Borazine, also known as "inorganic benzene," has the molecular formula \( \text{B}_3\text{N}_3\text{H}_6 \) and is a six-membered cyclic compound. It has the following characteristics:
- It is indeed a cyclic compound, so statement (1) is correct.
- Borazine exhibits electronic delocalization similar to benzene due to the alternating single and double bonds between boron and nitrogen, making statement (2) correct.
- Borazine can react with water to form boric acid and ammonia, so statement (3) is also correct.
- The term "banana bonds" typically refers to bonds in compounds like diborane, where boron atoms form unconventional bonds with hydrogen. Borazine does not contain banana bonds; instead, it has regular covalent bonds. Therefore, statement (4) is incorrect.
Thus, the incorrect statement is (4).
Given below are two statements. 
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements:
Statement I: Nitrogen forms oxides with +1 to +5 oxidation states due to the formation of $\mathrm{p} \pi-\mathrm{p} \pi$ bond with oxygen.
Statement II: Nitrogen does not form halides with +5 oxidation state due to the absence of d-orbital in it.
In the light of the above statements, choose the correct answer from the options given below:
Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. $(\mathrm{B}<\mathrm{Al}),(\mathrm{Al}<\mathrm{Ga}),(\mathrm{Ga}<\mathrm{In})$ and $(\mathrm{In}<\mathrm{Tl})$ Identify the elements present in the incorrect pair and in that pair find out the element (X) that has higher ionic radius $\left(\mathrm{M}^{3+}\right)$ than the other one. The atomic number of the element (X) is

Let \( a \in \mathbb{R} \) and \( A \) be a matrix of order \( 3 \times 3 \) such that \( \det(A) = -4 \) and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where \( I \) is the identity matrix of order \( 3 \times 3 \).
If \( \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) \) is \( 2^m 3^n \), \( m, n \in \{ 0, 1, 2, \dots, 20 \} \), then \( m + n \) is equal to: