Check statement (A): atomic radii order in group 13

Group 13 elements are $\mathrm{B, Al, Ga, In, Tl}$.

Due to poor shielding by $d$ and $f$ electrons, the size trend is not perfectly regular. In particular:

• $\mathrm{Ga}$ is smaller than expected and is very close to/almost equal to $\mathrm{Al}$ due to $d$-block contraction.
• $\mathrm{Tl}$ is close to $\mathrm{In}$ because of lanthanoid contraction.

The simple decreasing order $\mathrm{Tl > In > Ga > Al > B}$ is not correct, because generally $\mathrm{Al}$ is slightly larger than $\mathrm{Ga}$.

So, (A) is false.

Check statement (B): electronegativity decreases from top to bottom

In group 13, electronegativity does not decrease regularly down the group. Approximate trend: $\mathrm{B} > \mathrm{Al} < \mathrm{Ga} \approx \mathrm{In} < \mathrm{Tl}$ There are irregularities because of poor shielding by intervening $d$ and $f$ electrons.

Hence the statement "down the group 13 electronegativity decreases from top to bottom" is false.

Check statement (C): behavior of Al with acids

• Aluminum dissolves in dilute $\mathrm{HCl}$: $2\mathrm{Al} + 6\mathrm{HCl} \rightarrow 2\mathrm{AlCl}_3 + 3\mathrm{H}_2$
• Concentrated $\mathrm{HNO}_3$ makes Al passive by forming a protective oxide film on the surface.

Therefore, (C) is true.

Check statement (D): all group 13 elements exhibit highly stable +1 oxidation state

Group 13 elements generally show +3 oxidation state. The +1 oxidation state becomes more stable only for heavier members due to the inert pair effect, especially for $\mathrm{Tl}$.

Thus, it is wrong to say that all group 13 elements exhibit highly stable $+1$ oxidation state.

So, (D) is false.

Check statement (E): hybridisation in $[\mathrm{Al}(\mathrm{H_2O})_6]^{3+}$

In the hexaaqua complex, Al is coordinated by 6 water molecules, so the coordination number is 6. Such a structure is octahedral, and in classical hybridisation language this is written as: $\mathrm{sp}^3\mathrm{d}^2$

Therefore, (E) is true.

Collect the correct statements

• (A) False
• (B) False
• (C) True
• (D) False
• (E) True

Hence the correct set is: $\boxed{(C)\text{ and }(E)\text{ only}}$

Match with options

This corresponds to Option B.