GATE ECE 2014 Set 2
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## GATE ECE

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain Av0, input resistanc
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In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are ðīc
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The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is
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The power spectral density of a real stationary random process X(t) is given by $${S_x}\left( f \right) = \left\{ {\ma View Question The input to a 1-bit quantizer is a random variable X with pdf$${f_x}(x) = 2{e^{ - 2x}}\,\,for\,\,x \ge 0$$and$${f_x}
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The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 + View Question Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms$${s_1}\,(t)\, = \,\alp
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The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3,
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For the following system, When X1(s) = 0 , the transfer function $$\frac{\mathrm Y\left(\mathrm s\right)}{{\mathrm X}_2 View Question The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. If the system is connected in a View Question An unforced linear time invariant (LTI) system is represented by$$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet View Question Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is View Question The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is ______ View Question For an n - variable Boolean function maximum number of prime implicants is View Question In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by View Question The outputs of the two flip-flops Q1, Q2 in the figure shown are initialized to 0, 0. The sequence generated at Q1 upon View Question In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W1, W2, W3 and W4. View Question To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $$\lambda View Question Which one of the following field patterns represents a TEM wave traveling in the positive$$x$$direction? View Question In the transmission line shown, the impedance$${Z_{in}}$$(in ohms) between node A and the ground is View Question If the electric field of a plane wave is$$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t -
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For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a &gt; b), the cut-off frequency for the $$T{ View Question Assume electronic charge q = 1.6Ã10-19 C, kT/q = 25 mV and electron mobility Îžn = 1000 cm2/V-s. If the concentration gra View Question Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width Xn on the N-side of the ju View Question An increase in the base recombination of a BJT will increase View Question In CMOS technology, shallow P-well or N-well regions can be formed using View Question For the n-channel MOS transistor shown in the figure, the threshold voltage VTh is 0.8V. Neglect channel length modulati View Question For the MOSFETs shown in the figure, the threshold voltage |Vt| = 2V and K=$${1 \over 2}\mu {C_{OX}}\left( {{W \over L}}
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The system of linear equations $$\left( {\matrix{ 2 &amp; 1 &amp; 3 \cr 3 &amp; 0 &amp; 1 \cr 1 &amp; 2 &am View Question The determinant of matrix$$A$$is$$5$$and the determinant of matrix$$B$$is$$40.$$The determinant of matrix$$AB$View Question The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______. View Question For $$0 \le t &lt; \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occ View Question The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is View Question If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarr View Question Let$$X$$be a random variable which is uniformly chosen from the set of positive odd numbers less than$$100.$$The exp View Question If the characteristic equation of the differential equation$$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + View Question The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The ima View Question For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI0 â DI7) from an external device is View Question In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other View Question Norton's theorem states that a complex network connected to a load can be replaced with an equivalent impedance View Question In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then the magnitude of the c View Question A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such t View Question In the h-parameter model of the 2-port network given in the figure shown, the value of h22 (in S) is _____ . View Question In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current View Question Consider the periodic square wave in the figure shown. The ratio of the power in the 7th harmonic to the power in the 5 View Question Let x$$\left[ n \right]$$ = x$$\left[- n \right]$$ . Let X(z) be the z-transform of x$$\left[ n \right]$$. if 0.5 +j 0.2 View Question An FIR system is described by the system function $$H(z) = 1 + {7 \over 2}{z^{ - 1}} + {3 \over 2}{z^{ - 2}}$$$
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The input-output relationship of a causal stable LTI system is given as ðĶ[ð] = ðž ðĶ[ð â 1] + $$\beta$$ x[n]. If
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The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}}$$ (5t) dt is
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Consider a discrete-time signal x\left[ n \right] = \left\{ {\matrix{ {n\,\,for\,\,0 \le n \le 10} \cr {0\,\
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