Which test should be considered necessarily to verify the consistency while we select an appropriate index formula

In price index, when a new commodity is required to be added, which of the following index is used?

Fisher's ideal formula for calculating index number satisfies the ________

Shifted Price Index = $\displaystyle \frac{\text{Original Price Index}}{\text{Price Index of the year on which it has to be shifted}} \times 100$

If Laspeyres's Index Number is 250 and Paasche's Index Number is 160, then Fisher's Index number is

If $\displaystyle \sum P_0q_0 = 240$, $\displaystyle \sum P_1q_0 = 480$, $\displaystyle \sum P_0q_1 = 600$ and $\displaystyle \sum P_1q_1 = 192$, then Laspeyres's Index Number is

If $\displaystyle \Sigma P_n q_n = 249$, $\displaystyle \Sigma P_0 q_0 = 150$, $\displaystyle \Sigma P_n q_0 = 145$ and Paasche's Index Number = 150, then Fisher's Ideal Price Index Number is