The correct statement about \(d-\)block elements is

\(V_2O_5\) is amphoteric in nature

The correct answer is option 1. \(V_2O_5\) is amphoteric in nature.

Let us delve into each statement:

1. \(V_2O_5\) is amphoteric in nature: This statement is correct. Vanadium pentoxide (\(V_2O_5\)) is an oxide of vanadium that exhibits amphoteric behavior. Amphoteric oxides can react with both acids and bases to form salts. In the case of \(V_2O_5\), it can react with both acids and bases to form salts like vanadates.

2. Ziegler catalyst consists of \(Al(CH_3)_3\) and \(ZrCl_4\): This statement is incorrect. The Ziegler-Natta catalyst typically consists of a transition metal compound, such as titanium tetrachloride (\(TiCl_4\)), along with an organoaluminum compound, such as triethylaluminum (\(Al(C_2H_5)_3\)) or diethylaluminum chloride (\(Al(C_2H_5)_2Cl\)). Zirconium tetrachloride (\(ZrCl_4\)) is not typically used in Ziegler-Natta catalysts.

3. \(Cu^+\) ions do not show disproportionation reaction: This statement is incorrect. Copper(I) ions (\(Cu^+\)) are unstable in aqueous solutions and tend to disproportionate into copper(II) ions (\(Cu^{2+}\)) and metallic copper (\(Cu\)). The disproportionation reaction of copper(I) ions is often observed in various redox reactions.

4. \(MnF_7\) is more stable than \(Mn_2O_7\): This statement is incorrect. \(MnF_7\) does not exist; the highest oxidation state of manganese in fluorides is +4. On the other hand, \(Mn_2O_7\) (manganese heptoxide) is a powerful oxidizing agent and is relatively unstable. It can easily decompose and is not commonly encountered in practice.

In summary, the correct statement about \(d-\) block elements is:\(V_2O_5\) is amphoteric in nature.