Step 1: Analyze each statement
Statement (A):
The correct order of atomic radii in group 13 elements is \(\text{Tl} > \text{In} > \text{Al} > \text{Ga} > \text{B}\), not \(\text{Tl} > \text{In} > \text{Ga} > \text{Al} > \text{B}\).
- This statement is incorrect.
2.Statement (B):
Down the group, electronegativity generally decreases. However, due to the presence of \(d\)-electrons in \(\text{Ga}\), \(\text{In}\), and \(\text{Tl}\), their electronegativity values do not follow a simple trend.
- This statement is incorrect.
3.Statement (C):
\(\text{Al}\) reacts with dilute \(\text{HCl}\) to release \(\text{H}_2\):
\[2\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2.\]
Concentrated \(\text{HNO}_3\) forms a passive oxide layer on \(\text{Al}\), protecting it from further reaction.
- This statement is correct.
4.Statement (D):
In group 13, the \(+3\) oxidation state is more stable than \(+1\). The \(+1\) state is exhibited by \(\text{Tl}\) due to the inert pair effect, but it is
not highly stable for all elements.
- This statement is incorrect.
5.Statement (E):
In \([\text{Al}(\text{H}_2\text{O})_6]^{3+}\), the hybridization of \(\text{Al}\) is \(\text{sp}^3\text{d}^2\), corresponding to an octahedral geometry. - This statement is correct.
Step 2: Conclusion
The correct statements are (C) and (E).
Final Answer: (1).
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to: