Which of the following reacts with $KMnO_4$ but does not react with $AgNO_3$?

The correct statement about $C$ and $D$ is:
$CH_3-C \equiv C-CH_3$ $\xrightarrow{H_2/Pd-BaSO_4} A$ $\xrightarrow{Br_2/CCl_4} C$
$CH_3-C \equiv C-CH_3$ $\xrightarrow{Na/Liq. NH_3} B$ $\xrightarrow{Br_2/H_2O} D$

Rank the following alkenes in order of increasing $\lambda_{max}$:
$(1)$ $A$ conjugated diene in a bicyclic system.
$(2)$ An isolated diene in a bicyclic system.
$(3)$ $A$ conjugated diene in a bicyclic system (different substitution pattern).

The predominant product formed when $3$-methyl-$2$-pentene reacts with $HOCl$ is:

The reaction of an alkene $X$ with bromine produces a compound $Y$,which has $22.22 \% \ C$,$3.71 \% \ H$ and $74.07 \% \ Br$. The ozonolysis of alkene $X$ gives only one product. The alkene $X$ is,
[Given,atomic mass of $C = 12$; $H = 1$; $Br = 80$ ]

Which reaction has the lowest $\Delta G^{\ddagger}$ (Activation Energy)?