GATE ECE 2010

## GATE ECE

In the silicon BJT circuit shown below, assume that the emitter area of transistor
Q1 is half that of transistor Q2.The

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The amplifier circuit shown below uses a silicon transistor. The capacitors CC and
CE can be assumed to be short at sign

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Consider the common emitter amplifier shown below with the following circuit parameters:
$$\beta = 100,\,{g_m} = 0.3861

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Consider the common emitter amplifier shown below with the following circuit parameters:
$$\beta = 100,\,{g_m} = 0.3861

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The transfer characteristic for the precision rectifier circuit shown below is (assume ideal OP-AMP and practical diode

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Assuming the OP-AMP to be ideal, the voltage gain of the amplifier shown below is

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Consider an angle modulated signal x(t) = 6cos[2$$\mathrm\pi$$x106
t+2sin(8000$$\mathrm\pi$$t) +
4cos(8000$$\mathrm\pi$$

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X(t) is a stationary process with the power spectral density Sx(f) > 0 for all f. The process is passed through a s

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Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

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Consider a base band binary PAM receiver shown below. The additive channel noise
$$n(t)$$ is white with power spectral d

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Consider a base band binary PAM receiver shown below. The additive channel noise
$$n(t)$$ is white with power spectral d

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The transfer function Y(s)/R(s) of the system shown is

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For the asymptotic Bode magnitude plot shown below, the system transfer function
can be

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A system with the transfer function
$${{Y(s)} \over {X(s)}} = {s \over {s + p}},$$ has an output
y(t)=$$\cos \left( {2t

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A unity negative feedback closed loop system has a plant with the transfer function $$G(s) = {1 \over {{s^2} + 2s + 2}}$

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The signal flow graph of a system is shown below.
The state variable representation of the system can be

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The signal flow graph of a system is shown below.
The transfer function of the system is

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Match the logic gates in column A with their equivalents in column B.

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For the output F to be 1 in the logic circuit shown, the input combination should be

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The Boolean function realized by the logic circuit shown is

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Assuming that all flip-flops are in reset condition initially, the count sequence
observed at QA in the circuit shown is

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If $$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_

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A transmission line has a characteristic impedance of 50 $$\Omega $$ and a resistance of 0.1 $$\Omega $$/m. If the line

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If the scattering matrix [S] of a two port network is $$$\left[ S \right] = \left[ {\matrix{
{0.2\,\angle \,\,{0^ \ci

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In the circuit shown, all the transmission line sections are lossless. The Voltage Standing Wave Ration (VSWR) on the 60

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A plane wave having the electric field component
$$${\overrightarrow E _i} = 24\,\,\cos \,\,\left( {3 \times {{10}^8}\,

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The silicon sample with unit cross-sectional area shown below is in thermal
equilibrium. The following information is gi

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The silicon sample with unit cross-sectional area shown below is in thermal
equilibrium. The following information is gi

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In a uniformly doped BJT, assume that NE, NB and NC are the emitter, base and
collector dopings in atoms/cm3, respective

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The eigen values of a skew-symmetric matrix are

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If $$\,{e^y} = {x^{1/x}}\,\,$$ then $$y$$ has a

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If $$\overrightarrow A = xy\,\widehat a{}_x + {x^2}\widehat a{}_y\,\,$$ then $$\,\,\oint {\overrightarrow A .d\overrigh

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A fair coin is tossed independently four times. The probability of the event ''The number of times heads show up is more

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A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right

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Consider a differential equation $${{dy\left( x \right)} \over {dx}} - y\left( x \right) = x\,\,$$ with initial conditio

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The residues of a complex function $$X\left( z \right) = {{1 - 2z} \over {z\left( {z - 1} \right)\left( {z - 2} \right)}

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In the circuit shown, the device connected to Y5 can have address in the range

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In the circuit shown, the device connected to Y5 can have address in the range

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For the 8085 assembly language program given below, the content of the accumulator after the executions of the program i

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In the circuit shown, the power supplied by the voltage source is

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For parallel RLC circuit, which one of the following statements is NOT correct?

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The current I in the circuit shown is

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For the two-port network shown below, the short-circuit admittance parameter
matrix is

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In the circuit shown, the switch S is open for a long time and is closed at t=0. The
current i(t) for t ≥ 0+ is

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The trigonometric Fourier series for the waveform f(t) shown below contains

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Given f(t) = $${L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {K - 3} \right)s}}} \right].$$
If $$\matrix{

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For an N-point FFT algorithm with N = $${2^m}$$ which one of the following statements is TRUE?

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Consider the z-transform
X(z)=5$${z^2} + 4{z^{ - 1}} + 3;0 < \left| z \right| < \infty $$.
The inverse z - trans

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A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)

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Two discrete time systems with impulse responses $${h_1}\left[ n \right]\, = \delta \left[ {n - 1} \right]$$ and $${h_2}

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The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \ove

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Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

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A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output
$$y(t) = \cos \lef

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The Nyquist sampling rate for the signal $$s(t) = {{\sin \,(500\pi t)} \over {\pi \,t}} \times {{\sin \,(700\pi t)} \ove

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Consider an angle modutated signal $$x(t) = 6\,\,\cos \,[2\,\pi \, \times {10^6}t + 2\sin (8000\pi t)\,4\cos (8000\pi t

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## General Aptitude

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All
were born on 1st January. The

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If 137+276=435 how much is 731+672?

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5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall
in 25 days; 10 unskilled workers

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Modern warfare has changed from large scale clashes of armies to suppression of
civilian populations. Chemical agents th

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Given digits 2,2,3,3,3,4,4,4,4 how many distinct 4 digit numbers greater than
3000 can be formed?

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25 persons are in a room. 15 of them play hockey, 17 of them play football and 10
of them play both hockey and football.

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Which of the following options is the closest in meaning to the world below:
Circuitous

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The question below consists of a pair of related of related words followed by four
pairs of words. Select the pair that

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Choose the most appropriate word from the options given below to complete the
following sentence:
If we manage to ______

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Choose the most appropriate word from the options given below to complete the
following sentence:
His rather casual rema

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