STATEMENT-1 `:` Electric field at a point due to an infinite sheet of uniformly distributed charge is independent of distance between the point from the sheet.
STATEMENT-2 `:` Electric field at a pont due to an uniformly distributed long charged rod is inversity proportional to distance between the point and rod.
STATEMENT-3 `:` Electric field at a point due to an electric dipole is inversely proportional to the cube of distance between point and centre of dipole.

Options

A. F F T
B. T T T
C. F T F
D. T T F

Answer

To analyze the three statements regarding electric fields, we will evaluate each statement step by step.

### Step 1: Evaluate Statement 1
**Statement 1:** Electric field at a point due to an infinite sheet of uniformly distributed charge is independent of the distance between the point and the sheet.

**Solution:**
- For an infinite sheet of charge with surface charge density \( \sigma \), the electric field \( E \) is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
- This formula indicates that the electric field is constant and does not depend on the distance from the sheet. Thus, the electric field remains the same regardless of how far you are from the sheet.

**Conclusion:** Statement 1 is **True**.

### Step 2: Evaluate Statement 2
**Statement 2:** Electric field at a point due to a uniformly distributed long charged rod is inversely proportional to the distance between the point and the rod.

**Solution:**
- For a long charged rod with linear charge density \( \lambda \), the electric field \( E \) at a distance \( r \) from the rod is given by:
\[ E = \frac{2k\lambda}{r} \]
where \( k \) is Coulomb's constant.
- This shows that the electric field is inversely proportional to the distance \( r \). As you move farther from the rod, the electric field decreases.

**Conclusion:** Statement 2 is **True**.

### Step 3: Evaluate Statement 3
**Statement 3:** Electric field at a point due to an electric dipole is inversely proportional to the cube of the distance between the point and the center of the dipole.

**Solution:**
- For an electric dipole consisting of charges \( +q \) and \( -q \) separated by a distance \( 2a \), the electric field \( E \) at a point along the axis of the dipole at a distance \( r \) from its center is given by:
\[ E = \frac{k \cdot p}{r^3} \]
where \( p = q \cdot 2a \) is the dipole moment.
- This formula indicates that the electric field due to a dipole decreases with the cube of the distance \( r \).

**Conclusion:** Statement 3 is **True**.

### Final Conclusion
All three statements are true:
- Statement 1: True
- Statement 2: True
- Statement 3: True

Thus, the overall conclusion is that all statements are true.