GATE ECE 2017 Set 1
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GATE ECE

For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and coll
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In the figure shown, the npn transistor acts as a switch. For the input vin(t)as shown in the figure, the transistor
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The Miller effect in the context of a Common Emitter amplifier explains
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For the operational amplifier circuit shown, the output saturation voltages are $$ \pm \,\,15V$$. The upper and lower th
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The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an
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In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier trans
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Which one of the following statements about differential pulse code modulation (DPCM) is true?
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Let $$X(t)$$ be a wide sense stationary random process with the power spectral density $${S_x}\left( f \right)$$ as show
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In binary frequency shift keying (FSK), the given signal wave forms are $$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0
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Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_
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The open loop transfer function $$$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\ma
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Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the
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A linear time invariant (LTI) system with the transfer function $$$G\left(s\right)=\frac{K\left(s^2+2s+2\right)}{s^2-3s+
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Consider a stable system with transfer function $$$G\left(s\right)=\frac{s^p+b_1s^{p-1}+....+b_p}{s^q+a_1s^{q-1}+....+a_
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The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$
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Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?
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Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2}
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Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation
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In the latch circuit shown, the NAND gates have non-zero, but unequal propagation delays. The present input condition is
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A 4-bit shift register circuit configured for right-shift operation is $${D_{in}}\, \to \,A,\,A\, \to B,\,B \to C,\,C \t
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A finite state machine (FSM) is implemented using the D flip-flops A and B and logic gates, as shown in the figure below
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The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $$V(l) =
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The expression for an electric field in free space is $$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right)
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A half wavelength dipole is kept in the x-y plane and oriented along $${45^ \circ }$$ from the x-axis. Determine the dir
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Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and stric
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An optical fiber is kept along the$$\widehat Z$$ direction. The refractive indices for the electric fields along $$\wid
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A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in t
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The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has
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For a narrow base PNP BJT, the excess minority carrier concentration ($$\bigtriangleup n_E$$ for emitter, $$\bigtriangle
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For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage Vtn = 1 V and its trans
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The rank of the matrix $$M = \left[ {\matrix{ 5 & {10} & {10} \cr 1 & 0 & 2 \cr 3 & 6 &
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Consider the $$5 \times 5$$ matrix $$A = \left[ {\matrix{ 1 & 2 & 3 & 4 & 5 \cr 5 & 1 &
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Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series a
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A three dimensional region $$R$$ of finite volume is described by $$\,\,{x^2} + {y^2} \le {z^3},\,\,\,0 \le z \le 1$$ W
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If the vector function $$\,\,\overrightarrow F = \widehat a{}_x\left( {3y - k{}_1z} \right) + \widehat a{}_y\left( {k{
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Let $$\,\,\,{\rm I} = \int_c {\left( {2z\,dx + 2y\,dy + 2x\,dz} \right)} \,\,\,\,$$ where $$x, y, z$$ are real, and let
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Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on t
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Consider the following statements about the linear dependence of the real valued functions $${y_1} = 1,\,\,{y_2} = x$$ a
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Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left
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Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's me
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The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 $$\mu $$s,
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The following five instructions were executed on an 8085 microprocessor. MVI A, 33H MVI B, 78H ADD B CMA ANI 32H
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In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which magnitude of the phase
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In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $$${V_{IN}}\,\left( t \right) = \left\
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The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The
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A periodic signal x(t) has a trigonometric Fourier series expansion $$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_
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Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier ser
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Two discrete-time signals x [n] and h [n] are both non-zero only for n = 0, 1, 2 and are zero otherwise. It is given tha
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Let h[n] be the impulse response of a discrete time linear time invariant (LTI) filter. The impulse response is given by
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Consider the following statements for continuous-time linear time invariant (LTI) system. I. There is no bounded input
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A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a lin
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Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right
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General Aptitude

40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a sl
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In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer h
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Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be dedu
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S, T, U, V, W, X, Y and Z are seated around a circular table. T's neighbors are Y and V. Z is seated third to the left o
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She has a sharp tongue and it can occasionally turn
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There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every s
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I ___________ made arrangements had I ___________informed earlier.
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“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason
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A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geo
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Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck
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