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## GATE ECE 2009

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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## GATE ECE

A small signal source V<sub>i</sub>(t) = A cos 20t + B sin 10<sup>6</sup> t, is ...
A communication channel with AWGN operating at a signal to noise ratio SNR &gt; ...
The amplitude of random signal is uniformly distributed between $$-$$5V and 5V ...
The amplitude of random signal is uniformly distributed between $$-$$5V and 5V ...
The unit step response of an under-damped second order system has steady state v...
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We a...
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We a...
The magnitude plot of a rational transfer function G(s), with real coefficient i...
Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\m... If X=1 in the logic equation$$\left[ {X + Z\left\{ {\overline Y + (\overline Z...
What are the minimum number of 2-to 1 multiplexers required to generate a 2-inpu...
What are the counting states (Q<sub>1</sub>, Q<sub>2</sub>) for the counter show...
The full forms of the abbreviations TTL and COMS in reference to logic families...
Two infinitely long wires carrying current are as shown in the figure below. One...
A transmission line terminates in two branches, each of length $$\lambda /4$$, a...
Which of the following statements is true regarding the fundamental mode of the ...
In the circuit below, the diode is ideal. The voltage V is given by <img alt="ga...
Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is incre...
Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is incre...
The eigen values of the following matrix $$\left[ {\matrix{ { - 1} &amp; 3 &a... The Taylor series expansion of$$\,\,{{\sin x} \over {x - \pi }}\,\,$$at$$x = ...
If a vector field$$\overrightarrow V$$ is related to another field $$\overrigh... A fair coin is tossed$$10$$times. What is the probability that only the first ... A discrete random variable$$X$$takes value from$$1$$to$$5$$with probabilit... Consider two independent random variables$$X$$and$$Y$$with identical distrib... Match each differential equation in Group$$I$$to its family of solution curve... The order of differential equation$$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{...
Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace ...
If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| ... <p>In the interconnection of ideal sources shown in the figure, it is known that... In the circuit shown, what value of R<sub>L</sub> maximizes the power delivered ... The time domain behavior of an RL circuit is represented by$$$\mathrm L\frac{\m... The switch in the circuit shown was on position ‘a’ for a long time and is moved... An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \lef... If the transfer function of the following network is$$\,{{{V_0}(s)} \over {{V_i... The Fourier series of a real periodic function has only <p>P. Cosine terms if it... A function is given by f(t) = sin<sup>2</sup>t +cos2t . Which of the following i... Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transfor... The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left... The ROC of Z-transform of the discrete time sequence <br> x(n)=$${\left( {{1 \o... Consider a system whose input x and output y are related by the equation $$y(t... A system with transfer function H(z) has impulse response h(.) defined as h(2) =... A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-ti... An LTI system having transfer function$${{{s^2} + 1} \over {{s^2} + 2s + 1}}$\$ ...

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