I have searched the Internet and found that pushing the bicycle in a race is allowed in two scenarios. If there is some mechanical fault developed in the bicycle, or if there is some technical difficulty in some portion of track where it is not possible to pass without getting off the bicycle.
"Climbing difficult hills is a challenging aspect of bicycle racing, and riders are expected to use their cycling skills and physical abilities to navigate these sections without getting off the bike. Getting off and pushing the bike can provide an advantage by allowing a rider to use their body weight to their advantage and potentially make faster progress uphill compared to someone who remains on the bike."
Do we have any official rules mentioning whether pushing is allowed or not during race?