Assertion A: Product of Pressure ($$P$$) and time ($$t$$) has the same dimension as that of coefficient of viscosity.
Reason: Coefficient of viscosity = $$\frac{\text{Force}}{\text{Velocity gradient}}$$

We need to check both the Assertion and the Reason.

Checking Assertion A: Dimension of P × t

Pressure $$P$$ has dimensions: $$[P] = [ML^{-1}T^{-2}]$$

Time $$t$$ has dimensions: $$[t] = [T]$$

So, $$[P \times t] = [ML^{-1}T^{-2}] \times [T] = [ML^{-1}T^{-1}]$$

Dimension of coefficient of viscosity ($$\eta$$):

From the formula: $$\eta = \frac{F}{A \times \text{velocity gradient}}$$

Velocity gradient = $$\frac{dv}{dx}$$ has dimensions $$[T^{-1}]$$

So, $$[\eta] = \frac{[MLT^{-2}]}{[L^2][T^{-1}]} = \frac{[MLT^{-2}]}{[L^2T^{-1}]} = [ML^{-1}T^{-1}]$$

Since $$[P \times t] = [ML^{-1}T^{-1}] = [\eta]$$, the Assertion is TRUE.

Checking Reason R:

The Reason states: Coefficient of viscosity = $$\frac{\text{Force}}{\text{Velocity gradient}}$$

The correct formula is: $$F = \eta A \frac{dv}{dx}$$, which gives $$\eta = \frac{F}{A \times \frac{dv}{dx}}$$

The Reason is missing the area $$A$$ in the denominator. So the Reason is FALSE.

Since Assertion A is true but Reason R is false, the correct answer is Option C.