GATE EE 2010 Question Paper (14-Feb-2010) (Shift 1)

X(t) is a positive rectangular pulse from t = -1 to t = +1 with unit height as shown in the figure. The value of $\underset{-\infty }{\overset{\infty }{\int }}{\left|X\left(\omega \right)\right|}^{2}d\omega$ {where X (ω) is the Fourier transform of X(t)} is.

Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is

If the 12 Ω resistor draws a current of 1 A as shown in the figure, the value of resistance R is

The two – port network P shown in the figure has ports 1 and 2, denoted by terminals (a, b) and (c, d) respectively. It has an impedance matrix Z with parameters denoted by Zᵢⱼ. A 1 Ω resistor is connected in series with the network at port 1 as shown in the figure. The impedance matrix of the modified two – port network (shown as a dashed box) is

The Maxwell's bridge shown in figure is at balance. The parameters of the inductive coil are