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