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(C) Ionic radii of trivalent cations increase down the group due to the addition of new shells: $B^{3+} < Al^{3+} < Ga^{3+} < In^{3+} < Tl^{3+}$. Thus

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$C$ and $D$ only

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(C) Ionic radii of trivalent cations increase down the group due to the addition of new shells: $B^{3+} $(B)$ Electronegativity does not decrease regularly down the group due to poor shielding of $d$ and $f$ orbitals: $B > Tl > In > Ga > Al$. Thus, statement $(B)$ is incorrect.$(C)$ Boron has the smallest atomic size in the group, leading to the highest first ionisation enthalpy: $B > Tl > Ga > Al > In$. Thus, statement $(C)$ is correct.$(D)$ According to Fajan's rule, small cations with high charge density form covalent bonds. Trichlorides and triiodides of group $13$ elements are covalent in nature. Thus, statement $(D)$ is correct.

List-$I$ (Element)	List-$II$ (Application)
$A$. $Cs$	$I$. High temperature thermometer
$B$. $Ga$	$II$. Water repellent sprays
$C$. $B$	$III$. Photoelectric cells
$D$. $Si$	$IV$. Bullet proof vest

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