GATE 2009 Electronics & Communication

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer function has these properties?

The time domain behavior of an RL circuit is represented by $$$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm{dt}}+\mathrm{Ri}\;=\;{\mathrm V}_0\left(1\;+\;\mathrm{Be}^{...

What are the minimum number of 2-to 1 multiplexers required to generate a 2-input AND gate and a 2-input EX-OR gate?

Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is

If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} \,\,dz$$ is given

The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi $$ is given by

Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\,\,{\rm B} = \left[ {\matrix{ p \cr q \cr } } \righ...

The eigen values of the following matrix $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & 0 & 3 \cr } } \right]$$ are

The order of differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e^{ - t}}\,\,$$ is

A communication channel with AWGN operating at a signal to noise ratio SNR > > 1 and band width B has capacity $${{C_1}}$$ . If the SNR is doubled keeping B constant, the resulting...

The amplitude of random signal is uniformly distributed between $$-$$5V and 5V If the signal to quantization noise ratio required in uniformly quantizing the signals is 43.5 dB, th...

The amplitude of random signal is uniformly distributed between $$-$$5V and 5V If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the nega...

If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$...

Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ with probability $$1/2,$$ $$1/4...

The full forms of the abbreviations TTL and COMS in reference to logic families are

If a vector field$$\overrightarrow V $$ is related to another field $$\overrightarrow A $$ through $$\,\overrightarrow V = \nabla \times \overrightarrow A ,$$ which of the followin...

A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?

Match each differential equation in Group $$I$$ to its family of solution curves from Group $$II.$$ Group $$I$$ $$P:$$$$\,\,\,$$ $${{dy} \over {dx}} = {y \over x}$$ $$Q:$$$$\,\,\,$...

The Fourier series of a real periodic function has only P. Cosine terms if it is even Q. Sine terms if it is even R. Cosine terms if it odd S. Sine terms if it is odd Which of the...

A function is given by f(t) = sin 2 t +cos2t . Which of the following is true?

The ROC of Z-transform of the discrete time sequence x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1)$$ is

An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in steady state. The output is sampled at a rate $${\omega _s}\,\,ra...

A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise. Consider the following statements. S1: H(z) is a low-pass fi...

Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau } $$ is

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is