A catalyst is a substance, which increases the rate of reaction without itself being consumed at the end of the reaction, and the phenomenon I'd called catalysis. There are some catalysts which decreases the rate of reaction & such catalysts are negative catalyst.
Obviously, the catalyst accelerating the rate will be positive catalyst. However, the term positive is seldom used & catalyst itself implies positive catalyst. Catalyst are generally foregine substance but sometimes one of the product formed may act as a catalyst & such a catalyst is called "auto catalyst " & the phenomenon is called auto catalytic.

And, here
Thermal decomposition of KClO3 is found to be accelerating by the presence of MnO2.

2KCl3 + MnO2 ---> 2KCl + 3O2 + MnO2.

So, correct answer is option (B)...

$$Hope it's help... $$

Autocatalytic Reaction: Decomposition of Nitroglycerine

Nitroglycerine is a highly explosive compound that is commonly used in the production of explosives. The decomposition of nitroglycerine is an example of an autocatalytic reaction, where the reaction itself acts as a catalyst and accelerates the rate of the reaction.

What is Autocatalysis?
Autocatalysis is a process in which a reaction product acts as a catalyst for the same reaction. In other words, the reaction speeds up as the concentration of the product increases. This positive feedback loop results in a rapid increase in the reaction rate.

Decomposition of Nitroglycerine:
Nitroglycerine, chemically known as trinitroglycerin, has the molecular formula C3H5N3O9. It is an unstable compound with a high potential for explosive decomposition. The decomposition of nitroglycerine occurs spontaneously over time or can be triggered by heat, shock, or friction.

Autocatalytic Nature of the Reaction:
The decomposition of nitroglycerine is an autocatalytic reaction because one of the products, nitrogen dioxide (NO2), acts as a catalyst for the further decomposition of nitroglycerine. The reaction can be represented by the following equation:

2C3H5N3O9 → 6CO2 + 5H2O + 3N2 + 2NO2

In this reaction, the initial decomposition of nitroglycerine produces nitrogen dioxide (NO2) as one of the products. The nitrogen dioxide then reacts with more nitroglycerine molecules, increasing the rate of the reaction. This positive feedback loop accelerates the decomposition process, leading to a rapid release of energy and the explosive nature of nitroglycerine.

Significance:
Understanding the autocatalytic nature of the decomposition of nitroglycerine is crucial for handling and storing this highly explosive compound safely. It highlights the importance of preventing the accumulation of nitrogen dioxide, as it can act as a catalyst for further decomposition and increase the risk of an explosion.

Conclusion:
The decomposition of nitroglycerine is an example of an autocatalytic reaction, where the reaction product (nitrogen dioxide) acts as a catalyst for the further decomposition of nitroglycerine. This autocatalytic nature of the reaction contributes to the explosive properties of nitroglycerine and emphasizes the need for careful handling and storage of this compound.