`{:((i),"Cottrell's", (a), "K kg mol"^(-1)),((ii), "Elevation of boiling point.", (b), "Raoult's law"),( (iii), "Dilute solution", (c ), "Osmotic pressure"),((iv), "Colligative property", (d), "Ebullioscopic method"),( (v) ,"Molal depression constant",(e ), "Relative lowering of vapour pressure"):}`

Answer

To solve the matching question, we need to pair each item from the first column with the correct item from the second column. Let's go through each item step by step.

### Step 1: Match Cottrell's Method
Cottrell's method is associated with the elevation of boiling point. This method is also known as the ebullioscopic method. Therefore, we match:
- **(i) Cottrell's** → **(d) Ebullioscopic method**

### Step 2: Match Elevation of Boiling Point
The elevation of boiling point is represented by the molal depression constant (Kb), which has the SI unit of K kg mol^(-1). Thus, we match:
- **(ii) Elevation of boiling point** → **(a) K kg mol^(-1)**

### Step 3: Match Dilute Solution
A dilute solution is often discussed in the context of Raoult's law, which describes the vapor pressure of a solution. Therefore, we match:
- **(iii) Dilute solution** → **(b) Raoult's law**

### Step 4: Match Colligative Property
Colligative properties depend on the number of solute particles in a solution, and osmotic pressure is a type of colligative property. Thus, we match:
- **(iv) Colligative property** → **(c) Osmotic pressure**

### Step 5: Match Molal Depression Constant
The molal depression constant (Kf) is related to the relative lowering of vapor pressure. Therefore, we match:
- **(v) Molal depression constant** → **(e) Relative lowering of vapor pressure**

### Final Matches
Now, we can summarize the matches:
1. (i) Cottrell's → (d) Ebullioscopic method
2. (ii) Elevation of boiling point → (a) K kg mol^(-1)
3. (iii) Dilute solution → (b) Raoult's law
4. (iv) Colligative property → (c) Osmotic pressure
5. (v) Molal depression constant → (e) Relative lowering of vapor pressure