(a) Activity of a catalyst:

The activity of a catalyst is its ability to increase the rate of a particular reaction. Chemisorption is the main factor in deciding the activity of a catalyst. The adsorption of reactants on the catalyst surface should be neither too strong nor too weak. It should just be strong enough to make the catalyst active. 

(b) Selectivity of the catalyst:

The ability of the catalyst to direct a reaction to yield a particular product is referred to as the selectivity of the catalyst. For example, by using different catalysts, we can get different products for the reaction between ${\mathrm{H}}_2$ and CO. 

The example are as follows:

$\mathbf{\left(}\mathbf{I}\mathbf{\right)}\mathbf{ }{\mathrm{CO}}_{\left(\mathrm{g}\right)}+3{\mathrm{H}}_{2\left(\mathrm{g}\right)}\stackrel{\mathrm{Ni}}{\to }{\mathrm{CH}}_{4\left(\mathrm{g}\right)}+{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{g}\right)}$

$\mathbf{\left(}\mathbf{II}\mathbf{\right)}\mathbf{ }{\mathrm{CO}}_{\left(\mathrm{g}\right)}+2{\mathrm{H}}_{2\left(\mathrm{g}\right)}\stackrel{\mathrm{Cu}/\mathrm{ZnO}-{\mathrm{CrO}}_3}{\to }{\mathrm{CH}}_3{\mathrm{OH}}_{\left(\mathrm{g}\right)}$

$\mathbf{\left(}\mathbf{III}\mathbf{\right)}\mathbf{ }{\mathrm{CO}}_{\left(\mathrm{g}\right)}+{\mathrm{H}}_{2\left(\mathrm{g}\right)}\stackrel{\mathrm{Cu}}{\to }{\mathrm{HCHO}}_{\left(\mathrm{g}\right)}$