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GATE 2016
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Microprocessor
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Number Analogies
Class 8
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GATE 2016
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Consider a plant with the transfer function G(s) = 1/(s +
1)3. Let Ku and Tu be the ultimate gain and ultimate period corresponding to the frequency response based closed loop Ziegler-Nichols cycling method,respectively.
The Ziegler-Nichols tuning rule for a P-controller is given as : K = 0.5 Ku. The values of Ku and Tu, respectively, are
2√2 and 2π/√3
8 and 2π
2√2 and 2π
8 and 2π/√3
Two ammeters A1 and A2 measure the same current and provide readings I1 and I2 ,respectively.
The ammeter errors can be characterized as independent zero mean Gaussian random variables of standard deviations σ1 and σ2 ,respectively.
The value of the current is computed as : I = μ I1 +
(1 - μ) I2 The value of μ which gives the lowest standard deviation of I is
σ1/(σ12 + σ22)
σ2/(σ12 + σ22)
σ12/(σ12 + σ22)
σ22/(σ12 + σ22)
Three capacitors C1, C2 and C3 whose values are 10μF,5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2Vrespectively.
For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are, respectively,
7 and 119
2.8 and 32
7 and 80
2.8 and 36
The type of the partial differential equation is
Parabolic
Hyperbolic
Nonlinear
Elliptic
A continuous random variable X has a probability density function f(x) = e-x, 0 < x <∞. Then P{X> 1} is
0.368
1.0
0.632
0.5
The Laplace Transform representation of the triangular pulse shown below is
1/s2[1 + e-2s]
1/s2[1 - 2e-s + e-2s]
1/s2[1 - e-s + e-2s]
1/s2[1 - e-s + 2e-2s]
A tungsten wire used in a constant current hot wire anemometer has the following parameters : Resistance at 0° C is 10Ω, Surface area is 10-4 m2, Linear temperature coefficient of resistance of the tungsten wire is 4.8 * 10-3 /°C, Convective heat transfer coefficient is 25.2W / m2 /°C, flowing air temperature is 30°C, wire current is 100 mA, mass-specific heat product is 2.5 * 10-5 J /°CThe thermal time constant of the hot wire under flowing air condition in ms is
3.0625
24.5
12.25
6.125
In the transistor circuit as shown below, the value of resistance RE in kΩ is approximately,
2.0
2.5
1.0
1.5
A differential amplifier with signal terminals X,Y,Z is connected as shown inFig.
(a) below for CMRR measurement where the differential amplifier has an additional constant offset voltage in theoutput.
The observations obtained are: when Vi = 2 V, V0 = 3 mV, and when Vi = 3 V, V0 = 4 mV Assuming its differential gain to be 10 and the op-amp to be otherwise ideal, the CMRR is
102
104
105
103
The following arrangement consists of an ideal transformer and an attenuator, which attenuates by a factor of 0.8. An ac voltage VWX1 = 100V is applied across WX to get an open circuit voltage VYZ1 across YZ. Next, an ac voltage VYZ2 100V is applied across YZ to get an open circuit voltage VWX2 across WX. Then, VYZ1/VWX1, VWX2/VYZ2 are respectively,
100/100 and 80/100
125/100 and 80/100
100/100 and 100/100
80/100 and 80/100
While numerically solving the differential equation dy/dx + 2xy2 = 0, y (0) =1 using Euler’s predictorcorrector (improved Euler-Cauchy) method with a step size of 0.2, the value of y after the first step is
1.00
1.03
0.96
0.97
The operational amplifier shown in the circuit below has a slew rate of 0.8 Volts /μ s. The input signal is 0.25 sin (wt)
. The maximum frequency of input in kHz for which there is no distortion in the output is
25.0
23.84
50.0
46.60
For the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V across RL , the minimum value of the load resistor RL in Ω and the minimum power rating of the Zener diode in mW, respectively, are
250 and 250
250 and 125
125 and 125
125 and 250
The signal flow graph for a system is givenbelow.
The transfer function Y(s)/U(s) for this system is given as
(s + 1)/(s2 + 4s + 2)
(s + 1)/(5 s2 + 6s + 2)
(s + 1)/(s2 + 6s + 2)
1/(5 s2 + 6s + 2)
For a vector E, which one of the following statements is NOT TRUE
If ∇ * E = 0, E is called conservative.
If ∇ . E = 0, E is called irrotational.
If ∇ * E = 0, E is called irrotational.
If ∇ . E = 0, E is called solenoidal.
Signals from fifteen thermocouples are multiplexed and each one is sampled once per second with a 16-bitADC.
The digital samples are converted by a parallel to serial converter to generate a serial PCMsignal.
This PCM signal is frequency modulated with FSK modulator with 1200 Hz as 1 and 960 Hz as 0. The minimum band allocation required for faithful reproduction of the signal by the FSK receiver without considering noise is
720 Hz to 1440 Hz
960 Hz to 1200 Hz
840 Hz to 1320 Hz
1080 Hz to 1320 Hz
In the circuit shown below what is the output voltage (Vout) out V in Volts if a silicon transistor Q and an ideal op-amp are used
-15
-0.7
+15
+0.7
An accelerometer has input range of 0 to 10g, natural frequency 30 Hz and mass 0.001 kg. The range of the secondary displacement transducer in mm required to cover the input range is
0 to 11.20
0 to 2.76
0 to 52.10
0 to 9.81
The transfer function V2 (s)/V1 (s) of the circuit shown below is
(s + 2)/(s + 1)
(3 s + 6)/(s + 2)
(s + 1)/(s + 2)
(0.5 s + 1)/(s + 1)
A tungsten wire used in a constant current hot wire anemometer has the following parameters : Resistance at 0° C is 10Ω, Surface area is 10-4 m2, Linear temperature coefficient of resistance of the tungsten wire is 4.8 * 10-3 /°C, Convective heat transfer coefficient is 25.2W / m2 /°C, flowing air temperature is 30°C, wire current is 100 mA, mass-specific heat product is 2.5 * 10-5 J /°CAt steady state, the resistance of the wire in Ω is
12.152
14.128
10.144
10.000
Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network shown in the figure below is
0.5
2.0
1.3
1.4
For a periodic signal v(t) = 30 sin100t +10cos300t + 6 sin
(500t + π/4), the fundamental frequency in rad/s is
1500
300
500
100
The differential pressure transmitter of a flow meter using a venturi tube reads 2.5 × 105 Pa for a flow rate of 0.5 m3/s. The approximate flow rate in m3/s for a differential pressure 0.9 × 105 Pa is
0.18
0.83
0.30
0.60
The dimension of the null space of the matrix is
3
1
2
The maximum value of the solution y (t) of the differential equation y(t) + ӱ(t) = 0 with initial conditions ӱ(0) = 1 and y(0) = 1, for t ≥ 0 is
1
2
π
√2
In the circuit shown below, if the source voltage VS = 100∠53.13o Volts, then the Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is
100∠90o
800∠0o
800∠90o
100∠60o
Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operatingfrequency.
Their respective resistances are R1 and R2. When connected in series, the effective Q factor of the series combination at the same operating frequency is
(1/q1) + (1/q2)
(q1 R1 + q2 R2)/(R1 + R2)
q1 + q2
(q1 R2 + q2 R1)/(R1 + R2)
The circuit below incorporates a permanent magnet moving coil milli-ammeter of range 1 mA having a series resistance of 10 kΩ. Assuming constant diode forward resistance of 50 Ω, a forward diode drop of 0.7 V and infinite reverse diode resistance for each diode, the reading of the meter in mA is
0.9
0.7
0.45
0.5
A source vs (t) = V cos 100 πt has an internal impedance of 4 + j3 Ω. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be
3
5
7
4
A signal Vi (t) = 10 +10 sin100 πt + 10sin 4000 πt + 10sin100000 πt is supplied to a filter circuit (shown below) made up of ideal op-amps.
The least attenuated frequency component in the output will be
0 Hz
2 kHz
50 kHz
50 Hz
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