Match List-I with List-II and select the correct option.
Step 1: Analyze the given complexes and their coordination geometry
\([NiCl_4]^{2-}\) is a tetrahedral complex, typically exhibiting \(sp^3\) hybridization.
It also has a magnetic moment of 3.87 BM.
\([Ni(CN_4)]^{2-}\) is a square planar complex, usually exhibiting \(dsp^2\) hybridization.
It shows no unpaired electrons, so the magnetic moment is 0 BM.
\([CoCl_4]^{2-}\) is an octahedral complex, usually with \(sp^3d^2\) hybridization.
Its magnetic moment is 2.82 BM.
\([Ni(H_2O)_6]^{2+}\) is a tetrahedral complex, exhibiting \(sp^3\) hybridization and a magnetic moment of 2.82 BM.
Step 2: Match the complexes with their characteristics
A.
\([NiCl_4]^{2-}\) matches with IV.
\(sp^3\), tetrahedral, 3.87 BM.
B.
\([Ni(CN_4)]^{2-}\) matches with II.
\(dsp^2\), square planar, 0 BM.
C.
\([CoCl_4]^{2-}\) matches with I.
\(sp^3d^2\), octahedral, 2.82 BM.
D.
\([Ni(H_2O)_6]^{2+}\) matches with III.
\(sp^3\), tetrahedral, 2.82 BM.
A solution of aluminium chloride is electrolyzed for 30 minutes using a current of 2A. The amount of the aluminium deposited at the cathode is _________
If \[ \int \frac{2x^2 + 5x + 9}{\sqrt{x^2 + x + 1}} \, dx = \sqrt{x^2 + x + 1} + \alpha \sqrt{x^2 + x + 1} + \beta \log_e \left( \left| x + \frac{1}{2} + \sqrt{x^2 + x + 1} \right| \right) + C, \] where \( C \) is the constant of integration, then \( \alpha + 2\beta \) is equal to ________________