Preparation of potassium permanganate from $MnO_2$ involves a two-step process in which the $1^{st}$ step is a reaction with $KOH$ and $KNO_3$ to produce:

Fill in the blanks:
$1.$ Heating lanthanoids with sulfur gives .......
$2.$ Mixed oxides of lanthanoids are used as catalysts in ..........

Correct statement for $CeO_2$ is/are:
$1$. It is diamagnetic in nature.
$2$. It is a good oxidising agent.
$3$. It is a colourless compound.

Which of the following are used as catalysts in petroleum cracking?

Which one of the following is an amphoteric oxide?

Fill in the blanks:
$(1)$ ......... acid is added to perform titrations with $KMnO_4$ and $K_2Cr_2O_7$.
$(2)$ Crystals of potassium dichromate are of ......... color,while crystals of potassium chromate are of ......... color.
$(3)$ The color of $MnO_4^{2-}$ is ......... and the color of $MnO_4^-$ is ......... .