1. Identify what is being asked

We need the pair that represents:

• strong reducing agent first
• strong oxidizing agent second

So we must check which ion is most easily oxidized (thus acts as a reducing agent) and which ion is most easily reduced (thus acts as an oxidizing agent).

2. Use standard lanthanide stability ideas

Among lanthanides, certain oxidation states are especially stable because of electronic configurations:

• $\mathrm{Ce}^{4+}$ has configuration close to stable $4f^0$
• $\mathrm{Eu}^{2+}$ has especially stable half-filled configuration $4f^7$
• $\mathrm{Tb}^{4+}$ is less common but can exist

Now, chemical behavior:

(a) $\mathrm{Ce}^{4+}$

$\mathrm{Ce}^{4+}$ readily gains an electron to become $\mathrm{Ce}^{3+}$: $\mathrm{Ce}^{4+} + e^- \rightarrow \mathrm{Ce}^{3+}$ Since it gets reduced easily, it acts as a strong oxidizing agent.

(b) $\mathrm{Eu}^{2+}$

$\mathrm{Eu}^{2+}$ readily loses an electron to become $\mathrm{Eu}^{3+}$: $\mathrm{Eu}^{2+} \rightarrow \mathrm{Eu}^{3+} + e^-$ Thus it acts as a strong reducing agent.

This is a standard result in lanthanide chemistry:

• $\mathrm{Eu}^{2+}$ is a strong reducing agent.
• $\mathrm{Ce}^{4+}$ is a strong oxidizing agent.

3. Check each option

Option A: $\mathrm{Ce}^{4+}$ and $\mathrm{Eu}^{2+}$

This says:

• reducing agent = $\mathrm{Ce}^{4+}$ ❌
• oxidizing agent = $\mathrm{Eu}^{2+}$ ❌ Reversed.

Option B: $\mathrm{Eu}^{2+}$ and $\mathrm{Ce}^{4+}$

This says:

• reducing agent = $\mathrm{Eu}^{2+}$ ✅
• oxidizing agent = $\mathrm{Ce}^{4+}$ ✅ Correct.

Option C: $\mathrm{Ce}^{4+}$ and $\mathrm{Tb}^{4+}$

$\mathrm{Ce}^{4+}$ is not the strong reducing agent, so this is incorrect. ❌

Option D: $\mathrm{Ce}^{3+}$ and $\mathrm{Ce}^{4+}$

$\mathrm{Ce}^{4+}$ is a strong oxidizing agent, but $\mathrm{Ce}^{3+}$ is not the strongest reducing agent among these. ❌

4. Final conclusion

The strong reducing and oxidizing agents respectively are: $\boxed{\mathrm{Eu}^{2+} \text{ and } \mathrm{Ce}^{4+}}$ So the correct option is B.

5. Comparison with stored answer

Stored correct answer: B

Our derived answer: B

They agree.