Among the following,the compound that is both paramagnetic and coloured is

Which of the following statements is false?

$I$. $4FeCr_2O_4 + 16NaOH + 7O_2 \rightarrow 8Na_2CrO_4 + 2Fe_2O_3 + 8H_2O$ (where $A = Na_2CrO_4$)
$II$. $2Na_2CrO_4 + H_2SO_4 \rightarrow Na_2Cr_2O_7 + Na_2SO_4 + H_2O$ (where $B = H_2SO_4$)
Compounds $(A)$ and $(B)$ are :

The green paramagnetic species formed by heating $KMnO_4$ at $513 \ K$ is

Identify the correctly matched pairs:
$(i)$ $TiO_2$ - pigment industry
$(ii)$ $MnO_2$ - dry battery cells
$(iii)$ $Cu/Ni$ alloy - $UK$ 'copper' coins

Fusion of $MnO_2$ with $KOH$ in presence of $O_2$ produces a salt $W$. Alkaline solution of $W$ upon electrolytic oxidation yields another salt $X$. The manganese containing ions present in $W$ and $X$,respectively,are $Y$ and $Z$. Correct statement$(s)$ is (are)
$(1)$ $Y$ is diamagnetic in nature while $Z$ is paramagnetic
$(2)$ Both $Y$ and $Z$ are coloured and have tetrahedral shape
$(3)$ In both $Y$ and $Z$,$\pi$-bonding occurs between $p$-orbitals of oxygen and $d$-orbitals of manganese.
$(4)$ In aqueous acidic solution,$Y$ undergoes disproportionation reaction to give $Z$ and $MnO_2$.