GATE ECE 2015 Set 1
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## GATE ECE

In the circuit shown, I1 = 80 mA and I2 b= 4mA. Transistors T1 and T2 are identical. Assume that the thermal voltage VT
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In the circuit shown, assume that the opamp is ideal. The bridge output voltage V0 (in mV) for $$\delta = 0.05$$ is___
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The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillati
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Consider the signal $$s\left(t\right)\;=\;m\left(t\right)\;\cos\left(2{\mathrm{πf}}_\mathrm c\mathrm t\right)\;+\widehat View Question In the system shown in figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pas View Question A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size$$\Delta $$of t View Question The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common bandwidth using TDMA. If at a View Question The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over proba View Question A source emits bit 0 with probability$${1 \over 3}$$and bit 1 with probability$${2 \over 3}$$. The emitted bits are c View Question Negative feedback in a closed-loop control system DOES NOT View Question The damping ratio of a series RLC circuit can be expressed as View Question A unity negative feedback system has the open-loop transfer function$$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right View Question The open-loop transfer function of a plant in a unity feedback configuration is given as $$G\left(s\right)=\frac{K\left( View Question A plant transfer function is given as$$$G\left(s\right)=\left(K_p+\frac{K_1}s\right)\left(\frac1{s\left(s+2\right)}\rig
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The popular plot of the transfer function G(s)=$${{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}}$$ for $$0 View Question A lead compensator network includes a parallel combination of 'R' and 'C' in the feed-forward path. If the transfer func View Question The Boolean expression F(X, Y, Z)=$$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$View Question All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1 until time t = 0. At View Question A 3-input majority gate is defined by the logic function M (a,b,c) = ab+bc+ca. Which one of the following gates is repr View Question A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of rows is equal to the n View Question Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 0001 are 0 V View Question The electric field component of a plane wave traveling in a lossless dielectric medium is given by$$$\overrightarrow E View Question The electric field intensity of a plane wave traveling in free space is given by the following expression $$E\left( {x, View Question Consider a uniform plane wave with amplitude$$\left( {{E_0}} \right)$$of$$10\,\,\,V/m$$and$$1.1 GHz$$frequency tra View Question The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric c View Question A silicon sample is uniformly doped with donor type impurities with a concentration of$$10^{16}/cm^3$$.The electron and View Question A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction View Question In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6V. The output voltage V0 (in volts) is __ View Question The built-in potential of an abrupt p-n junction is 0.75V. If its junction capacitance (CJ) at a reverse bias (VR) of 1. View Question A MOSFET in saturation has a drain current of 1 mA for VDS =0.5V. If the channel length modulation coefficient is 0.05 View Question For the NMOSFET in the circuit shown, in the threshold voltage is Vth, where Vth&gt;0. The source voltage Vss is varied View Question Consider system of linear equations :$$$x-2y+3z=-1$x-3y+4z=1$$and$$$-2x+4y-6z=k,$$The value of$$'k'$$for View Question The value of$$'P'$$such that the vector$$\left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$is an eig View Question A function$$f\left( x \right) = 1 - {x^2} + {x^3}\,\,$$is defined in the closed interval$$\left[ { - 1,1} \right].$$View Question The maximum area (in square units) of a rectangle whose vertices lie on the ellipse$${x^2} + 4{y^2} = 1\,\,$$is View Question Which one of the following graphs describes the function?$$f\left( x \right) = {e^{ - x}}\left( {{x^2} + x + 1} \right)
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A vector $$\overrightarrow P$$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrig View Question Suppose$$A$$&amp;$$B$$are two independent events with probabilities$$P\left( A \right) \ne 0$$and$$P\left( B \ri
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The input $$X$$ to the Binary Symmetric Channel (BSC) shown in the figure is $$'1'$$ with probability $$0.8.$$ The cross
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The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\le View Question Let$$z=x+iy$$be a complex variable. Consider that contour integration is performed along the unit circle in anticlockw View Question In an 8085 microprocessor, the shift registers which store the result of an addition and the overflew bit are, respectiv View Question In the given circuit, the values of V1 and V2 respectively are View Question In the network shown in the figure, all resistors are identical with R = 300$$\Omega$$. The resistance Rab (in$$\Omega
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In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The energy (in $$\mu J$$) tak
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In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is _________
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In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is ___________________.
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In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of vc(t) (in Volts) at t
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The damping ratio of a series $$RLC$$ circuit can be expressed as
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The solution of the differential equation $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}\,\,\,\,\,{{{d^2}y} \ov View Question Two sequences [a, b, c ] and [A, B, C ] are related as,$$\left[ {\matrix{ A \cr B \cr C \cr } } \ri
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Consider two real sequences with time- origin marked by the bold value, $${x_1}\left[ n \right] = \left\{ {1,\,2,\,3,\,0 View Question The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has mu View Question For the discrete-time system shown in the figure, the poles of the system transfer function are located at View Question The result of the convolution$$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$is View Question In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pas View Question The waveform of a periodic signal x(t) is shown in the figure. A signal g(t) is defined by$$g(t) = x\left( {{{t - 1
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## General Aptitude

If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is
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Operators $$\square$$,◊,$$\rightarrow$$ are defined by : a $$\square$$ b = $$\frac{a-b}{a+b}$$; a ◊ b = \frac{a+b}{a-b
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