Which statements are correct:

Options

A. (a) Heterogeneous catalyst used in polymerisation of alkene is Ziegler Natta catalyst (for the synthesis of HDPE).
B. (b) Homogeneous catalyst used in the hydrogenation of alkenes is Wilkinson's catalyst.
C. (c) Formula for Ziegler Natta catalyist is `[RhCl(PPh_3)_3]` and for Wilkinson's catalyst is `TiCl_4+Et_3Al`.
D. (d) Wilkinson's catalyst also reduces acid (RCOOH) to alcohol `(RCH_2OH)`.

Answer

To solve the question regarding which statements are correct about catalysts used in the polymerization and hydrogenation of alkenes, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Understanding Ziegler-Natta Catalyst**:
- The Ziegler-Natta catalyst is used for the polymerization of alkenes, specifically for producing high-density polyethylene (HDPE).
- The correct formula for the Ziegler-Natta catalyst is TiCl4 + Et3Al (where TiCl4 is titanium tetrachloride and Et3Al is triethylaluminum).

**Hint**: Remember that Ziegler-Natta catalysts are specifically designed for alkene polymerization.

2. **Understanding Wilkinson Catalyst**:
- The Wilkinson catalyst is a homogeneous catalyst used for the hydrogenation of alkenes.
- Its formula is often represented as Rh(PPh3)3Cl, where Rh is rhodium, and PPh3 is triphenylphosphine.

**Hint**: Focus on the role of the Wilkinson catalyst in hydrogenation reactions.

3. **Evaluating the Statements**:
- **Statement A**: "A heterogeneous catalyst used in a polymerization of alkene is Ziegler-Natta catalyst."
- This statement is **correct** because Ziegler-Natta catalysts are indeed used for alkene polymerization.

- **Statement B**: "A homogeneous catalyst used in a hydrogenation of alkene is Wilkinson catalyst."
- This statement is also **correct** as the Wilkinson catalyst is used for hydrogenating alkenes.

- **Statement C**: "Formula for the Ziegler-Natta catalyst is RHCl PbH3 whole twice and for Wilkinson catalyst is TiCl4 plus Et3Al."
- This statement is **incorrect**. The correct formula for Ziegler-Natta catalyst is TiCl4 + Et3Al, not RHCl PbH3 whole twice.

- **Statement D**: "Wilkinson catalyst also reduces acid RCOH to RCH2OH."
- This statement is **correct** because the Wilkinson catalyst can reduce carboxylic acids (RCOOH) to primary alcohols (RCH2OH).

4. **Conclusion**:
- The correct statements are A, B, and D.
- Therefore, the correct answer includes statements A, B, and D.

### Final Answer:
The correct statements are A, B, and D.