DU in A, B, and `C=((2xx6+2)-10)/(2)=27^@`.
Structure of (A):
(A) reacts with ammoniacal `AgNO_3` solution, which shows that it is a terminal alkyne with straight chain of six C atoms (because on hydrogenation it gives hexane). Therefore, (A) is hex-1-yne.
Structure of (B):
(B) does not react with `[Ag(NH_3)_2]^(o+)` and hence it must be internal alkyne with straight chain of six C atoms (because on hydrogenation it gives hexane).
Location of triple bond is determined by oxidative cleavage. As it gives propanoic acid (3C-atom acid), it should be symmetrical internal alkyne.
Therefore, (B) is hex-3-yne.
Structure of (C):
It absorbs 1 mol of `H_2` and the product (D) `(C_6H_(12))` after catalytic hydrogenation has 1 DU. So (D) must be a 6C-atom cyclic compound. Therefore, (C) is cyclohexene.