Which of the following hydroxides is the most basic?

Fill in the blanks:
$1.$ The size of $M^{3+}$ ions in the actinoid series ........... with an increase in atomic number.
$2.$ The common oxidation state of elements in the actinoid series is .......... .
$3.$ The appearance of elements in the actinoid series is like .......... .

Which of the following statements related to lanthanoids is incorrect?

The main reason for the larger number of oxidation states exhibited by the actinoids compared to the corresponding lanthanoids is:

Discuss the trends in oxidation states shown by actinoids.

Rare-earth elements are exhibited by