(A) An aqueous solution of AgNO$_3$ using silver electrodes.

Cathode - Reduction - $$Ag_{(aq)}^ + + {e^ - } \to Ag(s)$$

Anode - Oxidation - $$Ag(s) \to Ag_{(aq)}^ + + {e^ - }$$

Solid silver will be deposited at the cathode. Solid anode (silver) will dissolve, releasing silver ions into the solution.

So, there is no formation of O$_2$ gas in this electrolysis.

(B) An aqueous solution of AgNO$_3$ using platinum electrodes.

Cathode - Reduction - $$Ag_{(aq)}^ + + {e^ - } \to Ag(s)$$

Anode - Oxidation - $$2{H_2}O \to 4{H^ + } + {O_2} + 4{e^ - }$$

When platinum electrodes are used, Ag$^+$ from solution is reduced and deposited at cathode whereas O$_2$ is produced at the anode.

(C) A dilute soution of H$_2$SO$_4$ using platinum electrodes.

Cathode - Reduction - $$2{H^ + } + 2{e^ - } \to {H_2}$$

Anode - Oxidation - $$2{H_2}O \to {O_2} + 4{H^ + } + 4{e^ - }$$

H$_2$ gas is produded at the cathode and O$_2$ gas is produced at the anode.

(D) a high concentration solution of H$_2$SO$_4$ using platinum electrodes.

O$_2$ gas is not formed in this case.

Cathode - Reduction - The substance formed is H$_2$ gas.

Anode - Oxidation - The substance formed is not O$_2$ gas.

So, statements (B) and (C) are correct.