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GATE 2016
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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
-15
+0.7
-0.7
The signal flow graph for a system is givenbelow.
The transfer function Y(s)/U(s) for this system is given as
(s + 1)/(5 s2 + 6s + 2)
1/(5 s2 + 6s + 2)
(s + 1)/(s2 + 4s + 2)
(s + 1)/(s2 + 6s + 2)
Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network shown in the figure below is
1.3
1.4
2.0
0.5
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
q1 + q2
(1/q1) + (1/q2)
(q1 R1 + q2 R2)/(R1 + R2)
(q1 R2 + q2 R1)/(R1 + R2)
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
103
105
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
π
√2
1
2
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
7 and 80
2.8 and 32
2.8 and 36
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
0.60
0.18
0.30
0.83
The Laplace Transform representation of the triangular pulse shown below is
1/s2[1 - 2e-s + e-2s]
1/s2[1 - e-s + e-2s]
1/s2[1 - e-s + 2e-2s]
1/s2[1 + e-2s]
The complex function tanh (s) is analytic over a region of the imaginary axis of the complex s-plane if the following is TRUE everywhere in the region for all integers n
Im(s) ≠ nπ/3
Im(s) ≠ (2n + 1)π/2
Re (s) = 0
Im(s) ≠ nπ
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
4
3
7
5
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
σ12/(σ12 + σ22)
σ22/(σ12 + σ22)
σ2/(σ12 + σ22)
σ1/(σ12 + σ22)
The dimension of the null space of the matrix is
2
1
3
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
23.84
50.0
25.0
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
125 and 125
250 and 250
250 and 125
125 and 250
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
0.7
0.9
0.5
0.45
For a periodic signal v(t) = 30 sin100t +10cos300t + 6 sin
(500t + π/4), the fundamental frequency in rad/s is
100
1500
500
300
For a vector E, which one of the following statements is NOT TRUE
If ∇ * E = 0, E is called irrotational.
If ∇ * E = 0, E is called conservative.
If ∇ . E = 0, E is called irrotational.
If ∇ . E = 0, E is called solenoidal.
The transfer function V2 (s)/V1 (s) of the circuit shown below is
(s + 1)/(s + 2)
(0.5 s + 1)/(s + 1)
(3 s + 6)/(s + 2)
(s + 2)/(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
14.128
10.000
10.144
12.152
A continuous random variable X has a probability density function f(x) = e-x, 0 < x <∞. Then P{X> 1} is
0.632
0.368
1.0
0.5
Match the following biomedical instrumentation techniques with their applicationsP : Otoscopy U : Respiratory volume measurementQ : Ultrasound Technique V : Ear diagnosticsR : Spirometry W : Echo-cardiographyS : Thermodilution Technique X : Heart volume measurement
P-V, Q-U, R-X, S-W
P-U, Q-V, R-X, S-W
P-V, Q-W, R-X, S-U
P-V, Q-W, R-U, S-X
Consider a delta connection of resistors and its equivalent star connection asshown.
If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of
k2
1/k
k
√k
The open-loop transfer function of a dc motor is given as w(s)/Va (s) = 10/
(1 + 10 s). When connected in feedback as shown below, the approximate value of Ka that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is
1
10
100
5
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
0.96
1.03
0.97
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
8 and 2π
2√2 and 2π/√3
8 and 2π/√3
2√2 and 2π
The type of the partial differential equation is
Nonlinear
Parabolic
Elliptic
Hyperbolic
The digital circuit shown below uses two negative edge-triggered D-flip-flops.
Assuming initial condition of Q1 and Q0 as zero, the output Q1Q0 of this circuit is
00,01,10,11,00 …
00,01,11,10,00 …
00,01,11,11,00 …
00,11,10,01,00 …
The discrete-time transfer function
(1 - 2 z-1)/
(1 - 0.5 z-1) is
minimum phase and stable.
non-minimum phase and stable.
non-minimum phase and unstable.
minimum phase and unstable.
In the transistor circuit as shown below, the value of resistance RE in kΩ is approximately,
2.0
1.0
2.5
1.5
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