As per the VSEPR theory, shapes of SO₃^2-,CO₃^2- and BrF₄^- are, respectively

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Correct option is C

​​Valence shell electron pair repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other. The greater the repulsion, the higher in energy (less stable) the molecule is. Therefore, the VSEPR-predicted molecular geometry of a molecule is the one that has as little of this repulsion as possible.
VSEPR theory is used to predict the arrangement of electron pairs around central atoms in molecules, especially simple and symmetric molecules. A central atom is defined in this theory as an atom which is bonded to two or more other atoms, while a terminal atom is bonded to only one other atom.
The overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. The bonding electron pair shared in a sigma bond with an adjacent atom lies further from the central atom than a nonbonding (lone) pair of that atom, which is held close to its positively charged nucleus. VSEPR theory therefore views repulsion by the lone pair to be greater than the repulsion by a bonding pair. As such, when a molecule has 2 interactions with different degrees of repulsion, VSEPR theory predicts the structure where lone pairs occupy positions that allow them to experience less repulsion. Lone pair–lone pair (lp–lp) repulsions are considered stronger than lone pair–bonding pair (lp–bp) repulsions, which in turn are considered stronger than bonding pair–bonding pair (bp–bp) repulsions, distinctions that then guide decisions about overall geometry when 2 or more non-equivalent positions are possible
The electronic geometry of a molecule depends on the number of bond pairs and lone pairs, while the shape depends only on the number of bond pairs.
The steric number of a central atom in a molecule is the number of atoms bonded to that central atom, called its coordination number, plus the number of lone pairs of valence electrons on the central atom.

SO₃^2-:The structure of the sulfite anion can be described with three equivalent resonance structures. In each resonance structure, the sulfur atom is double-bonded to one oxygen atom with a formal charge of zero (neutral), and sulfur is singly bonded to the other two oxygen atoms, which each carry a formal charge of −1, together accounting for the −2 charge on the anion. There is also a non-bonded lone pair on the sulfur, so the structure predicted by VSEPR theory is trigonal pyramidal. In the hybrid resonance structure, the S−O bonds are equivalently of bond order one and one-third.

Sulfur is a six electron donor. Oxygen is a six electron donor. Stearic number is 4. Hybridization is sp³. Geometry is tetrahedral. Shape is trigonal pyramidal.

CO₃^2-:The carbonate ion is the simplest oxocarbon anion. It consists of one carbon atom surrounded by three oxygen atoms, in a trigonal planar arrangement.

Carbon is a four electron donor. Stearic number is 3. Hybridization is sp². Geometry (and shape) is trigonal planar.

BrF₄^-: Bromine is a seven electron donor. Fluorine is a seven electron donor. Stearic number is 6. Hybridization is sp³d². Geometry is octahedral. Shape is square planar.