Let y = y(x) be the solution of the differential equation, x$${{dy} \over {dx}}$$ + y = x log_e x, (x > 1). If 2y(2) = log_e 4 $$-$$ 1, then y(e) is equal to :

For the given cyclic process CAB as shown for a gas, the work done is :

The output of the given logic circuit is :

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $$\mu $$m diameter of a wire is :