The product obtained when $2-$methylpropan$-2-$ol is treated with alumina $(Al_2O_3)$ at $423 \ K$ is

Identify the wrong statement for the following reactions:
$CH_3-CH(CH_3)-CH=CH_2 \xrightarrow{HBr} A$
$CH_3-CH(CH_3)-CH=CH_2 \xrightarrow{HBr + ROOR} B$
$CH_3-CH(CH_3)-CH=CH_2 \xrightarrow{NBS} C$

Propanal and pentan-$3$-one are the ozonolysis products of an alkene. What is the structural formula of the alkene?

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

Taking into account the stability of various cycloalkanes and carbocations,as well as the rules governing mechanisms of carbocation rearrangements,what is the most likely product of this reaction?

In which of the following,addition of $HBr$ does not take place against Markownikoff's rule,or for which is the Anti-Markownikoff addition of $HBr$ not observed?