Step 1: Understanding the Concept:
This question tests general knowledge of the properties of $f$-block elements, including physical properties, reactivity, and electronic configurations.
Step 2: Detailed Explanation:
Statement (a): Lanthanoids are silvery-white metals. Like almost all transition and inner-transition metals, they possess delocalized valence electrons that allow for the conduction of heat and electricity. This is a correct statement.
Statement (b): Actinoids are indeed very reactive. They react with boiling water, dilute acids, and non-metals. When they are finely divided (powdered), their surface area increases, making them extremely reactive (even pyrophoric in some cases). This is a correct statement.
Statement (c): Actinoid contraction refers to the decrease in atomic/ionic radii across the series. It is greater than Lanthanoid contraction because $5f$ electrons have even poorer shielding effects than $4f$ electrons. As a result, the nucleus exerts a stronger pull on the outer shells. This is a correct statement.
Statement (d): Trivalent lanthanoid ions ($Ln^{3+}$) typically have partially filled $4f$ subshells ($4f^1$ to $4f^{13}$). These ions undergo $f-f$ transitions, which fall in the visible region of the spectrum, giving them characteristic colors. For example, $Pr^{3+}$ is green, $Nd^{3+}$ is pink/violet, and $Er^{3+}$ is pink. Only ions with $f^0, f^7,$ or $f^{14}$ configurations (like $La^{3+}, Gd^{3+}, Lu^{3+}$) are typically colourless. Since most have other configurations, most are coloured. This statement is incorrect.
Step 3: Final Answer:
Statement (d) is the false statement.