GATE ECE 2008
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## GATE ECE

In the following transistor circuit, VBE = 0.7V, re = 25m/IE, $$\beta$$ and all the capacitances are very large. T
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In the following transistor circuit, VBE = 0.7V, re = 25m/IE, $$\beta$$ and all the capacitances are very large.
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Consider the following circuit using an ideal Op-Amp. The I-V characteristics of the diode is described by the relation
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The Op-Amp circuit shown above represents a
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Consider the Schmitt trigger circuit shown below. A triangular wave which goes from -12V to 12V is applied to the inve
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Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For demodulating th
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The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is
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Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-d
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Four messages band limited to W, W, 2 W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM
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A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Ea
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A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Ea
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A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each
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A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n
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Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a se
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Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the f
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A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s
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The number of open right half plane poles of $$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$View Question Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step re View Question A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter. View Question The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes t View Question The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over { View Question The impulse response h(t) of a linear time invariant system is given by h(t) =$${e^{ - 2t}}u(t),$$where u(t) denotes t View Question The pole-zero plot given below corresponds to a View Question Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition View Question A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is View Question For the circuit shown in the following figure$${I_0}$$-$${I_3}$$are inputs to the 4:1 multiplexer R(MSB) and S are c View Question Which of the follwing Boolean expression correctly represents the relation between P, Q, R and M1? View Question For each of the positive edge-triggered J-K flip flop used in the following future, the propagation delay is$$\Delta $$View Question The logic function implemented by the following circuit at the terminal OUT is View Question In the following circuit, the comparator output is logic “I” if V1 &gt; V2 and is logic “0” otherwise. The D/A conversio View Question In the following circuit, the comparator output is logic “I” if V1 &gt; V2 and is logic “0” otherwise. The D/A conversio View Question The value of the integral of the function$$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$a View Question One end of loss-less transmission line having the characteristic impedance of 75$$\Omega $$and length of 1 cm is short View Question A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant View Question A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in$$T{E_{11}}$$mode. The min View Question For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is View Question At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is View Question Which of the following is true? View Question Which of the following is NOT associated with a P-N junction? View Question In the following limiter circuit, an input voltage$${\mathrm V}_\mathrm i\;=\;10\sin\left(100\mathrm{πt}\right)$$appli View Question The drain current of a MOSFET in saturation is given by$$I_D\;=\;K\left(V_{GS}\;-V_T\right)^2$$where 'K' is a constant View Question A silicon wafer has 100 mm of oxide on it and is inserted in a furnace at a temperature above 1000ºC for further oxidati View Question Two identical NMOS transistors M1 and M2 are connected as shown below. Vbias is chosen so that both transistors are in s View Question For the circuit shown in the following figure, transistors M1 and M2 are identical NMOS transistors. Assume that M2 is i View Question The measured transconductance gm of an NMOS transistor operating in the linear region is plotted against the gate voltag View Question All the four entries of$$2x2$$matrix$$P = \left[ {\matrix{ {{p_{11}}} &amp; {{p_{12}}} \cr {{p_{21 View Question The system of linear equations $$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$ has View Question For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is View Question The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line View Question Which of the following function would have only odd powers of $$x$$ in its Taylor series expansion about the point $$x=0 View Question In the Taylor series expansion of$${e^x} + \sin x$$about the point$$x = \pi ,$$the coefficient of$${\left( {x = \p View Question Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q View Question Which of the following is a solution to the differential equation$${d \over {dt}}x\left( t \right) + 3x\left( t \right) View Question The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is View Question The equation sin(z) = 10 has View Question The residue of the function $$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is View Question An 8085 executes the following instructions 2710 LXI H, 30A0H DAD H PCHL All addresses and constants are in Hex. L View Question The Thevenin equivalent impedance Zth between the nodes P and Q in the following circuit is View Question In the following circuit, the switch S is closed at t=0. The rate of change of current $$\frac{di}{dt}(0^+)$$ is given b View Question The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For View Question The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For View Question The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The View Question In the following graph, the number of trees (P) and the number of cut-sets (Q) are View Question A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltme View Question The driving point impedance of the following network is given by $$Z(s) = {{0.2\,s} \over {{s^2}\, + \,0.1\,s\, + \,2}} View Question A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltme View Question {x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) View Question In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequ View Question In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency View Question The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptio View Question The impulse response h(t) of a linear time-invariant continuous time system is described by$$h\left( t \right) = \,\,\e View Question A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 an View Question Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with View Question The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr View Question A discrete time linear shift - invariant system has an impulse response$$h\left[ n \right]$$with$$h\left[ 0 \right]$\$
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