I1 ) + ( A.B + A . B' . I2 ) + A . B
= ( A + A' . I1 ) B + A . ( B + B' . I2 ) + A.B
= ( A + I1 ) B + A . ( B + I2 ) + A.B
= AB + B. I1 + A . I2 -------> (3)
Compare (3) with (1)
I1 = Cin and I2 = Cin
For multiple choice go with substitution by options, then you get answer very quickly