The resultant gate and its Boolean expression in the given circuit is

The current amplification factor of a transistor is 50 . The input resistance when used in common emitter mode is $1 \mathrm{k} \Omega$. The peak value for an a.c. input voltage of 0.01 V peak is

In the logic circuit diagram, when all the four inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are one, the outputs $\mathrm{Y}_1, \mathrm{Y}_2, \mathrm{Y}_3$ are respectively $(1,1,0)$. When all the inputs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are changed to 'zero', the outputs $\mathrm{Y}_1, \mathrm{Y}_2, \mathrm{Y}_3$ respectively change to

For the diagram shown, the resistance between points A and B when the ideal diode ' $D$ ' is forward biased is ' $R_1$ ' and that when reverse biased is ' $R_2$ '. The ratio $\frac{R_1}{R_2}$ is