Compound $(P)$ is formed by the acid-catalyzed rearrangement of $1$-methyl-$1$-cyclohexyl hydrogen peroxide. The reaction is shown below. Identify compound $(P)$.

Which of the following reactions converts $Acetone$ into a hydrocarbon having the same number of carbon atoms?

In the following reactions,$P, Q, R$,and $S$ are the major products.
The correct statement$(s)$ about $P, Q, R$,and $S$ is(are):
$(A)$ Both $P$ and $Q$ have asymmetric carbon$(s)$.
$(B)$ Both $Q$ and $R$ have asymmetric carbon$(s)$.
$(C)$ Both $P$ and $R$ have asymmetric carbon$(s)$.
$(D)$ $P$ has asymmetric carbon$(s)$,$S$ does not have any asymmetric carbon.

$CH_3CH=CHCHO$ is oxidized to $CH_3CH=CHCOOH$ using

Which of the following will fail to react with potassium dichromate and dilute sulphuric acid?

$C_{7}H_{10}O$ reacts with $CH_{3}MgBr$ to give a compound $C_{8}H_{12}O$ which gives a positive iodoform test. Identify the structure of $A$.