Given below are two statements:
Statement I : The diamagnetic property depends on temperature.
Statement II : The included magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.
In the light of given statement, choose the correct answer from the options given below:
Step 1: Analyzing the given statements
Statement I: Diamagnetic properties are independent of temperature. Therefore, Statement I is incorrect.
Statement II: In diamagnetic materials, the induced magnetic dipole moment is opposite to the external magnetic field, which makes Statement II true.
Thus, the correct answer is that Statement I is incorrect, and Statement II is true.

An infinite wire has a circular bend of radius \( a \), and carrying a current \( I \) as shown in the figure. The magnitude of the magnetic field at the origin \( O \) of the arc is given by:

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: