[LTK]

A compound with the formula C5H6 takes up 2 moles of H2 on catalytic hydrogenation & a compound of C6H10 takes up 1 mole of H2 on reduction. What would be a possible structure for each of these examples?

[SVXX]

C₆H₁₀ is an alkene with the double bond present in any place in the molecule.
C₅H₆ is for sure a diene. At first I thought it's an alkyne, but alkynes don't have such a general formula. This formula matches with that of a ring. With five carbons, I'd place my bet on cyclopentadiene.

[LTK]

Thanks, that's what I was thinking for the C6H10, but really was unsure of the C5H6 example. 

[Schrödinger]

C6H10 could be cyclohexene and C5H6, as suggested by SVXX, could be cyclopentadiene.

But you can always come up with different structures taking into consideration isomers of the above compounds.