GATE ECE 2017 Set 2
GATE ECE
1
The output V0 of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the
diode, is ____________.
2
In the circuit shown, transistors Q1 and Q2 are biased at a collector current of 2.6 mA.
Assuming that transistor current gains are sufficiently large to assume collector current equal
to emitter current and thermal voltage of 26m V, the magnitude of voltage gain Vo/Vs
in the
mid-band frequency range is _____________ (up to second decimal place).
3
In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors Q1,
Q2,….., Q32 are identical in all respects and have infinitely large values of common – emitter
current gain $$\beta $$. The collector current (IC) of the transistors is related to their base emitter voltage (VBE) by the relation IC = IS exp (VBE/VT); where Is is the saturation current. Assume that the
voltage VP shown in the figure is 0.7 V and the thermal voltage VT=26mV
The output voltage Vout (in volts) is _____.
4
A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal to quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is ________ .
5
Consider the random process
x(t) = U + Vt.
Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is _________________
x(t) = U + Vt.
Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is _________________
6
Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P?
7
Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure.
The channel is
The channel is8
The un-modulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a
sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduced
to 40%, then the maximum un-modulated carrier power (in kW) that can be used without
overloading the transmitter is ___________
9
A modulating signal given By $$x\left(t\right)=5\sin\left(4\mathrm\pi10^3\mathrm t\;-\;10\mathrm{πcos}2\mathrm\pi10^3\mathrm t\right)$$ V
is fed to a phase modulator
with phase deviation constant kp=0.5rad/V. If the carrier frequency is 20 kHz, the
instantaneous frequency (in kHz) at t = 0.5 ms is __________
10
For the system shown in the figure, Y (s) / X (s) = __________.
11
A unity feedback control system is characterized by the open-loop transfer function
$$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$$
The value of k for which the system oscillates at 2 rad/s is ________.
12
Which of the following statement is incorrect?
13
A unity feedback control system is characterized by the open loop transfer function
$$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^2} + 10} \right)}}$$
The Nyquist path and the corresponding Nyquist plot of g(s) are shown in the figures below.
If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is
If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is
14
Consider the state space realization
$$$\left[ {\matrix{
{\mathop x\limits^ \bullet } & {\left( t \right)} \cr
{\mathop x\limits^ \bullet } & {\left( t \right)} \cr
} } \right] = \left[ {\matrix{
0 & 0 \cr
0 & { - 9} \cr
} } \right]\left[ {\matrix{
{{x_1}} & {\left( t \right)} \cr
{{x_2}} & {\left( t \right)} \cr
} } \right] + \left[ {\matrix{
0 \cr
{45} \cr
} } \right]u\left( t \right),$$$ with the initial condition $$\left[ {\matrix{
{{x_1}} & {\left( 0 \right)} \cr
{{x_2}} & {\left( 0 \right)} \cr
} } \right] = \left[ {\matrix{
0 \cr
0 \cr
} } \right];$$
Where u(t) denotes the unit step function.
The value of $$\mathop {Lt}\limits_{x \to \infty } \left| {\sqrt {{x_1}^2\left( t \right) + {x_2}^2\left( t \right)} } \right|$$ is ______
Where u(t) denotes the unit step function.
The value of $$\mathop {Lt}\limits_{x \to \infty } \left| {\sqrt {{x_1}^2\left( t \right) + {x_2}^2\left( t \right)} } \right|$$ is ______
15
A second order LTI system is described by the following state equation.
$$$\eqalign{
& {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr
& {d \over {dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right) \cr} $$$
When x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t)=X1(t). The systyem is
16
In a DRAM,
17
A programmable logic array (PLA) is shown in the figure.
The Boolean function F implemented is
The Boolean function F implemented is 18
Consider the circuit shown in the figure.
The Boolean expression F implemented by the circuit is
The Boolean expression F implemented by the circuit is
19
Figure I shows a 4-bits ripple carry adder realized using full adders and Figure II shows the circuit of a full-adder (FA). The
propagation delay of the XOR, AND and OR gates in Figure II are 20 ns, 15 ns and 10 ns respectively. Assume all the inputs to
the 4-bit adder are initially reset to 0.
At t=0, the inputs to the 4-bit adder are changed to $${X_3}$$$${X_2}$$$${X_1}$$$${X_0}$$ =1100, $${Y_3}$$$${Y_2}$$$${Y_1}$$$${Y_0}$$ = 0100 and $${Z_0}$$=1.
The output of the ripple carry adder will be stable at t (in ns) = ____
At t=0, the inputs to the 4-bit adder are changed to $${X_3}$$$${X_2}$$$${X_1}$$$${X_0}$$ =1100, $${Y_3}$$$${Y_2}$$$${Y_1}$$$${Y_0}$$ = 0100 and $${Z_0}$$=1.
The output of the ripple carry adder will be stable at t (in ns) = ____
20
The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input 'In' and an output 'Out'. The initial state of the FSM is S0.
If the input sequence is 10101101001101, starting with the left-most bit, then the number of times 'Out' will be 1 is __________.
21
A two wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is
22
Standard air filled rectangular waveguides of dimensions a = 2.29cm and b = 1.02cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $$T{E_{10}}$$ mode with the operating frequency at least 25% above the cut-off frequency of the $$T{E_{10}}$$ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is
23
The permittivity of water at optical frequencies is $$1.75{\varepsilon _0}$$. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius $$5m$$, as shown in the figure. The critical angle is $${\theta _c}$$
The value of $$d$$ (in meter) is ______ .
24
An electron (q1) is moving in free space with velocity 105 m/s towards a stationary electron
(q2) far away. The closest distance that this moving electron gets to the stationary electron
before the repulsive force diverts its path is ___________ ×10-8m.
[Given, mass of electron m = 9.11×10-31 kg, charge of electron e = -1.6×10-19 C , and permittivity $$\varepsilon_0=\left(1/36\mathrm\pi\right)\times10^{-9}\;\mathrm F/\mathrm m$$].
25
Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and
connected by a long, thin conducting wire, as shown in the figure.
For some charge placed on this structure, the potential and surface electric field on S1 are Va and Ea , and that on S2 are Vb and Eb, respectively, which of the following is CORRECT?
26
An n-channel enhancement mode MOSFET is biased at VGS > VTH and VDS > (VGS - VTH), where
VGS is the gate-to-source voltage, VDS is the drain-to-source voltage and VTH is the threshold
voltage. Considering channel length modulation effect to be significant, the MOSFET behaves
as a
27
For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent
density (JL) is 2.5 mA/cm2
and the open-circuit voltage (V$$_{oc}$$) is 0.451 V. consider thermal
voltage (V$$_T$$) to be 25 mV. If the intensity of the incident light is increased by 20 times,
assuming that the temperature remains unchanged. V$$_{oc}$$ (in volts) will be ______.
28
Consider the circuit shown in the figure. Assume base-to-emitter voltage VBE=0.8 V and common base current gain $$\left(\alpha\right)$$ of the transistor is unity.
The value of the collector-to–emitter voltage VCE (in volt) is _______.
The value of the collector-to–emitter voltage VCE (in volt) is _______.29
An npn bipolar junction transistor (BJT) is operating in the active region. If the reverse bias
across the base-collector junction is increased, then
30
For the circuit shown in the figure, P and Q are the inputs and Y is the output.
The logic implemented by the circuit is
The logic implemented by the circuit is
31
Consider an n-channel MOSFET having width W, length L, electron mobility in the channel
$$\mu_n$$ and oxide capacitance per unit area $$C_{ox}$$. If gate-to-source voltage VGS=0.7 V, drain-to source
voltage VDS=0.1V, $$\left(\mu_nC_{ox}\right)\;=\;100\;\mu A/V^2$$, threshold voltage VTH=0.3 V and (W/L) = 50,
then the transconductance gm (in mA/V) is ___________.
32
Assuming that transistor M1 and M2 are identical and have a threshold voltage of 1V, the state of transistors M1 and M2 are respectively
33
A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV
and electron affinity of Si is 4.0 eV, Ec - EF = 0.9 eV; where Ec and EF are conduction band minimum and the Fermi energy levels of Si, respectively. Oxide$${\varepsilon _r} = \,\,3.9,\,\,\,{\varepsilon _{0\,\,}}=\,8.85 \times {10^{ - 14}}$$ F/cm, oxide thickness $${t_{ox}} = 0.1\,\mu m$$
and electronic charge q = $$1.6 \times {10^{ - 19}}$$ C. If the measured flat band
voltage of the capacitor is –1V, then the magnitude of the fixed charge at the oxide semiconductor
interface, in nC/cm2, is __________.
34
Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double of T1. Both the transistor are biased in the saturation region of operation, but the gate overdrive voltage (VGS - VTH) of T2 is double that of T1, where VGS and VTH are the gate-to-source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T1 are ID1 and gm1 respectively ; the corresponding values of these two parameters for T2 are
35
The rank of the matrix $$\left[ {\matrix{
1 & { - 1} & 0 & 0 & 0 \cr
0 & 0 & 1 & { - 1} & 0 \cr
0 & 1 & { - 1} & 0 & 0 \cr
{ - 1} & 0 & 0 & 0 & 1 \cr
0 & 0 & 0 & 1 & { - 1} \cr
} } \right]$$ is __________.
36
The values of the integrals $$\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dy} } \right)} dx\,\,$$ and $$\,\,\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dx} } \right)} dy\,\,$$ are
37
The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$ - 100 \le x \le $$ $$100$$ occurs at $$x=$$ __________.
38
The smaller angle (in degrees) between the planes $$x+y+z=1$$ and $$2x-y+2z=0$$ is ________.
39
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $$40$$% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is ___________.
40
$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: chemistry $$(329)$$, physics $$(186)$$, Mathematics $$(295)$$, chemistry and physics $$(83)$$, chemistry and Mathematics $$(217)$$, and physic and Mathematics $$(63)$$, How many students are taking all $$3$$ subjects?
41
The general solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} - 5y = 0\,\,\,$$ in terms of arbitrary constants $${K_1}$$ and $${K_2}$$ is
42
An integral $${\rm I}$$ over a counter clock wise circle $$C$$ is given by $${\rm I} = \oint\limits_c {{{{z^2} - 1} \over {{z^2} + 1}}} \,\,{e^z}\,dz$$
If $$C$$ is defined as $$\left| z \right| = 3,$$ then the value of $${\rm I}$$ is
If $$C$$ is defined as $$\left| z \right| = 3,$$ then the value of $${\rm I}$$ is
43
The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are
44
In the circuit shown, $$V$$ is a sinusoidal voltage source. The current $$I$$ is in phase with voltage $$V$$. The ratio $${{{\rm{Amplitude of voltage across the capacitor }}} \over {{\rm{Amplitude of voltage across the resistor }}}}$$ is ______.
45
The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0. The current i(t) (in ampere) at t = 0.5 seconds is ________
46
Consider the circuit shown in the figure.
The Thevenin equivalent resistance (in Ω) across P – Q is _________.
47
A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10 Ω, 5 Ω, 2 Ω are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ____________.
48
Consider the parallel combination of two LTI systems shown in the figure.
$${h_1}(t) = 2\delta (t + 2)\, - 3\delta (t + 1)$$
$${h_2}(t) = \delta (t - 2)$$
If the input x(t) is a unit step signal, then the energy of y(t) is__________________.
The impulse responses of the systems are
$${h_1}(t) = 2\delta (t + 2)\, - 3\delta (t + 1)$$
$${h_2}(t) = \delta (t - 2)$$
If the input x(t) is a unit step signal, then the energy of y(t) is__________________.
49
The input x(t) and the output y(t) of a continuous time system are related as
$$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du.} $$. The system is
50
Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{
{1 - \,{{\left| f \right|} \over {20}},} & {\left| f \right| \le 20} \cr
{0,} & {\left| f \right| > 20} \cr
} } \right.$$$ and phase response Arg[H(f)]= - 2f.
If the input to the system is $$x(t) = 8\cos \left( {20\pi t + \,{\pi \over 4}} \right) + \,16\sin \left( {40\pi t + {\pi \over 8}} \right) + 24\,\cos \left( {80\pi t + {\pi \over {16}}} \right)$$
Then the average power of the output signal y(t) is_____________.
If the input to the system is $$x(t) = 8\cos \left( {20\pi t + \,{\pi \over 4}} \right) + \,16\sin \left( {40\pi t + {\pi \over 8}} \right) + 24\,\cos \left( {80\pi t + {\pi \over {16}}} \right)$$
Then the average power of the output signal y(t) is_____________.
51
The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = $$\left[ {\sin (t)/\pi t} \right]u(t);$$ where u(t) is a unit step function. The system output y(t) as $$t \to \infty $$ is _____________________.
52
An LTI system with unit sample response
$$h\left( n \right) = 5\delta \left[ n \right] - 7\delta \left[ {n - 1} \right] + 7\delta \left[ {n - 3} \right] - 5\delta \left[ {n - 4} \right]$$ is a
$$h\left( n \right) = 5\delta \left[ n \right] - 7\delta \left[ {n - 1} \right] + 7\delta \left[ {n - 3} \right] - 5\delta \left[ {n - 4} \right]$$ is a
53
The signal x(t) = $$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response H(f) as following: $$H(f) = \left\{ {\matrix{
{1,} & {\left| f \right| \le \,12\,kHz} \cr
{0,} & {\left| f \right| > \,12\,kHz} \cr
} } \right.$$
What is the number of sinusoids in the output and their frequency inkHz?
General Aptitude
1
“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the
reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this
mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages
for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately
associated with the actors, to get the perspective needed for the impartial recording of these matters.”
Which of the following statement best reflects the author’s opinion?
Which of the following statement best reflects the author’s opinion?
2
It is ____ to read this year’s textbook _____ the last year’s.
3
Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y married and have two children
P and Q, Z is grandfather of the daughter ‘S’ of P. Further Z and W married and are parents of R. Which
one of the following must necessarily be FALSE?
4
The number of 3 digit numbers such that the digit 1 is never to the immediate right of 2 is
5
1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to
build the same bridge. How many men will be needed to build the bridge in one week?
6
The ninth and the tenth of this month are Monday and Tuesday _______.
7
A contour line joins locations having the same height above the mean sea level. The following is a contour
plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.
Which of the following is the steepest path leaving from P?
Which of the following is the steepest path leaving from P?
8
Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She
then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How
far is she from point P, and in which direction should she go to reach point P?
9
500 students are taking one or more courses out of Chemistry, Physics, and Mathematics.
Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and
Physics and Mathematics (63). How many students are taking all 3 subjects?
10
A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4
people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking beer.
What must be checked to ensure that the rule is being followed?