Consider the differential equation $$\left( {{t^2} - 81} \right){{dy} \over {dt}} + 5ty = \sin \left( t \right)\,\,$$ with $$y\left( 1 \right) = 2\pi .$$ There exists a unique solution for this differential equation when $$t$$ belongs to the interval

For the power semiconductor devices $$IGBT, MOSFET,$$ Diode and Thyristor, which one of the following statements is TRUE?

The figure below shows an uncontrolled diode bridge rectifier supplied form a $$220$$ Z$$V,$$ $$50$$ $$Hz,$$ $$1$$-phase $$ac$$ source. The load draws a constant $${{\rm I}_0}$$ $$=14A.$$ The conduction angle of the diode $${D_1}$$ in degrees (rounded off to two decimal places) is ______________.

The input voltage $${V_{DC}}$$ of the buck-boost converter shown below varies from $$32$$ $$V$$ to $$72$$ $$V.$$ Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio $$D$$ of the converter for which the magnitude of the steady state output voltage remains constant at $$48$$ $$V$$ is