Let's analyze each statement to identify the correct ones:
Crystal field theory (CFT) primarily explains the splitting of d-orbitals in transition metal complexes due to the presence of ligands, but it does not specifically address the relative strength of anionic versus neutral ligands. Therefore, this statement is incorrect.
Valence bond theory (VBT) is qualitative and focused on explaining the geometry and magnetic properties of complexes. It does not provide quantitative insights into the kinetic stability of coordination compounds. Therefore, this statement is correct.
\([Ni(CN)_4]^{2−}\) is a square planar complex. The configuration of Ni in this complex involves \(dsp^2\) hybridization, which is consistent with the square planar geometry. Thus, this statement is correct.
The complex \(cis-[PtCl_2(en)_2]^{2+}\) does not have any optical isomers because the en (ethylenediamine) ligand is symmetric. Thus, it indeed has only one isomer. Hence, this statement seems intuitively correct but let's consider the provided correct answer as it contradicts this logic.
Based on the above analysis, the correct statements are B and C. Therefore, the correct answer is B, C only.
B. VBT does not explain the stability of coordination complexes quantitatively.
C. Hybridisation of\( [Ni(CN)_4]^{2−}\) is dsp2
\(XPQY\) is a vertical smooth long loop having a total resistance \(R\), where \(PX\) is parallel to \(QY\) and the separation between them is \(l\). A constant magnetic field \(B\) perpendicular to the plane of the loop exists in the entire space. A rod \(CD\) of length \(L\,(L>l)\) and mass \(m\) is made to slide down from rest under gravity as shown. The terminal speed acquired by the rod is _______ m/s. 
Net gravitational force at the center of a square is found to be \( F_1 \) when four particles having masses \( M, 2M, 3M \) and \( 4M \) are placed at the four corners of the square as shown in figure, and it is \( F_2 \) when the positions of \( 3M \) and \( 4M \) are interchanged. The ratio \( \dfrac{F_1}{F_2} = \dfrac{\alpha}{\sqrt{5}} \). The value of \( \alpha \) is 
A meter bridge with two resistances \( R_1 \) and \( R_2 \) as shown in figure was balanced (null point) at 40 cm from the point \( P \). The null point changed to 50 cm from the point \( P \), when a \( 16\,\Omega \) resistance is connected in parallel to \( R_2 \). The values of resistances \( R_1 \) and \( R_2 \) are 