Recently I was doing some work on the induction motor where I found some general theory on starting speed torque curve of the induction motor. Where the theory is the starting torque will be 1.5x of rated torque & pull out torque will be 2x. Is this the always a condition or is there a any chance for the pull out torque can be 4x or 5x of the rated torque. Speed torque curve of induction motor
Induction motor designs have considerable variation in the pull-out torque actually provided. Across the power range of available induction motors manufactured to international standards, there is some variation in the minimum pull-out torque required. However 4x or 5x would be quite difficult to find in a normal motor. High-slip motors have the highest pull-out torque - above 3x. There are special low-slip designs that have about 2.7x.
In custom designed motors, pretty much anything you want to pay for is available.
The curve referenced and the information in the question and in the above response pertain to three-phase induction motors. A single-phase motor with a permanently-connected capacitor (PSC motor) would typically have pull-out torque above 4x starting torque and be capable of continuous operation at nearly 2x starting torque. If you re-define rated torque as 60% of starting torque, that becomes a motor with pull-out torque equal to 5x rated.