Concept:
Dye uptake depends on dye concentration, liquor ratio, diffusion rate, and fibre affinity. However, increase in dye availability does not always directly increase dye uptake due to equilibrium and saturation limits.
Step 1: Analyze Assertion [A].
• Dye uptake depends on affinity and diffusion equilibrium
• Simply increasing dye quantity does not guarantee higher uptake
So, Assertion [A] is not universally true.
Step 2: Analyze Reason [R].
• Lower liquor ratio increases dye concentration
• Higher concentration increases molecular mobility and collision frequency
So Reason [R] is true.
Step 3: Final evaluation.
• [A] is false
• [R] is true
\[
\boxed{\text{Option (C)}}
\]