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${\text{BC}}{{\text{l}}_{\text{3}}}$ molecule is planar while ${\text{NC}}{{\text{l}}_{\text{3}}}$ molecule is pyramidal because:
(A) ${\text{BC}}{{\text{l}}_{\text{3}}}$ does not have lone pair on B but ${\text{NC}}{{\text{l}}_{\text{3}}}$ has a lone pair of electron on N.
(B) B-Cl bond is more polar than N-Cl bond.
(C) N atoms are smaller than B atoms.
(D) N-Cl bond is more covalent than B-Cl bond.

Answer
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Hint: In the above question, we are asked why the structure of ${\text{BC}}{{\text{l}}_{\text{3}}}$ and ${\text{NC}}{{\text{l}}_{\text{3}}}$ is different. The reason for this is that the presence and absence of lone pairs decides the structure of the molecule.

Complete step by step solution
Since, we are asked about the structure difference between ${\text{BC}}{{\text{l}}_{\text{3}}}$ and ${\text{NC}}{{\text{l}}_{\text{3}}}$. Let us first calculate the number of bond pairs and lone pairs present in the molecule.
For ${\text{BC}}{{\text{l}}_{\text{3}}}$:
Atomic number of B = 5
We know that the maximum number of electrons present in a particular shell is given by ${\text{2}}{{\text{n}}^{\text{2}}}$. Hence, in the first shell only two electrons are present, and the rest three in the second shell.
So, number of valence electrons = 3
Number of chlorine atom attached to it = 3
There is no lone pair. Hence, the shape is planar.
For ${\text{NC}}{{\text{l}}_{\text{3}}}$:
Atomic number of N = 7
So, in the first shell only two electrons and rive five electrons in the second shell.
Number of valence electrons = 5
Number of chlorine atom attached to it = 3
Two electrons are left which forms a lone pair. The lone pair bond pair repulsion is more than the bond pair bond pair repulsion. And hence, the structure of ${\text{NC}}{{\text{l}}_{\text{3}}}$ is pyramidal.
So we can conclude that ${\text{BC}}{{\text{l}}_{\text{3}}}$ molecule is planar whereas ${\text{NC}}{{\text{l}}_{\text{3}}}$ molecule is pyramidal because ${\text{BC}}{{\text{l}}_{\text{3}}}$ does not have lone pair on B but ${\text{NC}}{{\text{l}}_{\text{3}}}$ has a lone pair of electron on N.
Therefore, the correct option is Option-A.

Note
In this type of question, first we have to find out the number of valence electrons present on the central atom. Then we can decide the structure keeping in mind if there is any lone pair or not.