GATE ECE 2015 Set 1

## 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

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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

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A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size $$\Delta $$ of t

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The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common bandwidth using TDMA. If at a

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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-over proba

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A source emits bit 0 with probability $${1 \over 3}$$ and bit 1 with probability $${2 \over 3}$$. The emitted bits are
c

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Negative feedback in a closed-loop control system DOES NOT

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The damping ratio of a series RLC circuit can be expressed as

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A unity negative feedback system has the open-loop transfer function
$$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right

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The open-loop transfer function of a plant in a unity feedback configuration is given as $$G\left(s\right)=\frac{K\left(

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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

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A lead compensator network includes a parallel combination of 'R' and 'C' in the feed-forward path. If
the transfer func

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The Boolean expression
F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$

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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

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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

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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

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Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 0001 are 0 V

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The electric field component of a plane wave traveling in a lossless dielectric medium is given by
$$$\overrightarrow E

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The electric field intensity of a plane wave traveling in free space is given by the following expression
$$E\left( {x,

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Consider a uniform plane wave with amplitude $$\left( {{E_0}} \right)$$ of $$10\,\,\,V/m$$ and $$1.1 GHz$$ frequency tra

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The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric c

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A silicon sample is uniformly doped with donor type impurities with a concentration of $$10^{16}/cm^3$$.The electron and

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A region of negative differential resistance is observed in the current voltage characteristics
of a silicon PN junction

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In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6V. The output
voltage V0 (in volts) is __

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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.

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A MOSFET in saturation has a drain current of 1 mA for VDS =0.5V. If the channel length modulation coefficient is 0.05

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For the NMOSFET in the circuit shown, in the threshold voltage is Vth, where Vth>0. The source voltage Vss is varied

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Consider system of linear equations :
$$$x-2y+3z=-1$$$
$$$x-3y+4z=1$$$ and
$$$-2x+4y-6z=k,$$$
The value of $$'k'$$ for

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The value of $$'P'$$ such that the vector $$\left[ {\matrix{
1 \cr
2 \cr
3 \cr
} } \right]$$ is an eig

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A function $$f\left( x \right) = 1 - {x^2} + {x^3}\,\,$$ is defined in the closed interval $$\left[ { - 1,1} \right].$$

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The maximum area (in square units) of a rectangle whose vertices lie on the ellipse $${x^2} + 4{y^2} = 1\,\,$$ is

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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

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Suppose $$A$$ & $$B$$ 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

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Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockw

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In an 8085 microprocessor, the shift registers which store the result of an addition and the overflew bit are, respectiv

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In the given circuit, the values of V1 and V2 respectively are

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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

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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

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The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has
mu

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For the discrete-time system shown in the figure, the poles of the system transfer function are located at

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The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ is

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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

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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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