Permanent hardness in water refers to the presence of calcium and magnesium ions in the form of sulfates, chlorides, or bicarbonates. These ions cannot be removed by boiling the water and are responsible for the formation of scale deposits in pipes, appliances, and boilers.

When alum (Al2(SO4)3) is added to water, it forms aluminum hydroxide (Al(OH)3) and sulfates. The aluminum hydroxide precipitates out of the solution and reacts with the calcium and magnesium ions present in the water.

Here is a detailed explanation of why option B, CaSO4, indicates permanent hardness when alum is added to water:

1. Formation of aluminum hydroxide:
- Alum, which is a hydrated double sulfate of aluminum and potassium, dissociates into aluminum ions (Al3+) and sulfate ions (SO42-) in water.
- These aluminum ions react with water to form aluminum hydroxide precipitates (Al(OH)3) according to the following equation:
2Al3+ + 3H2O → Al(OH)3 + 3H+

2. Reaction with calcium ions:
- Calcium ions (Ca2+) present in the water react with the aluminum hydroxide precipitates.
- The reaction can be represented as:
Al(OH)3 + 3Ca2+ → Al(OH)3 + 3Ca2+

3. Formation of calcium sulfate:
- The reaction between aluminum hydroxide and calcium ions results in the formation of calcium hydroxide (Ca(OH)2) and aluminum ions.
- The aluminum ions can further react with sulfate ions (SO42-) from the alum to form aluminum sulfate (Al2(SO4)3).
- The overall reaction can be written as:
2Al(OH)3 + 3Ca2+ + 3SO42- → Al2(SO4)3 + 3Ca(OH)2

4. Precipitation of calcium sulfate:
- Calcium sulfate (CaSO4) is insoluble in water and forms a solid precipitate.
- The formation of calcium sulfate precipitates indicates the presence of calcium ions, which are responsible for permanent hardness.

Therefore, when alum is added to water, the formation of calcium sulfate indicates the presence of permanent hardness. It is important to note that the other options listed (Al(OH)3, CO2, and Ca(OH)3) do not directly indicate permanent hardness in water.