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

View Question In the circuit shown, assume that the opamp is ideal. The bridge output voltage V0 (in mV) for $$\delta = 0.05$$ is___

View Question The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillati

View Question 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

View Question 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>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)

View Question A vector $$\overrightarrow P $$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrig

View Question Suppose $$A$$ & $$B$$ are two independent events with probabilities $$P\left( A \right) \ne 0$$ and $$P\left( B \ri

View Question The input $$X$$ to the Binary Symmetric Channel (BSC) shown in the figure is $$'1'$$ with probability $$0.8.$$ The cross

View Question 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

View Question 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

View Question In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across
the capacitor is _________

View Question In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is ___________________.

View Question In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value
of vc(t) (in Volts) at t

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

View Question 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

View Question 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

View Question ## General Aptitude

If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is

View Question Operators $$\square$$,◊,$$\rightarrow$$ are defined by : a $$\square$$ b = $$\frac{a-b}{a+b}$$; a ◊ b = $$\frac{a+b}{a-b

View Question