1. Recall the condition for disproportionation

A species undergoes disproportionation when the same element in one oxidation state is simultaneously oxidized and reduced to two different oxidation states.

So we test each species for whether it can show disproportionation.

2. Check each species individually

(i) $\mathrm{ClO_2^-}$

Oxidation state of Cl: $x + 2(-2) = -1 \Rightarrow x=+3$ Chlorine in oxidation state $+3$ can disproportionate, e.g. $2\mathrm{ClO_2^-} \rightarrow \mathrm{ClO^-} + \mathrm{ClO_3^-}$ So, $\mathrm{ClO_2^-}$ shows disproportionation.

(ii) $\mathrm{F_2}$

Fluorine has oxidation state $0$ in $\mathrm{F_2}$. But fluorine is the most electronegative element and in compounds it shows only $-1$ oxidation state. It does not get oxidized to a positive oxidation state.

Hence $\mathrm{F_2}$ does not undergo disproportionation.

(iii) $\mathrm{MnO_4^-}$

Oxidation state of Mn: $x + 4(-2) = -1 \Rightarrow x=+7$ This is the highest common oxidation state of Mn, so Mn cannot be oxidized further. Therefore it cannot disproportionate.

So $\mathrm{MnO_4^-}$ does not show disproportionation.

(iv) $\mathrm{Cr_2O_7^{2-}}$

Oxidation state of Cr: $2x + 7(-2) = -2 \Rightarrow 2x=12 \Rightarrow x=+6$ This is the highest common oxidation state of Cr. Hence it cannot be oxidized further, so it does not disproportionate.

(v) $\mathrm{Cl_2}$

Chlorine in elemental state $0$ can disproportionate, for example in alkali: $\mathrm{Cl_2 + 2OH^- \rightarrow Cl^- + ClO^- + H_2O}$ So $\mathrm{Cl_2}$ shows disproportionation.

(vi) $\mathrm{Mn^{3+}}$

$\mathrm{Mn^{3+}}$ can disproportionate: $2\mathrm{Mn^{3+}} \rightarrow \mathrm{Mn^{2+}} + \mathrm{Mn^{4+}}$ So $\mathrm{Mn^{3+}}$ shows disproportionation.

(vii) $\mathrm{ClO_4^-}$

Oxidation state of Cl: $x + 4(-2) = -1 \Rightarrow x=+7$ This is the highest oxidation state of chlorine, so it cannot be oxidized further. Hence no disproportionation.

So $\mathrm{ClO_4^-}$ does not show disproportionation.

3. Evaluate the options

Option A: $\mathrm{ClO_2^-}$, $\mathrm{F_2}$, $\mathrm{MnO_4^-}$, $\mathrm{Cr_2O_7^{2-}}$

• $\mathrm{ClO_2^-}$: Yes
• $\mathrm{F_2}$: No
• $\mathrm{MnO_4^-}$: No
• $\mathrm{Cr_2O_7^{2-}}$: No

So not all show disproportionation.

Option B: $\mathrm{Cr_2O_7^{2-}}$, $\mathrm{MnO_4^-}$, $\mathrm{ClO_2^-}$, $\mathrm{Cl_2}$

• $\mathrm{Cr_2O_7^{2-}}$: No
• $\mathrm{MnO_4^-}$: No
• $\mathrm{ClO_2^-}$: Yes
• $\mathrm{Cl_2}$: Yes

So not all show disproportionation.

Option C: $\mathrm{MnO_4^-}$, $\mathrm{ClO_2^-}$, $\mathrm{Cl_2}$, $\mathrm{Mn^{3+}}$

• $\mathrm{MnO_4^-}$: No
• $\mathrm{ClO_2^-}$: Yes
• $\mathrm{Cl_2}$: Yes
• $\mathrm{Mn^{3+}}$: Yes

So not all show disproportionation.

Option D: $\mathrm{ClO_4^-}$, $\mathrm{MnO_4^-}$, $\mathrm{ClO_2^-}$, $\mathrm{F_2}$

• $\mathrm{ClO_4^-}$: No
• $\mathrm{MnO_4^-}$: No
• $\mathrm{ClO_2^-}$: Yes
• $\mathrm{F_2}$: No

So not all show disproportionation.

4. Conclusion

None of the given options contains species all of which undergo disproportionation.

The species that do show disproportionation are: $\mathrm{ClO_2^-},\; Cl_2,\; Mn^{3+}$ But every option includes at least one species such as $\mathrm{F_2}$, $\mathrm{MnO_4^-}$, $\mathrm{Cr_2O_7^{2-}}$, or $\mathrm{ClO_4^-}$ that does not disproportionate.

Therefore, no option is correct as written.