GATE ECE 2009
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## GATE ECE

A small signal source Vi(t) = A cos 20t + B sin 106 t, is applied to a transistor Amplifier as shown in fig. The transis
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A communication channel with AWGN operating at a signal to noise ratio SNR &gt; &gt; 1 and band width B has capacity $${ View Question The amplitude of random signal is uniformly distributed between$$-$$5V and 5V If the signal to quantization noise rati View Question The amplitude of random signal is uniformly distributed between$$-$$5V and 5V If the positive values of the signal are View Question The unit step response of an under-damped second order system has steady state value of -2. Which one of the following t View Question The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the cl View Question The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the cl View Question The magnitude plot of a rational transfer function G(s), with real coefficient is shown in figure. Which of the followin View Question Consider the system$${{dx} \over {dt}} = Ax + Bu$$with$${\rm A} = \left[ {\matrix{ 1 &amp; 0 \cr 0 &amp; 1
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If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right] View Question What are the minimum number of 2-to 1 multiplexers required to generate a 2-input AND gate and a 2-input EX-OR gate? View Question What are the counting states (Q1, Q2) for the counter shown in the figure below? View Question The full forms of the abbreviations TTL and COMS in reference to logic families are View Question Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel t View Question A transmission line terminates in two branches, each of length$$\lambda /4$$, as shown.The branches are terminated by 5 View Question Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown? View Question In the circuit below, the diode is ideal. The voltage V is given by View Question Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased from zero, while the gate voltage o View Question Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased from zero, while the gate voltage o View Question The eigen values of the following matrix$$\left[ {\matrix{ { - 1} &amp; 3 &amp; 5 \cr { - 3} &amp; { - 1} &amp;
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The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi$$ is given by
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If a vector field$$\overrightarrow V$$ is related to another field $$\overrightarrow A$$ through $$\,\overrightarrow View Question A fair coin is tossed$$10$$times. What is the probability that only the first two tosses will yield heads? View Question A discrete random variable$$X$$takes value from$$1$$to$$5$$with probabilities as shown in the table. A student cal View Question Consider two independent random variables$$X$$and$$Y$$with identical distributions. The variables$$X$$and$$Y$$ta View Question Match each differential equation in Group$$I$$to its family of solution curves from Group$$II.$$Group$$IP:$View Question The order of differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e View Question Given that$$F(s)$$is the one-sided Laplace transform of$$f(t),$$the Laplace transform of$$\int\limits_0^t {f\left( View Question If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} View Question In the interconnection of ideal sources shown in the figure, it is known that the 60V source is absorbing power. Which View Question In the circuit shown, what value of RL maximizes the power delivered to RL? View Question The time domain behavior of an RL circuit is represented by$$$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm
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The switch in the circuit shown was on position ‘a’ for a long time and is moved to position ‘b’ at time t = 0. The curr
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A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-time. Assume that, during the talk-time, t
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An AC source of RMS voltage $$20$$ $$V$$ with internal impedance $${Z_s} = \left( {1 + 2j} \right)\Omega$$ feeds a loa
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If the transfer function of the following network is $$\,{{{V_0}(s)} \over {{V_i}(s)}} = {1 \over {2\, + \,sCR}}$$ The
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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. Cos
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A function is given by f(t) = sin2t +cos2t . Which of the following is true?
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Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \r View Question The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence$$\left\{ {1,\,0,\,2,\,3} \right\}$$is View Question The ROC of Z-transform of the discrete time sequence x(n)=$${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over
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Consider a system whose input x and output y are related by the equation $$y(t) = \int\limits_{ - \infty }^\infty {x( View Question A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise. View Question An LTI system having transfer function$${{{s^2} + 1} \over {{s^2} + 2s + 1}} and input x(t) = sin (t + 1) is in stead
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