Step 1: Understanding the Question:
The question provides experimental displacement observations for four metals (\(A\), \(B\), \(C\), \(D\)) with solutions of different metal nitrates/sulphates. We need to determine the correct reactivity order of these four metals.
Step 2: Key Formula or Approach:
According to the displacement reaction principles, a more reactive metal can displace a less reactive metal from its salt solution. A less reactive metal cannot displace a more reactive metal.
Step 3: Detailed Explanation:
• Let us analyze each metal's behavior from the given data:
- Metal-B: It can displace Silver, Copper, and Iron from their respective solutions. It only fails to displace Zinc. Since it can displace three of the metal ions, including Iron, it is highly reactive and occupies the highest position among the four.
- Metal-A: It can displace Silver and Copper, but it cannot displace Zinc or Iron. Since it can displace two metals but fails to displace Iron (which Metal-B displaced), its reactivity is lower than Metal-B but higher than the remaining metals.
- Metal-C: It can only displace Silver. It fails to displace Zinc, Copper, and Iron. This makes it less reactive than Metal-A (which could displace Copper).
- Metal-D: It cannot displace any of the metals (Silver, Zinc, Copper, Iron) from their solutions. This indicates that Metal-D is the least reactive of all.
• Ordering these metals from highest reactivity to lowest:
\[ B \gt A \gt C \gt D \]
• This matches the sequence given in Option (A).
Step 4: Final Answer:
The reactivity order of the metals is B $\gt $ A $\gt $ C $\gt $ D.