Question
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\[\begin{align}
  & A\xrightarrow{4KOH,{{O}_{2}}}\underset{green}{\mathop{2B}}\,+2{{H}_{2}}O \\
 & 3B\xrightarrow{4HCL}\underset{purple}{\mathop{2C}}\,+Mn{{O}_{2}}+2{{H}_{2}}O \\
 & 2B\xrightarrow{{{H}_{2}}O,KI}2A+2KOH+D \\
\end{align}\]
In the above sequence of reactions, A and D respectively are:
(A) $KI{{O}_{3}}and\text{ Mn}{{\text{O}}_{3}}$
(B) $KIand\text{ }{{\text{K}}_{2}}\text{Mn}{{\text{O}}_{4}}$
(C) $Mn{{O}_{2}}\text{and KI}{{\text{O}}_{3}}\text{ }$
(D) $KIand\text{ KMn}{{\text{O}}_{4}}$


Answer
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Hint: To solve this type of question it is important to know about the reagents used like in the first reaction the reagent is KOH, so we should know that KOH is hygroscopic and it is a water soluble base and oxygen means that after reaction with potassium hydroxide oxidation will takes place.

Complete step by step solution:
Reactions given in the question is mentioned below:
\[\begin{align}
  & A\xrightarrow{4KOH,{{O}_{2}}}\underset{green}{\mathop{2B}}\,+2{{H}_{2}}O \\
 & 3B\xrightarrow{4HCL}\underset{purple}{\mathop{2C}}\,+Mn{{O}_{2}}+2{{H}_{2}}O \\
 & 2B\xrightarrow{{{H}_{2}}O,KI}2A+2KOH+D \\
\end{align}\]
In the first reaction $Mn{{O}_{2}}$ is fused with potassium hydroxide and oxygen to form ${{K}_{2}}Mn{{O}_{4}}$ which is a green color compound. The reaction involved is shown below:
\[Mn{{O}_{2}}\xrightarrow{4KOH,{{O}_{2}}}\underset{green}{\mathop{2{{K}_{2}}Mn{{O}_{4}}}}\,+2{{H}_{2}}O\]
In the second reaction ${{K}_{2}}Mn{{O}_{4}}$ combined with hydrochloric acid and the reaction produces $KMn{{O}_{4}}$ which is a purple color compound along with manganese oxide and water molecule. The reaction involved is shown below:
\[3{{K}_{2}}Mn{{O}_{4}}\xrightarrow{4HCL}\underset{purple}{\mathop{2KMn{{O}_{4}}}}\,+Mn{{O}_{2}}+2{{H}_{2}}O\]
In the third reaction, ${{K}_{2}}Mn{{O}_{4}}$ combines with water molecule and potassium iodide and form $Mn{{O}_{2}}\text{ and KI}{{\text{O}}_{3}}$ along with potassium hydroxide. The reaction involved is shown below:
\[2{{K}_{2}}Mn{{O}_{4}}\xrightarrow{{{H}_{2}}O,KI}2Mn{{O}_{2}}+2KOH+KI{{O}_{3}}\]

Hence the correct answer is option (C) i.e. in the above sequence of reactions, A and D respectively are $Mn{{O}_{2}}\text{and KI}{{\text{O}}_{3}}\text{ }$.

Additional information:
Potassium permanganate is a purple colored chemical compound. It is a potassium salt of the manganic acid also known as the permanganate of potash and many other names such as chameleon minerals prcondy crystal and hypermagan.

Note: The above mentioned reaction should take place at an appropriate reaction condition especially the first reaction requires the temperature of around 350 to 450 degree centigrade. Potassium manganate and potassium permanganate should not be mixed up. They both have different chemical formulae and they even have different chemical properties.