GATE EE 2013 Question Paper (10-Feb-2013) (Shift 2)

$\int \frac{z^2-4}{z^2+4}dz$ evaluated anticlockwise around the circle |z - i| = 2 , where i = √−1 , is

The clock frequency applied to the digital circuit shown in the figure below is 1KHz. If the initial state of the output of the flip-flop is 0, the frequency of the output waveform Q in KHz is

In the circuit shown below, the BJT has negligible collector to emitter saturation voltage and the diode drops negligible voltage across it under Forward bias. If V${}_{CC}$ is +5V, X and Y are digital signals with 0 V as logic 0 and V${}_{CC}$ as logic 1, then the Boolean expression for Z is

In the circuit shown below the op – amp are ideal. The Vₒᵤₜ in volts is

The signal flow graph for a system is given below.



The transfer function $\frac{Y\left(s\right)}{U\left(s\right)}$ for this system is