A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :
`(A)` By changing the magnitude of the magnetic field within the coil.
(B) By changing the area of coil within the magnetic field.
(C) By changing the angle between the direction of magnetic field and the plane of the coil.
(D) By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below :

Options

A. `A `and `C` only
B. `A`, `B` and `C` only
C. `A`, `B` and `D` only
D. `A` and `B`only

Answer

To solve the problem, we need to determine how the magnetic flux through a coil can be changed when the plane of the coil is perpendicular to the direction of the magnetic field. The magnetic flux (Φ) through a coil is given by the formula:

\[ Φ = B \cdot A \cdot \cos(θ) \]

Where:
- \(Φ\) is the magnetic flux,
- \(B\) is the magnetic field strength,
- \(A\) is the area of the coil,
- \(θ\) is the angle between the magnetic field and the normal (perpendicular) to the plane of the coil.

Since the plane of the coil is perpendicular to the magnetic field, the angle \(θ\) is 0 degrees, and thus \(\cos(θ) = 1\). Therefore, the magnetic flux simplifies to:

\[ Φ = B \cdot A \]

Now, let's analyze each option given in the question:

**(A)** By changing the magnitude of the magnetic field within the coil.
- Yes, changing \(B\) will change the magnetic flux \(Φ\). This option is correct.

**(B)** By changing the area of the coil within the magnetic field.
- Yes, changing the area \(A\) will also change the magnetic flux \(Φ\). This option is correct.

**(C)** By changing the angle between the direction of the magnetic field and the plane of the coil.
- Since the coil is perpendicular to the magnetic field, the angle \(θ\) is 0 degrees. If we change the angle, it will affect the flux. This option is correct.

**(D)** By reversing the magnetic field direction abruptly without changing its magnitude.
- Reversing the direction of the magnetic field does not change the magnitude of the magnetic field, but it does change the direction of the magnetic field. However, since the magnitude remains the same, the flux will still be calculated with the same value of \(B\) and \(A\). This option is incorrect.

Thus, the correct options are (A), (B), and (C). Since the question asks for the most appropriate answer, we can conclude that options (A), (B), and (C) are valid, but (D) is not.

### Final Answer:
The most appropriate answer is: **(A), (B), and (C)**.