(i) Origin is the only point which lies on both the axes.
(ii) The point `(2,-2)` and point `(-2,2)` lies in the same quadrant.
(iii) If a point lies on y-axis at a distance 2 units from x-axis, then its coordinates are (2, 0).
(iv) Abscissa of a point is positive in I quadrant and also in II quadrant.

Options

A. `{:("(i)","(ii)","(iii)","(iv)"),("F","T","F","T"):}`
B. `{:("(i)","(ii)","(iii)","(iv)"),("T","F","F","F"):}`
C. `{:("(i)","(ii)","(iii)","(iv)"),("F","T","T","F"):}`
D. `{:("(i)","(ii)","(iii)","(iv)"),("T","F","T","F"):}`

Answer

Let's analyze each statement step by step and determine whether they are true or false.

### Step 1: Analyze the first statement
**Statement:** "Origin is the only point which lies on both the axes."

**Analysis:**
- The origin is the point (0, 0).
- The x-axis is the line where y = 0, and the y-axis is the line where x = 0.
- The only point that satisfies both conditions (x = 0 and y = 0) is the origin.

**Conclusion:** This statement is **True**.

### Step 2: Analyze the second statement
**Statement:** "The point (2, -2) and point (-2, 2) lies in the same quadrant."

**Analysis:**
- The point (2, -2) has a positive x-coordinate and a negative y-coordinate, which places it in the **fourth quadrant**.
- The point (-2, 2) has a negative x-coordinate and a positive y-coordinate, which places it in the **second quadrant**.
- Since these points are in different quadrants, they do not lie in the same quadrant.

**Conclusion:** This statement is **False**.

### Step 3: Analyze the third statement
**Statement:** "If a point lies on y-axis at a distance of 2 units from x-axis, then its coordinates are (2, 0)."

**Analysis:**
- A point on the y-axis has an x-coordinate of 0.
- If it is at a distance of 2 units from the x-axis, the y-coordinate can be either +2 or -2.
- Therefore, the possible coordinates are (0, 2) or (0, -2), not (2, 0).

**Conclusion:** This statement is **False**.

### Step 4: Analyze the fourth statement
**Statement:** "Abscissa of a point is positive in I quadrant and also in II quadrant."

**Analysis:**
- The abscissa is the x-coordinate of a point.
- In the **first quadrant**, both x and y coordinates are positive, so the abscissa is positive.
- In the **second quadrant**, the x-coordinate (abscissa) is negative while the y-coordinate is positive.

**Conclusion:** This statement is **False**.

### Final Summary of Statements:
1. True
2. False
3. False
4. False

### Final Answer:
- The first statement is **True**.
- The second statement is **False**.
- The third statement is **False**.
- The fourth statement is **False**.