Which of the following do not exist?

$A$ circular loop of radius $R$ carrying current $I$ lies in the $x-y$ plane with its centre at the origin. The total magnetic flux through the $x-y$ plane is:

Imagine rolling a sheet of paper into a cylinder and placing a bar magnet near its end as shown in the figure. What can you say about the sign of $\vec B \cdot d\vec A$ for every area element $d\vec A$ on the surface of the cylinder?

The dimensional formula of magnetic flux is:

$A$ coil is placed in a magnetic field such that the plane of the coil is perpendicular to the direction of the magnetic field. The magnetic flux $\phi$ through the coil can be changed by:
$(A)$ Changing the magnitude of the magnetic field $B$.
$(B)$ Changing the area of the coil $A$.
$(C)$ Changing the angle $\theta$ between the magnetic field and the plane of the coil.
$(D)$ Reversing the direction of the magnetic field.

Assertion $(A)$: Magnetic flux is a vector quantity.
Reason $(R)$: Value of magnetic flux can be positive, negative, or zero.