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\[A{g_2}Cr{O_4}\]​ ppt. is soluble in :
\[
  {A.{\text{ }}dil.HNO_3} \\
  {B.{\text{ }}aq.NH_3} \\
  {C.{\text{ }}both{\text{ }}(a){\text{ }}and{\text{ }}(b)}
\]
D. None of these

Answer
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Hint: We must know that the \[A{g_2}Cr{O_4}\] is insoluble in solvents with neutral pH. But silver chromate is soluble in solvents having very acidic \[pH\], or having strong alkaline \[pH\].

Complete answer:
\[A{g_2}Cr{O_4}\] is Silver chromate, that is a brown-red colored crystal compound.
Silver chromate is generally produced by reacting silver nitrate solution \[\left( {AgN{O_3}} \right)\] with potassium chromate \[\left( {{K_2}Cr{O_4}} \right)\] or sodium chromate \[\left( {N{a_2}Cr{O_4}} \right)\]. Such a reaction produces a dark brick red colored precipitate of \[A{g_2}Cr{O_4}\].
Silver chromate is sparingly soluble in aqueous solutions.
Silver chromate is considered as insoluble in aqueous solution, which indicates that in aqueous solution, equilibrium might have been established between the dissolved cations & anions and the un-dissolved solid.
Brisk red ppt. of \[A{g_2}Cr{O_4}\]​ is soluble in dilute acids and \[N{H_4}OH\], in nitric acid, ammonia, alkali cyanides, and chromate solutions. It is insoluble in water and acetic acid, ether, etc.
So, from the options given, \[A{g_2}Cr{O_4}\] precipitate is soluble in dilute nitric acid \[\left( {HN{O_3}} \right)\] ​or aqueous \[N{H_3}\]​.
Hence, the correct option is option C.

Additional information:
Silver chromate is used in developing pictures in photography.
The reaction of silver chromate preparation is also one of the important reactions in neuroscience, as it is used in the "Golgi method" for staining nerve cells or neurons for microscopy. The morphology or structure of neurons gets visible when the silver chromate produced precipitates inside neurons.

Note:
Silver chromate is used in developing pictures in photography.
The reaction of silver chromate preparation is also one of the important reactions in neuroscience, as it is used in the "Golgi method" for staining nerve cells or neurons for microscopy. The morphology or structure of neurons gets visible when the silver chromate produced precipitates inside neurons.