GATE ECE 2014 Set 4
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GATE ECE

For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then
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If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will
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Consider the common-collector amplifier in the figure (bias circuitry ensures that the transistor operates in forward ac
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A BJT in common-base configuration is used to amplify a signal received by a $$50\,\Omega $$ antena. Assume kT/q = 25 m
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For the common collector amplifier shown in the figure, the BJT has high $${V_{CE\left( {sat} \right)}},$$ and $${V_{BE
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The circuit shown represents
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An M - level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth
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Consider the Z- channel given in the figure. The input is 0 or 1 with equal probability. If the output is 0, the probab
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If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival
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Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The
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Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal- dependent. In particular, given the tr
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For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is
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Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ wit
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The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop transfer function G(s) has
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In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-po
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The state transition matrix $$\phi \left( t \right)$$ of a system $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bull
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In the circuit shown in the figure, if C = 0, the expression for Y is
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A 16-bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure. The carry-propagatio
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An 8-to-1 multiplexer is used to implement a logical function Y as shown in the figure. The output Y is given by
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The output (Y) of the circuit shown in the figure is
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If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\
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The electric field (assumed to be one-dimensional) between two points A and B is shown. Let $$\psi_A$$ and $$\psi_B$$ be
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For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 m V/m. Given that int
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Match column A with column B. Column 1. Point electromagnetic source 2. Dish antenna 3. Yagi-Uda antenna Colum
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In the figure ln(ρi) is plotted as a function of 1/T, where ρi the intrinsic resistivity of silicon, T is is the tempera
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The cut-off wavelength (in µm) of light that can be used for intrinsic excitation of a semiconductor material of bandgap
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Consider a silicon sample doped with ND = 1×1015/cm3 donor atoms. Assume that the intrinsic carrier concentration ni = 1
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An N-type semiconductor having uniform doping is biased as shown in the figure. If EC is the lowest energy level of th
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Consider two BJT's biased at the same collector current with area A1 = 0.2 μm × 0.2 μm and A2 = 300 μm × 300 μm. Assumin
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For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have m
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The series $$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,} $$ converges to
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The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(
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The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$
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Given $$\,\,\overrightarrow F = z\widehat a{}_x + x\widehat a{}_y + y\widehat a{}_z.\,\,$$ If $$S$$ represents the po
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Let $$X$$ be a zero mean unit variance Gaussian random variable. $$E\left[ {\left| X \right|} \right]$$ is equal to ____
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Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a proba
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If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival
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With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equati
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If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}}
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The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilate
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An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the Accumu
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The circuit shown in the figure represents a
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The magnitude of current (in mA) through the resistor R2 in the figure shown is _____.
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In the circuit shown in the figure, the value of V0(t) (in Volts) for $$t\rightarrow\infty$$ is ______.
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For the two-port network shown in the figure, the impedance (Z) matrix (in Ω) is
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The steady state output of the circuit shown in the figure is given by $$$y\left( t \right) = {\rm A}\left( \omega \ri
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The equivalent resistance in the infinite ladder network shown in the figure, is$${R_e}$$ The value of $${R_e}/R$$ is
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A Fourier transform pair is given by $${\left( {{2 \over 3}} \right)^n}$$ u $$\left[ {n + 3} \right]\,\mathop \Leftrigh
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The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral
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A stable linear time invariant (LTI) system has a transfer function H(s) = $${1 \over {{s^2} + s - 6}}$$. To make this s
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A casual LTI system has zero initial conditions and impulse response h(t). Its input x(t) and output y(t) are related th
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The N-point DFT X of a sequence x[n] 0 ≤ n ≤ N − 1 is given by $$X\left[ k \right] = {1 \over {\sqrt N }}\,\,\sum\lim
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The sequence x $$\left[ n \right]$$ = $${0.5^n}$$ u[n], where u$$\left[ n \right]$$ is the unit step sequence, is conv
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A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linea
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