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(D) To determine which molecules have a non-zero dipole moment,we analyze the symmetry of each:$I$. Gauche conformation of $1, 2$-dibromoethane: Due t

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$I, IV$ and $VI$

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(D) To determine which molecules have a non-zero dipole moment,we analyze the symmetry of each:$I$. Gauche conformation of $1, 2$-dibromoethane: Due to the gauche arrangement,the dipole moments of the $C-Br$ bonds do not cancel out,resulting in a non-zero net dipole moment.$II$. Anti conformation of $1, 2$-dibromoethane: The $C-Br$ bond dipoles are equal and opposite,canceling each other out. The net dipole moment is zero.$III$. Trans-$1, 4$-dibromocyclohexane: In the chair conformation,the two $Br$ atoms are in equatorial positions or axial positions such that the dipoles cancel out due to the center of inversion. The net dipole moment is zero.$IV$. Cis-$1, 4$-dibromocyclohexane: The molecule lacks a center of inversion,and the dipoles of the $C-Br$ bonds do not cancel out. The net dipole moment is non-zero.$V$. Tetrabromomethane $(CBr_4)$: This molecule has a tetrahedral geometry ($T_d$ symmetry),where the four $C-Br$ bond dipoles cancel each other out. The net dipole moment is zero.$VI$. $1, 1$-dibromocyclohexane: The two $C-Br$ bonds are on the same carbon atom,and their dipoles do not cancel out. The net dipole moment is non-zero.Therefore,molecules $I, IV,$ and $VI$ have non-zero dipole moments. The correct option is $D$.

Which of the following molecules have non-zero dipole moments?
$I$. Gauche conformation of $1, 2$-dibromoethane
$II$. Anti conformation of $1, 2$-dibromoethane
$III$. Trans-$1, 4$-dibromocyclohexane
$IV$. Cis-$1, 4$-dibromocyclohexane
$V$. Tetrabromomethane
$VI$. $1, 1$-dibromocyclohexane

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Which of the following molecules have non-zero dipole moments?$I$. Gauche conformation of $1, 2$-dibromoethane$II$. Anti conformation of $1, 2$-dibromoethane$III$. Trans-$1, 4$-dibromocyclohexane$IV$. Cis-$1, 4$-dibromocyclohexane$V$. Tetrabromomethane$VI$. $1, 1$-dibromocyclohexane