(A) : An electron moving with uniform velocity enters uniform magnetic field perpendicularly and then a uniform electric field in the same direction. Nature of paths followed by electron in both the fields will be same.
(R) : The force applied by magnetic and electric field on electron are in the same direction.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is false

Answer

To solve the question, we need to analyze the two statements (A) and (R) regarding the motion of an electron in a magnetic field and an electric field.

### Step-by-Step Solution:

1. **Understanding the Motion in a Magnetic Field:**
- When an electron enters a uniform magnetic field perpendicularly (at a 90-degree angle), it experiences a magnetic force given by the formula:
\[ F_B = q \cdot v \cdot B \cdot \sin(\theta) \]
where \( q \) is the charge of the electron, \( v \) is its velocity, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the velocity and the magnetic field. Since the angle is 90 degrees, \( \sin(90) = 1 \), thus:
\[ F_B = q \cdot v \cdot B \]
- This force acts perpendicular to the velocity of the electron, causing it to move in a circular path.

2. **Understanding the Motion in an Electric Field:**
- When the same electron enters a uniform electric field, it experiences an electric force given by:
\[ F_E = q \cdot E \]
where \( E \) is the electric field strength.
- The direction of this force is along the direction of the electric field, meaning the electron will accelerate in a straight line in the direction of the electric field.

3. **Comparing the Paths:**
- In the magnetic field, the electron follows a circular path due to the perpendicular force acting on it.
- In the electric field, the electron follows a straight line path due to the constant force acting in the direction of the electric field.

4. **Evaluating Statement (A):**
- Statement (A) claims that the nature of paths followed by the electron in both fields will be the same. This is **false** because the paths are different: circular in the magnetic field and straight in the electric field.

5. **Evaluating Statement (R):**
- Statement (R) claims that the forces applied by the magnetic and electric fields on the electron are in the same direction. This is also **false** because the magnetic force acts perpendicular to the motion of the electron, while the electric force acts in the direction of the electric field.

### Conclusion:
Both statements (A) and (R) are false.