Let's analyze each statement:

Statement (I): $s{p}^3$ hybrid orbitals are at $90^{\circ }$ to one another.

In $s{p}^3$ hybridization, the four hybrid orbitals are directed towards the corners of a tetrahedron, and the angle between any two $s{p}^3$ hybrid orbitals is approximately $109.5^{\circ }$. Therefore, this statement is False.

Statement (II): $s{p}^3{d}^2$ adjacent hybrid orbitals are at $90^{\circ }$ to one another.

In $s{p}^3{d}^2$ hybridization, the six hybrid orbitals are directed towards the corners of an octahedron. The adjacent orbitals are at $90^{\circ }$ to each other, and opposite orbitals are at $180^{\circ }$. Therefore, this statement is True.

Statement (III): $s{p}^2$ hybrid orbitals are at $120^{\circ }$ to one another.

In $s{p}^2$ hybridization, the three hybrid orbitals lie in a plane and are directed towards the corners of an equilateral triangle. The angle between any two $s{p}^2$ hybrid orbitals is $120^{\circ }$. Therefore, this statement is True.

Statement (IV): Bond order of N-O bond in $N{O}_3^{-}$ is 1.33.

The nitrate ion ($N{O}_3^{-}$) has three resonance structures. In each resonance structure, there is one N=O double bond and two N-O single bonds. The total number of bonds between nitrogen and oxygen is 4 (one double bond and two single bonds). The number of resonating structures is 3. Therefore, the bond order = (Total number of bonds) / (Total number of resonating structures) = $4/3=1.33$. Therefore, this statement is True.

Based on the analysis, the truth values for the statements are F, T, T, T.

Option Analysis:

• A) T F T F: Incorrect, as statement (I) is False and (II) is True.
• B) T T F F: Incorrect, as statement (I) is False and (III) and (IV) are True.
• C) F T T T: Correct, as statements (I) is False, and (II), (III), (IV) are True.
• D) F T F T: Incorrect, as statement (III) is True.

Correct Answer: (C)