Two bubbles A and B (A > B) are joined through a narrow tube. Then

The correct option is: The size of A will increase.

To understand why this happens, we must look at the relationship between the size of a soap bubble and the excess pressure inside it.
The excess pressure $P$ inside a spherical soap bubble of radius $R$ in air is given by the formula:
$P=\frac{4T}{R}$
where $T$ is the surface tension of the soap solution.

This formula shows that the excess pressure is inversely proportional to the radius of the bubble:
$P\propto \frac{1}{R}$

We are given two bubbles, A and B, where bubble A is larger than bubble B.
Let $R_A$ be the radius of bubble A and $R_B$ be the radius of bubble B. Since A > B, we have:
$R_A>R_B$

Since excess pressure is inversely proportional to the radius, the pressure inside the smaller bubble B ($P_B$) will be greater than the pressure inside the larger bubble A ($P_A$):
$P_B>P_A$

When the two bubbles are connected by a narrow tube, air flows from the region of higher pressure to the region of lower pressure. Therefore, air will flow from the smaller bubble B (higher pressure) into the larger bubble A (lower pressure).

As air leaves bubble B, it shrinks (its size decreases), and as air enters bubble A, it expands (its size increases). Thus, the size of A will increase.