Consider the following transformations of a compound $P$ $(C_9H_{12})$:
$(i)$ $P \xrightarrow{NaNH_2, C_6H_5COCH_3, H_3O^+/\Delta} R$ (Optically active)
(ii) $P \xrightarrow{Pt/H_2} \text{propylcyclohexane}$
(iii) $P \xrightarrow{X, KMnO_4/H_2SO_4/\Delta} Q$ ($C_8H_{12}O_6$,Optically active acid)
Choose the correct option$(s)$:
$(A)$ $P$ is $3-$cyclohexylprop$-1-$yne
$(B)$ $X$ is $Pd-C/\text{quinoline}/H_2$
$(C)$ $P$ is $1-$cyclohexylprop$-2-$yne
$(D)$ $R$ is $1-$cyclohexyl$-4-$phenylbut$-3-$yn$-2-$ol

• A
  $B, C$
• B
  $A, C$
• C
  $A, D$
• D
  $A, B$