Two charges of $$5Q$$ and $$-2Q$$ are situated at the points $$(3a, 0)$$ and $$(-5a, 0)$$ respectively. The electric flux through a sphere of radius $$4a$$ having centre at origin is:

We need to find the electric flux through a sphere of radius $$4a$$ centered at origin with charges $$5Q$$ at $$(3a, 0)$$ and $$-2Q$$ at $$(-5a, 0)$$.

The sphere has radius $$4a$$ and center at origin.

Charge $$5Q$$ at $$(3a, 0)$$: distance from origin = $$3a < 4a$$. Inside the sphere.

Charge $$-2Q$$ at $$(-5a, 0)$$: distance from origin = $$5a > 4a$$. Outside the sphere.

$$\Phi = \frac{Q_{enclosed}}{\varepsilon_0} = \frac{5Q}{\varepsilon_0}$$

The electric flux is $$\frac{5Q}{\varepsilon_0}$$, which matches Option B.

Therefore, the answer is Option B.