Match List - I with List - II: 
Choose the correct answer from the given below options
- Structure (A) corresponds to a molecule with a methyl group attached to a pentene, and the correct IUPAC name is 4-methylpent-1-ene, so (A)-(I).
- Structure (B) is a dimethyl-substituted heptane, and the correct IUPAC name is 4, 4-dimethylheptane, so (B)-(III).
- Structure (C) is a compound with an ethyl group and a methyl group attached to a heptane chain, and the correct name is 3-ethyl-5-methylheptane, so (C)-(II).
- Structure (D) is a compound with a methyl group and a pentadiene chain, and the correct name is 2-methyl-1,3-pentadiene, so (D)-(IV).
Thus, the correct matching is (A)-(I), (B)-(III), (C)-(II), (D)-(IV).
Which of the following is the correct IUPAC name of the given organic compound (X)?
The structure of compound $ X $ is as follows:
$ \text{H}_3\text{C} - \text{CH}_3 - \text{CH} = \text{CH} - \text{H} - \text{Br} $
The IUPAC name of the following compound is:

The correct IUPAC name of the compound is: 
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.