When Airplane is reducing altitude from flight level (cruise), which one is more efficient
There are (mostly) two ways to reduce altitude:


Reduce speed until your wings don't generate enough lift in level flight. Typically the nose will drop by itself since you are no longer at your trimmed airspeed. You might be able to re-trim so that you are in a level descent.
Drop the nose manually without reducing (or even increasing) speed


Airliners at altitude operate very close to what is called the coffin corner where an increase in speed means you overspeed the aircraft, and a reduction in speed means you stall. So preferably the pilot will simultaneously reduce the throttles while lowering the nose to maintain a specific speed.

Tilting the aircraft up (nose up) will reduce your speed and eventually you will fall to the earth (as you stall). This is a very inefficient way to get down (not to mention it scares the hell out of the passengers). The aircraft buffets, a wing may drop if the plane is not kept coordinated, and is overall a very dangerous thing to do (see the coffin corner link above). 

The reason the nose is raised while landing is so that the aircraft can bleed off extra speed and reduce the descent rate for touch down (as well as reducing the stress on the nose gear). This is also a high-drag situation and is, in that effect, inefficient. 


  What is the allowed maximum angle tilt down nose?


90° because after that you're tilting up...

In all seriousness you can nose-down until you hit the maximum airframe speed without causing damage. For airliners this is usually a lot more than passengers are comfortable with (especially if the stewards have the rolling carts out), so pilots make a concerted effort to keep the floor as level as possible. For smaller aircraft like the 172, you can configure it such that you won't exceed this speed and point the thing almost straight down, it's actually pretty fun.