(A) : If an electron is not deflected while passing through a certain region of space, then only possibility is that there is no magnetic field in this region
(R) : Force on an electron moving in a magnetic field is inversely proportional to the magnetic field applied.

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 both the assertion (A) and the reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states: "If an electron is not deflected while passing through a certain region of space, then the only possibility is that there is no magnetic field in this region."

- An electron moving in a magnetic field experiences a magnetic force given by the equation:
\[ F = q(\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the electron, \( \mathbf{v} \) is its velocity, and \( \mathbf{B} \) is the magnetic field.

- If the electron is not deflected, it implies that the net force acting on it is zero. This can occur if:
1. There is no magnetic field (\( \mathbf{B} = 0 \)).
2. The velocity of the electron is zero.
3. The velocity is parallel to the magnetic field (in which case \( \mathbf{v} \times \mathbf{B} = 0 \)).

- Therefore, the assertion is not necessarily true because there are other conditions (like parallel motion) under which the electron can remain undeflected. Thus, the assertion is **false**.

### Step 2: Analyze the Reason (R)
The reason states: "Force on an electron moving in a magnetic field is inversely proportional to the magnetic field applied."

- The force on a charged particle in a magnetic field is given by:
\[ F = q(\mathbf{v} \times \mathbf{B}) \]

- This indicates that the force is **directly proportional** to the magnetic field strength \( \mathbf{B} \), not inversely proportional. Therefore, the reason is also **false**.

### Conclusion
Both the assertion (A) and the reason (R) are false. The correct answer is that both statements are false.

### Final Answer
- Assertion (A): False
- Reason (R): False