Question

If hydrogen burns in air to produce oxygen, why a rocket which contains hydrogen as fuel produces smoke during its launch?

Answer 1

Typically, the presence of actual fire and smoke is an indicator of incomplete combustion and with most large rockets occurs at the beginning of engine start, and often at the peripheral edge of the hot gas stream in the exhaust where non-optimum mixing with atmospheric gases interferes with any residual combustion still taking place.
Sometimes, what appears to be smoke is actually steam. This was the case normally for the Space Shuttle Main Engines (SSMEs), which burned hydrogen and oxygen and typically produced only water (steam) as an exhaust product