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).
Match the following:
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - ax - b = 0 \) with \( \text{Im}(\alpha) < \text{Im}(\beta) \). Let \( P_n = \alpha^n - \beta^n \). If \[ P_3 = -5\sqrt{7}, \quad P_4 = -3\sqrt{7}, \quad P_5 = 11\sqrt{7}, \quad P_6 = 45\sqrt{7}, \] then \( |\alpha^4 + \beta^4| \) is equal to:
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).