Therefore, the correct answer is (B) I, III, and IV.
I. The complex has octahedral geometry:
The\( [CoF_6]^{3−}[CoF_6]^{3-}[CoF6]^{3−}\) complex has a coordination number of 6 because it is coordinated to 6 fluoride ions. Thus, the complex will have octahedral geometry.
This statement is true.
II. Coordination number of Co is 3 and oxidation state is +6:
The coordination number of \( [CoF_6]^{3−}[CoF_6]^{3-}[CoF6]^{3−}\) is 6, as it is bonded to 6 fluoride ions. The oxidation state of cobalt is calculated as follows:
The charge of the fluoride ion is -1, and there are 6 fluoride ions, so the total charge contributed by fluoride is -6. The overall charge on the complex is -3, so the charge on Co must be +3.
Therefore, the oxidation state of Co is +3, not +6.
This statement is false.
III. The complex is sp³d² hybridised:
The coordination number of 6 indicates that the central metal ion is involved in six bonds, which leads to sp³d² hybridisation in an octahedral arrangement.
This statement is true.
IV. It is a high-spin complex:
Cobalt in the +3 oxidation state has an electron configuration that typically results in a low-spin complex when paired with ligands like fluoride. However, fluoride is a weak field ligand, which does not favor spin pairing, and the complex will not be high-spin.
This statement is false.
Thus, the correct answer is (B) I, III and IV.
Given below are two statements regarding conformations of n-butane. Choose the correct option. 
Consider a weak base \(B\) of \(pK_b = 5.699\). \(x\) mL of \(0.02\) M HCl and \(y\) mL of \(0.02\) M weak base \(B\) are mixed to make \(100\) mL of a buffer of pH \(=9\) at \(25^\circ\text{C}\). The values of \(x\) and \(y\) respectively are
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2