Mechanical Engineering is very diverse. The different
disciplines under it include energy/thermal systems engineering,
fluid mechanics, applied mechanics, robotics, aeronautical
engineering, oil and gas engineering, biomechanics.... you name
it.
I cannot say what the course is like at NTU, but at NUS you
learn a little bit of everything in the first three years. Then you
have a choice to specialize in any of those disciplines, though you
can choose not to if you want.
I think you can already guess what kind of industries require
mechanical engineers. Energy industries, water systems industries,
construction industries, oil and gas industries.... you name
it.