(A) : The electron passing parallel to both magnetic and electric field is always deflected from its path
(R) : If velocity of electrons is equal to ratio of magnetic and electric field in crossed fields applied then electron beam remains undeflected.

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

### Step 1: Analyze the Assertion (A)
The assertion states: "The electron passing parallel to both magnetic and electric field is always deflected from its path."

- When an electron moves in a magnetic field, the force acting on it is given by the Lorentz force equation:
\[ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) \]
where \( q \) is the charge of the electron, \( \vec{E} \) is the electric field, \( \vec{v} \) is the velocity of the electron, and \( \vec{B} \) is the magnetic field.

- If the electron is moving parallel to both the electric field and the magnetic field, then the velocity \( \vec{v} \) is parallel to \( \vec{B} \). The cross product \( \vec{v} \times \vec{B} \) will be zero because the sine of the angle between two parallel vectors is zero. Therefore, the magnetic force component becomes zero.

- The only force acting on the electron in this case is due to the electric field, which will cause a deflection. However, the assertion states that it is "always deflected," which is misleading because if the electric field is also zero, there would be no deflection.

**Conclusion**: The assertion is incorrect.

### Step 2: Analyze the Reason (R)
The reason states: "If the velocity of electrons is equal to the ratio of magnetic and electric field in crossed fields applied, then the electron beam remains undeflected."

- For an electron to remain undeflected in crossed electric and magnetic fields, the following condition must hold:
\[ \vec{E} = \vec{v} \times \vec{B} \]
or equivalently,
\[ v = \frac{E}{B} \]
where \( E \) is the electric field strength and \( B \) is the magnetic field strength.

- The reason states that the velocity of the electrons is equal to the ratio of magnetic and electric fields. However, it should be the ratio of electric field to magnetic field for the electron to remain undeflected. Therefore, the statement is incorrect.

**Conclusion**: The reason is also incorrect.

### Final Conclusion
Both the assertion and the reason are incorrect. Therefore, the correct answer is that both statements are false.