GATE ECE 2016 Set 2

## GATE ECE

Assume that the diode in the figure has on Von = 0.7V, but is otherwise ideal.
The magnitude of the current i2 (in mA)

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The figure shows a half-wave rectifier with a
475 µF
filter capacitor. The load draws a constant
current I0= 1 A from th

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Resistor R1 in the circuit below has been adjusted so that I1 = 1 mA. The bipolar transistor Q1 and Q2 are perfectly mat

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Which one of the following statements is correct about an ac-coupled common- emitter amplifier operating in the mid-band

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In the opamp circuit shown, the Zener diodes Z1 and Z2 clamp the output voltage Vo to +5 V or -5 V. The switch S is in

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An opamp has a finite open loop voltage gain of 100. Its input offset voltage Vios (= +5mV) is
modeled as shown in the

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A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through

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An information source generates a binary sequence $$\left\{ {{\alpha _n}} \right\}.{\alpha _n}$$ can take one of the two

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Consider random process $$X(t) = 3V(t) - 8$$, where $$V$$ $$(t)$$ is a zero mean stationary random process with autocorr

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An ideal band-pass channel 500Hz-2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate

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A discrete memoryless source has an alphabet $$({a_1},\,{a_2},\,{a_3},\,{a_4})\,$$ with corresponding probabilities$$\le

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A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the followin

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The response of the system
$$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$
to the unit

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In the feedback system shown below
$$$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$
The step response of the closed-loop sy

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The number and direction of encirclements around the point −1 + j0 in the complex plane by the
Nyquist plot of G(s) =$${

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In the feedback system shown below
$${\rm{G(s) = }}{1 \over {\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3

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The asymptotic Bode phase plot of
$${\rm{G(s) = }}{k \over {\left( {s + 0.1} \right)\left( {s + 10} \right)\left( {s +

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A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits to be added while

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Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor 𝑅 = 10 𝑘Ω and the supply

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The state transition diagram for a finite state machine with states A, B and C, and binary inputs X, Y and Z, is shown i

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For the circuit shown in the figure, the delay of the bubbled NAND gate is 2ns and that of the counter is assumed to be

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In an N bit flash ADC, the analog voltage is fed simultaneously to 2N− 1 comparators. The
output of the comparators is t

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A uniform and constant magnetic field
$$B=\widehat zB$$
exists in the
$$\widehat z$$
direction in vacuum. A particle of

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The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged
so that the energy stored

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Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E =

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A microwave circuit consisting of lossless transmission lines $$T_1$$ and $$T_2$$ is shown in the figure. The plot shows

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A lossless microstrip transmission line consists of a trace of width w. It is drawn over a practically infinite ground p

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Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian

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Light from free space is incident at an angle $${\theta _1}$$ to the normal of the facet of a step-index large core opti

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Consider a region of silicon devoid of electrons and holes, with an ionized donor density of
$${\mathrm N}_\mathrm d^+=1

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The Ebers-Moll model of a BJT is valid

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A long-channel NMOS transistor is biased in the linear region with VDS = 50 mV and is used
as a resistance. Which one o

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Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for
worst case charge and discharge

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A voltage VG is applied across a MOS capacitor with metal gate and p-type silicon substrate at
T=300 K. The inversion ca

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Consider a long-channel NMOS transistor with source and body connected together. Assume that
the electron mobility is in

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The value of $$x$$ for which the matrix $$A = \left[ {\matrix{
3 & 2 & 4 \cr
9 & 7 & {13} \cr

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The matrix $$A = \left[ {\matrix{
a & 0 & 3 & 7 \cr
2 & 5 & 1 & 3 \cr
0 & 0 &am

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As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \righ

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How many distinct values of $$x$$ satisfy the equation $$sin(x)=x/2,$$ where $$x$$ is in radians ?

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Suppose $$C$$ is the closed curve defined as the circle $$\,\,{x^2} + {y^2} = 1\,\,$$ with $$C$$ oriented anti-clockwis

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The ordinary differential equation $$\,\,{{dx} \over {dt}} = - 3x + 2,\,\,$$ with $$x(0)=1$$ is to be solved using the

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Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex va

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An 8 Kbyte ROM with an active low Chip Select input CS is to be used in an 8085
microprocessor based system. The ROM sho

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In the given circuit, each resistor has a value equal to 1 Ω.
What is the equivalent resistance across the terminals a

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In the circuit shown in the figure, the magnitude of the current (in amperes) through R2 is___________.

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In the circuit shown below, Vs is a constant voltage source and IL is a constant current load
The value of IL that maxi

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The switch has been in position 1for a long time and abruptly changes to position 2 at t = 0.
If time t is in seconds,

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The switch S in the circuit shown has been closed for a long time. It is opened at time t = 0 and
remains open after tha

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The figure shows an $$RLC$$ circuit with a sinusoidal current source.
At response, the ratio $$\left| {{{\rm I}_L}} \

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The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.

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The Discrete Fourier Transform (DFT) of the 4-point sequence
$$x\left[ n \right]$$= {x[0], x[1], x[2], x[3]}
= {3, 2,

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A continuous-time filter with transfer function $$\,H(S) = {{2s + 6} \over {{s^2} + 6s + 8}}$$ is converted to a discret

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## General Aptitude

Given (9 inches)1/2 = (0.25 yards)1/2, which one of the following statements is TRUE?

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S, M, E and F are working in shifts in a team to finish a project. M works with twice the
efficiency of others but for h

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