Electronics And Communication - ECE 2016 GATE Paper (Practice Test)

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,
Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total
of 5692000 fruits, how many of them are apples?

Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

Q.6 – Q.10 Carry two marks each

Q.

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.
However, only 30% of infected people develop the disease. What percentage of people moving
through a tuberculosis prone zone remains infected but does not shows symptoms of disease?

In a world filled with uncertainty, he was glad to have many good friends. He had always assisted
them in times of need and was confident that they would reciprocate. However, the events of the
last week proved him wrong.
Which of the following interference(s) is/are logically valid and can be inferred from the above
passage?
(i) His friends were always asking him to help them
(ii) He felt that when in need of help, his friends would let him down.
(iii) He was sure that his friends would help him when in need.
(iv) His friends did not help him last week.

Leela is older than her cousin Pavithra, pavithra’s brother Shiva is older than Leela. When Pavithra
and shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.
Which one of the following statements must be TRUE based on the above?

P,Q,R and S are working on a project. Q can finish the taks in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

Q.11 – Q.35 Carry one mark each.

Q. Let M4 = I (where I denotes the identity matrix)and M ? I, M2 ? I and M3 ? I. Then, for any
natural number k, M–1 equals:

The second moment of a Poisson-distributed random variables is 2. The mean of the random variable is _____.

Given the following statements about a function f: R→R, select the right option:
P : If f(x) is continuous at x = x0, then it is also differentiable at x = x₀
Q : If f(x) is continuous at x = x0, then it may not be differentiable at x = x₀
R : If f(x) is continuous at x = x0, then it is also different at x = x₀

Which one of the following is a property of the solutions to the Laplace equation : 

Consider the plot of f(x) versus x as shown below

Suppose which one of the following is a graph of F(x)?

Which one of the following is an eigen function of the class of all continuous-time, linear, timeinvariant
systems (u(t) denotes the unit-step function) ?

A continuous –time function x(t) is periodic with period T. The function is sampled uniformly with
a sampling period Ts. In which one of the following cases is the sampled signal periodic ?

Consider the sequence x[n] = aⁿ u[n] +bⁿ u[n], where u[n] denotes the until-step sequence and 0 <
|a| < |b| <1. The region of convergence (ROC) of the z-transform of x[n] is

Consider a two-port network with the transmission matrix :   If the network is
reciprocal, then

A continuous-time sinusoid of frequency 33 Hz is multiplie with a periodic Dirac impulse train of
frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a
cutoff frequency of 23Hz. The functional frequency (in Hz) of the output is _____.

A small percentage of impurity is added to intrinsic semiconductor at 300 K. Which one of the
following statements is true for the energy band diagram shown in the following figure?

Consider the following statements for a metal oxide semiconductor field after effect transistor
(MOSFET):
P : As channel length reduces, OFF-state current increases
Q : As channel length reduces, output resistance increases
R : As channel length reduces, threshold voltage remains constant
S: As channel reduces, ON current increases.
Which of the above statements are INCORRECT?

Consider the constant current source shown in the figure below. Let ? represent the current gain of
the transistor

The load current I0 through R_L is

The following signal Vi of peak voltage 8V is applied to the non-inverting terminal of an ideal
Opamp. The transistor has V_BE = 0.7 V, β = 100; V_LED = 1.5V, V_CC = 10V and –V_CC = – 10V.

The number of times the LED glows is –––––

Consider the oscillator circuit shown in the figure. The function of the network (shown in dotted
lines) consisting of the 100 k? resistor in series with the two diodes connected back-to-back is to:

The block diagram of a frequency synthesizer consisting of Phase Locked Loop (PLL) and a
divide-by-N counter (comprising /2, /4, /8, /16 outputs) is sketched below. The synthesizer is
excited with a 5 kHz signal (Input 1). The free-running frequency of the PLL is set to 20kHz.
Assume that the commutator switch makes contacts repeatedly in the order 1-2-3-4.

The corresponding frequencies synthesized are:

The output of the combinational circuit given below is

What is the voltage V_out in the following circuit?

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements
of first column in Routh’s Table of the system characteristic equation.
X: The system is stable …..                   P: … When all elements are positive
Y: The system is unstable …                Q: … When any on element is zero
Z: The test breaks down ….                  R: … When there is a change in sign of coefficients

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer
function

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude
modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth
(in kHz) required for a roll-off factor of 0.25 is –––––.

A superheterodyne receiver operates in the frequency range of 58 MHz-68MHz. The intermediate frequency f1F and local oscillator frequency f_LO are chosen such that f_1F f_LO. It is required that the image frequencies fall outside the 59 MHz – 68 MHz band. The minimum required f_1F (in MHz) is

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude
modulated signal s(t) = 5 cos 1600?t + 20 cos 1800 ?t + 5 cos 2000?t. The value of the modulation
index is –––––––.

Concentric spherical shells of radii 2m, 4m, and 8m carry uniform surface charge densities of 20
nC/m², –4 nC/m² and ρs, respectively. The value of ρs (nC/m²) required to ensure that the electric
flux density D = 0 at radius 10 m is –––––.

The propagation constant of a lossy transmission line is (2 +j5) m^-1 and its characteristic
impedance is (50 + j0) ? at ω = 10⁶ rad S^-1. The values of the line constants L,C,R,G are,
respectively,

A sequence x[n] is specified as

The initial conditions are x[0] = 1, x[1] = 1 and x[n] = 0 for n < 0. The value of x[12] is ––––

In the following integral, the contour C encloses the points 2πj and –2πj . The value of the integral

The region specified by  in cylindrical coordinates has volume of –––––.

The Laplace transform of the causal periodic square wave of period T shown in the figure below
is

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C)
elements, connected all in series or all in parallel, is excited with a source of the form

The source has nonzero impedance. Which one of the
following is a possible form of the output measured across a resistor in the network?

A first-order low-pass filter of time constant T is excited with different input signals (with zero
initial conditions up to t = 0 ). Match the excitation signals X,Y, Z with the corresponding time
responses for t 0:

X: Impulse                                   P: 1 – e^-t/T
Y: Unit step                                  Q: t – T(1 – e^-t/T)
Z: Ramp                                       R: e^-t/T

An AC voltage source V = 10 sin (t) volts is applied to the following network. Assume that
R1 = 3 k?, R2 = 6k? and R3 = 9k?, and that the diode is ideal.

Rms current I_rms (in mA) through the diode is _____

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor R is ––––.

Consider the signal x[n] =6δ[n +2] +3δ[n +1]+8δ[n]+7δ[n – 1] +4δ[n – 2].
If X(e^jω) is the discrete-time Fourier transform of x[n], then 

Consider a silicon p-n junction with a uniform acceptor doping concentration of 1017 cm-3 on the pside
and a uniform donor doping concentration of 1016 cm-3 on the n-side. No external voltage is
applied to the diode. Given: 

and q= 1.6 x 10^-19c
The charge per unit junction area (nC cm^-2) in the depletion region on the p-side is –––––.

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-tosource
voltage of 1.8V. Assume that W /L =4,  μ_NC_ox = 70 X10^-6AV^-2, the threshold voltage is 0.3V,
and the channel length modulation parameter is 0.09 V^-1, In the saturation region, the drain
conductance (in micro siemens)is –––––.

The figure below shows the doping distribution in a P-type semiconductor in log scale.

The magnitude of the electric field (in kV/cm) in the semiconductor due to non uniform doping is

Consider a silicon sample at T = 300 K, with a uniform donor density N_d = 5x1016 cm^-3
illuminated uniformly such that the optical generation rate is G_opt = 1.5 x10²⁰ cm^-3s^-1 through out
the sample. The incident radiation is turned off at t = 0. Assume low-level injection to be valid and
ignore surface effects. The carrier lifetimes are _po = 0.1 and _no = 0.5 ?s.

The hole concentration at t = 0 and the hole concentration at t = 0.3 μs, respectively, are

An ideal opamp has voltage source V₁, V₂, V₃, V₅, …. , V_N–1 connected to the non-inverting input
and V₂, V₄, V₆ ….V_N connected to the inverting input as shown in the figure below (+V_CC = 15
volt, –V_CC = –15 volt). The voltage V₁, V₂, V₃, V₅, V₆ …. are 1, –1/2, 1/3,–1/4, 1/5, –1/6, …..
volt, respectively. As N approaches infinity, the output voltage (in volt) is ________

A p-i-n photo diode of responsivity 0.8A/W is connected to the inverting input of an ideal opamp
as shown in the figure, +Vcc = 15V, –Vcc = –15V,Load resistor RL = 10 k?. If 10μW
of power is incident on the photodiode, then the value of the photocurrent (in μA) through the
load is _____.

Identify the circuit below.

The functionally implemented by the circuit below is

In a 8085 system, a PUSH operation requires more clock cycles than a POP operation, which one
of the following options is the correct reason for this?

The open-loop transfer function of a unity-feedback control system is

The value of K at the breakaway point of the feedback control system’s root-locus plot is ____

The open-loop transfer function of a unity-feedback control system is given by

For the peak overshoot of the closed-loop system to a until step input to be 10% , the value of K is

The transfer function of a linear time invariant systems is given by H(s) = 2s⁴–5s³+5s–2
The number of zeros in the right half of the s-plane is _____.

Consider a discreet memoryless source with alphabet S = {s0, s1, s2, s3, s4 …..} and respective
probabilities of occurrence

The entropy of the source (in bits ) is _____.

A digital communication system uses a repetition code for channel encoding/decoding. During
transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111).
It is assumed that the source puts out symbols independently and with equal probability . The
decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the
number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number
of zeros, the decoder decides in favor of a 1,Assuming a binary symmetric channel with crossover
probability p = 0.1, the average probability of error is ________.

An analog pulse s(t) is transmitted over an additive white Gaussian (AWGN) channel. The
received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral
density N₀/2 . The received signal is passed through a filter with impulse response h(t). Let E_s and
En denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise
ratio (SNR) is maximized at the output of the filter (SNR_max), which of the following holds?

The current density in a medium is given by

The total current and the average current density flowing through the portion of a spherical
surface  are given, respectively, by

An antenna pointing in a certain direction has a noise temperature of 50K. The ambient
temperature is 290K. The antenna is connected to pre-amplifier that has a noise figure of 2dB and
an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise
temperature Te for the amplifier and the noise power Pao at the output of the preamplifier,
respectively, are

Two lossless X-band horn antennas are separated by a distance of 200?. The amplitude reflection
coefficients at the terminals of the transmitting and receiving antennas are 0.15 and 0.18,
respectively. The maximum directivities of the transmitting and receiving antennas (over the
isotropic antenna) are 18dB and 22dB, respectively. Assuming that the input power in the lossless
transmission line connected to the antenna is 2 W, and that the antennas are perfectly aligned and
polarization matched, the power (in mW) delivered to the load at the receiver is ____

The electric filed of a uniform plane wave travelling along the negative z direction is given by the
following equation:

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric
field towards the incident wave is given by the following equation:

The polarization of the incident wave, the polarization of the antenna and losses due to the
polarization mismatch are, respectively,

The far-zone power density radiated by a helical antenna is approximated as:

The radiated power density is symmetrical with respect to ? and exists only in the upper
hemisphere: is a constant. The power radiated by the antenna (in watts)
and the maximum directivity of the antenna, respectively, are