Concept:
Uranium (U) and Plutonium (Pu) belong to the actinide series.
Actinides show variable oxidation states because both $5f$, $6d$, and $7s$ electrons can participate in bonding.
Step 1: Electronic idea.
Actinides commonly show:
$$+3,\ +4,\ +5,\ +6$$
Some also show higher states.
Step 2: Highest oxidation state of Uranium.
Uranium commonly reaches maximum:
$$+6$$
Example:
$$\text{UO}_2^{2+}$$
(uranyl ion)
Step 3: Highest oxidation state of Plutonium.
Plutonium can attain:
$$+7$$
under strongly oxidising conditions.
Step 4: Match option.
Thus:
$$\text{U} = +6,\qquad \text{Pu} = +7$$
Step 5: Final answer.
Hence correct option is:
$$\boxed{\text{(C)}}$$
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