Q.Decomposition of bleaching powder is

Limestone = calcium carbonate, CaCO3.

Limestone is a sedimentary rock made mainly of calcium carbonate, CaCO3. On heating it decomposes to quicklime: CaCO3 → CaO + …

Quicklime is calcium oxide, CaO, produced by heating (calcining) limestone (CaCO3).

When limestone (calcium carbonate, CaCO3) is strongly heated, it decomposes: CaCO3(s) → CaO(s) + CO2(g). The solid product, calcium oxide (CaO), is commonly called "quicklime" — it reacts vigorously (and exothermically) with water to form calcium hydroxide, Ca(OH)2 ("sla …

Plaster of Paris is calcium sulphate HEMIhydrate -- half a water molecule per formula unit, not one or two full waters.

Gypsum, CaSO4.2H2O, when heated to around 393 K (120 degrees C), loses three-quarters of its water of crystallisation to form calcium sulphate hemihydrate, CaSO4.(1/2)H2O -- commonly called Plaster of Paris. It has the well-known property of setting into a hard mass when mixed with water, which is why it's used for casts and moulds.

…

Quicklime is the common name for calcium oxide, CaO.

Heating calcium carbonate (limestone, CaCO3) strongly (thermal decomposition/calcination) drives off carbon dioxide and leaves behind calcium oxide: CaCO3 -> CaO + CO2. The calcium oxide product is commonly called quicklime.

CaCO3 itself is limestone (not quicklime); Ca(OH)2, formed when quicklime reacts with water, is called slaked lime.

…

Bleaching powder is calcium oxychloride, Ca(OCl)Cl — option (b).

From NCERT Class 11 Chemistry (s-Block Elements): bleaching powder is prepared by passing Cl₂ over slaked lime:

Ca(OH)₂ + Cl₂ → Ca(OCl)Cl + H₂O. …