Signals A,B,C,D and $$\overline D $$ are available. Using a single 8 - to - 1 multiplexer and no other gate, implement the Boolean function.

$$f(A,B,C,D) = B.C + A.B.\bar D + \bar A.\bar C.\bar D$$

A pulse train with a frequency of 1 MHz is counted using a modulo-1024 ripple-counter built with J-K flip flops. For proper operation of the counter, the maximum permissible propagation delay per flip flop stage is ______ n sec.

Given,$$\overrightarrow V=x\cos^2y\;\;\widehat{\mathrm i}\;+\;\mathrm x^2\mathrm e^\mathrm z\;\widehat{\mathrm j}\;+\;\mathrm{zsin}^2\mathrm y\;\widehat{\mathrm k}$$ and S the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes, the value of the integral is

A material is described by the following electrical parameters at a frequency of $$10$$ GHz is $$\sigma = {10^6}$$ mho/m, $$\mu = {\mu _0},$$ and $$ \in /{ \in _0} = 10.$$ The material at this frequency is considered to be $$\left( {{ \in _0} = {1 \over {36\,\,\pi }} \times {{10}^{ - 9}}\,\,F/m} \right)$$