firstly, dielectric cons is a inverse measure of the tendency of a material to let the electric field through it.....since a conductor doesn't allow so it has infinite......

 

2 charging thru induction doesn't involve transfer of charges.....so net charge will remain 0 as before.....

 

3)repulsion is a sure test for electrification as attraction can b bet 1 charged and 1 uncharged body but repulsion is only bet 2 charged bodies(that too opp charged..)

 

4)when apositively charged conduc is connec to earth,electrons will flow frm earth to it....ur ans given is wrong....