Step 1: Addition of HBr to propene.
The starting compound is propene:
\[
CH_3-CH=CH_2
\]
On reaction with
\[
HBr
\]
it follows Markovnikov addition.
Therefore, bromine attaches to the more substituted carbon and the product formed is:
\[
CH_3-CHBr-CH_3
\]
This compound is \(2\)-bromopropane.
Step 2: Reaction with aqueous \(NaOH\).
On treatment with
\[
NaOH,
\]
\(2\)-bromopropane undergoes nucleophilic substitution to form propan-\(2\)-ol:
\[
CH_3-CHBr-CH_3 \rightarrow CH_3-CHOH-CH_3
\]
Step 3: Dehydrogenation over copper at \(573\,K\).
Secondary alcohols on heating with copper at
\[
573\,K
\]
undergo dehydrogenation to form ketones.
Thus, propan-\(2\)-ol gives acetone:
\[
CH_3-CHOH-CH_3 \xrightarrow{Cu/573\,K} CH_3COCH_3
\]
Step 4: Condensation of acetone with \(Ba(OH)_2\) and heat.
Acetone undergoes aldol condensation in the presence of
\[
Ba(OH)_2
\]
followed by dehydration on heating.
The major product formed is mesityl oxide:
\[
CH_3COCH_3 \xrightarrow{Ba(OH)_2,\Delta} CH_3COCH=C(CH_3)_2
\]
Step 5: Final conclusion.
Therefore, the major product is
\[
\boxed{\text{Mesityl oxide}}
\]