GATE In Scholarship Test
.
- 1.
The root-locus diagram for a closed loop feedback system is shown in Figure The system is overdamped.
- A.
Only if zero < K < 1
- B.
Only if 1 < K < 5
- C.
Only if K > 5
- D.
If zero < K < 1 or K > 5
Correct Answer
D. If zero < K < 1 or K > 5Explanation
The root-locus diagram shows the location of the poles of the closed-loop transfer function as the gain parameter K varies. In an overdamped system, the poles are real and negative. From the given answer choices, the condition "if zero < K < 1 or K > 5" implies that the gain K must be either very small (approaching zero) or very large (greater than 5) for the system to be overdamped. This means that the poles will be located in the left-half of the complex plane, indicating stability and an overdamped response.Rate this question:
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- 2.
The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure. if G(s) has no pole in the right half of splane, the number of roots of the system characteristic equation in the right half of s-plane is
- A.
Zero
- B.
1
- C.
2
- D.
3
Correct Answer
A. ZeroExplanation
The Nyquist plot shows the frequency response of a system. In a unity negative feedback system, the Nyquist plot represents the stability of the system. If there are no poles in the right half of the s-plane, it means that all the poles of the system are located in the left half of the s-plane. The number of roots of the system characteristic equation in the right half of the s-plane is zero, indicating that there are no unstable poles in the system. Therefore, the answer is Zero.Rate this question:
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- 3.
The feedback control system in Figure is stable
- A.
for all K > Zero
- B.
Only if K > 1
- C.
Only if Zero < K < 1
- D.
None
Correct Answer
C. Only if Zero < K < 1Explanation
The given answer states that the feedback control system in the figure is stable only if the value of K is between zero and one. This means that if K is less than zero or greater than one, the system will not be stable. Stability in a feedback control system is crucial for its proper functioning, as it ensures that the system's output remains within acceptable limits and does not oscillate or diverge. Therefore, the system in the figure will only be stable when the gain parameter K is between zero and one.Rate this question:
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- 4.
Consider a system with the transfer function, G(s) = (s + 6) / {ks^2 + s + 6}. Its damping ratio will be 0.5 when the value of k is
- A.
2/6
- B.
3
- C.
1/6
- D.
6
Correct Answer
C. 1/6Explanation
The damping ratio of a system is a measure of how quickly the system's response decays after a disturbance. In this case, the transfer function of the system is given as G(s) = (s + 6) / {ks^2 + s + 6}. The damping ratio, denoted by ζ, can be calculated using the formula ζ = 1 / (2√(k)). Given that the damping ratio is 0.5, we can substitute this value into the formula and solve for k. By rearranging the formula, we get k = (1 / (4ζ^2)). Plugging in ζ = 0.5, we find that k = 1/6. Therefore, the value of k that corresponds to a damping ratio of 0.5 is 1/6.Rate this question:
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- 5.
A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has
- A.
A higher type number
- B.
Reduced damping
- C.
Higher noise amplification
- D.
Larger transient overshoot
Correct Answer
C. Higher noise amplificationExplanation
A PD controller is a proportional-derivative controller that is used to compensate a system. It helps to improve the stability and performance of the system by reducing the error between the desired and actual output. However, one of the drawbacks of using a PD controller is that it can amplify the noise in the system. This means that any disturbances or fluctuations in the input signal can be magnified by the controller, leading to higher noise amplification in the compensated system compared to the uncompensated system.Rate this question:
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- 6.
The signal flow graph of a system is shown in figure. The transfer function C(S)/R(S) of the system is
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 7.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 8.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 9.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 10.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. A -
- 11.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 12.
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
- A.
0.067
- B.
0.073
- C.
0.082
- D.
0.091
Correct Answer
C. 0.082Explanation
The probability that the fourth head appears at the tenth toss can be calculated using the binomial distribution formula. In this case, the probability of success (getting a head) is 0.5 since the coin is unbiased. The probability of failure (getting a tail) is also 0.5. The formula for the probability of exactly k successes in n independent Bernoulli trials is given by C(n,k) * p^k * (1-p)^(n-k), where C(n,k) is the binomial coefficient. Plugging in the values, we get C(10,4) * (0.5)^4 * (0.5)^(10-4) = 210 * (0.5)^10 = 0.082. Therefore, the correct answer is 0.082.Rate this question:
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- 13.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. A -
- 14.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 15.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 16.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 17.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 18.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. A -
- 19.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. C -
- 20.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 21.
If z = xyln(xy), then
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. CExplanation
The correct answer is C because the expression z = xyln(xy) represents the product of xy and the natural logarithm of xy. The natural logarithm of xy can be simplified as ln(xy) = ln(x) + ln(y) using the logarithm rules. Therefore, z = xyln(xy) can be rewritten as z = xy(ln(x) + ln(y)), which is equivalent to option C.Rate this question:
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- 22.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 23.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 24.
- A.
1
- B.
Zero
- C.
-1
- D.
3.14
Correct Answer
A. 1Explanation
The given answer is 1 because it is the only whole number among the options. Zero is not considered a positive or negative number, -1 is a negative number, and 3.14 is a decimal number. Therefore, 1 is the only option that is a whole number.Rate this question:
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- 25.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. A -
- 26.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. C -
- 27.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 28.
The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions correspond to a casual system?
- A.
Y(t) = x(t − 2) + x(t + 4)
- B.
Y(t) = (t − 4) x(t + 1)
- C.
Y(t) = (t + 4) x(t − 1)
- D.
Y(t) = (t + 5) x(t + 5)
Correct Answer
C. Y(t) = (t + 4) x(t − 1)Explanation
A casual system is a system in which the output at any given time depends only on the past and present values of the input. In the given options, the only description that fits this criteria is y(t) = (t + 4) x(t − 1). This equation shows that the output at time t depends on the input at time t-1, which is a past value. Therefore, this description corresponds to a casual system.Rate this question:
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- 29.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 30.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. C -
- 31.
In the circuit of figure, the equivalent impedance seen across terminals A, B is
- A.
(16/3) Ω
- B.
(8/3) Ω
- C.
(8/3 + 12j) Ω
- D.
None of the above
Correct Answer
B. (8/3) ΩExplanation
In the given circuit, the equivalent impedance across terminals A and B can be calculated using the formula for parallel combination of impedances. The circuit consists of a 12Ω resistor in parallel with a series combination of a 6Ω resistor and a 6jΩ reactance. The parallel combination of the 12Ω resistor and the series combination of the 6Ω resistor and 6jΩ reactance can be simplified to a single impedance. By calculating the equivalent impedance, it is found to be (8/3) Ω. Therefore, the correct answer is (8/3) Ω.Rate this question:
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- 32.
If 24 V is applied across 4 Ω resistor then the current flowing through the resistor is
- A.
6 A
- B.
24 A
- C.
48 A
- D.
96 A
Correct Answer
A. 6 AExplanation
When a voltage of 24 V is applied across a 4 Ω resistor, we can use Ohm's Law (V = IR) to calculate the current flowing through the resistor. Rearranging the formula, we get I = V/R. Plugging in the values, I = 24 V / 4 Ω = 6 A. Therefore, the correct answer is 6 A.Rate this question:
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- 33.
Superposition theorem is based on the concept of
- A.
Duality
- B.
Reciprocity
- C.
Linearity
- D.
Non linearity
Correct Answer
C. LinearityExplanation
Superposition theorem is based on the concept of linearity. Linearity refers to the property of a system where the output is directly proportional to the input. In the context of Superposition theorem, it states that in a linear circuit with multiple sources, the total response can be obtained by adding the individual responses due to each source acting alone. This principle allows for simplification and analysis of complex circuits by breaking them down into simpler components. Thus, linearity is the fundamental concept on which the Superposition theorem is based.Rate this question:
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- 34.
The value of the resistance, R, connected across the terminals, A and B, (ref. Fig.) which will absorb the maximum power is
- A.
4 kΩ
- B.
5 kΩ
- C.
8 kΩ
- D.
10 kΩ
Correct Answer
A. 4 kΩExplanation
To determine the value of resistance that will absorb the maximum power, we can use the concept of maximum power transfer theorem. According to this theorem, the maximum power is transferred from a source to a load when the load resistance is equal to the internal resistance of the source. In this case, the internal resistance is not given, but assuming it to be negligible, the resistance value that will absorb the maximum power is 4 kΩ, as it is closest to the typical internal resistance of a voltage source (which is usually around 0-5 kΩ).Rate this question:
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- 35.
Which of the following statement(s) about passive elements is / are correct? (i) These elements generate or produce electrical energy. (ii) These elements consume (receive) energy or store energy.
- A.
Only (i)
- B.
Only (ii)
- C.
Both (i) and (ii)
- D.
None
Correct Answer
B. Only (ii)Explanation
Passive elements are electrical components that do not generate or produce electrical energy on their own, but they consume or receive energy from an external source and can store energy. Therefore, statement (ii) is correct. Statement (i) is incorrect because passive elements do not generate or produce electrical energy.Rate this question:
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- 36.
Which of the following is linear element?
- A.
Voltage Source
- B.
Current Source
- C.
Resistor
- D.
None
Correct Answer
C. ResistorExplanation
A resistor is a linear element because it follows Ohm's Law, which states that the current flowing through a resistor is directly proportional to the voltage across it. In other words, the relationship between voltage and current in a resistor is linear. This means that if you double the voltage across a resistor, the current through it will also double. Therefore, a resistor can be considered a linear element.Rate this question:
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- 37.
The superposition theorem is valid for
- A.
All linear networks
- B.
Non-linear networks
- C.
Only linear networks having no dependent sources
- D.
Both (A) & (B)
Correct Answer
A. All linear networksExplanation
The superposition theorem states that in a linear network, the total response can be determined by summing the individual responses caused by each independent source acting alone, while all other independent sources are turned off. This principle holds true for all linear networks, regardless of whether they contain dependent sources or not. Therefore, the correct answer is "All linear networks".Rate this question:
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- 38.
In a practical voltage source, the terminal voltage
- A.
Cannot be less than source voltage
- B.
Cannot be higher than source voltage
- C.
Is always equal to source voltage
- D.
None
Correct Answer
B. Cannot be higher than source voltageExplanation
In a practical voltage source, the terminal voltage cannot be higher than the source voltage because there will always be some amount of voltage drop across the internal resistance of the source. This internal resistance causes a decrease in the terminal voltage compared to the source voltage. Therefore, the terminal voltage cannot exceed the source voltage.Rate this question:
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- 39.
The capacitance values of three capacitors C1, C2 & C3 are 1 F, 2 F & 3F respectively. If these capacitors are connected in parallel then the equivalent capacitance value is
- A.
(6 / 11) F
- B.
(11 / 6) F
- C.
6 F
- D.
2 F
Correct Answer
C. 6 FExplanation
When capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances. In this case, C1, C2, and C3 are connected in parallel, so the equivalent capacitance is 1 F + 2 F + 3 F = 6 F.Rate this question:
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- 40.
Nodal method of solving the network is based on
- A.
Ohm’s law
- B.
Kirchhoff’s Current Law (KCL)
- C.
Kirchhoff’s Voltage Law (KVL)
- D.
Both (A) & (B)
Correct Answer
D. Both (A) & (B)Explanation
The nodal method of solving a network is based on both Ohm's law and Kirchhoff's Current Law (KCL). Ohm's law states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance. KCL states that the algebraic sum of currents entering and leaving a node in an electrical circuit is zero. By using these two principles, the nodal method allows for the analysis and calculation of currents and voltages in a network.Rate this question:
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- 41.
When determining Thevenin’s resistance of a circuit
- A.
All sources must be open circuited
- B.
All sources must be short circuited
- C.
All voltage sources must be open circuited and all current sources must be short circuited
- D.
All sources must be replaced by their internal resistances
Correct Answer
D. All sources must be replaced by their internal resistancesExplanation
When determining Thevenin's resistance of a circuit, all sources must be replaced by their internal resistances. This is because Thevenin's resistance is calculated by removing all the voltage and current sources in the circuit and replacing them with their internal resistances. By doing this, the circuit is simplified to only include resistors, making it easier to calculate the equivalent resistance seen from the load terminals.Rate this question:
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- 42.
If 4 Ω resistor & 2 H inductor are connected in parallel then time constant of the circuit is
- A.
0.25 sec
- B.
0.5 sec
- C.
5 sec
- D.
8 sec
Correct Answer
B. 0.5 secExplanation
When a resistor and an inductor are connected in parallel, the time constant of the circuit can be calculated using the formula τ = L/R, where τ is the time constant, L is the inductance, and R is the resistance. In this case, the inductance is given as 2 H and the resistance is given as 4 Ω. Plugging these values into the formula, we get τ = 2/4 = 0.5 sec. Therefore, the correct answer is 0.5 sec.Rate this question:
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- 43.
The resistance values of three resistors R1, R2 & R3 are 1 Ω, 2 Ω & 4 Ω respectively. If these resistors are connected in series then the equivalent resistance value is
- A.
7/4 Ω
- B.
4/7 Ω
- C.
5/4 Ω
- D.
4/5 Ω
Correct Answer
B. 4/7 ΩExplanation
When resistors are connected in series, their equivalent resistance is the sum of their individual resistances. In this case, the resistors R1, R2, and R3 have resistance values of 1 Ω, 2 Ω, and 4 Ω respectively. Therefore, the equivalent resistance is 1 Ω + 2 Ω + 4 Ω = 7 Ω. However, the given answer is 4/7 Ω, which is incorrect.Rate this question:
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- 44.
A 12V DC source with an internal resistance of 2 Ω can supply maximum power to the resistive load when the value of load resistor is
- A.
8 Ω
- B.
4 Ω
- C.
2 Ω
- D.
1 Ω
Correct Answer
C. 2 ΩExplanation
The internal resistance of the DC source affects the power delivered to the load. When the load resistor is equal to the internal resistance of the source, the power delivered to the load is maximized. In this case, the internal resistance is 2 Ω, so the load resistor should also be 2 Ω to achieve maximum power transfer.Rate this question:
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- 45.
In steady state, the inductor behaves as
- A.
Open Circuit
- B.
Short Circuit
- C.
Both (A) & (B)
- D.
None
Correct Answer
B. Short CircuitExplanation
In steady state, the inductor behaves as a short circuit. This means that it allows current to flow through it without any impedance. In other words, the inductor acts as a low-resistance path for the current, similar to a wire. This behavior is due to the property of inductance, which opposes changes in current. As a result, in a steady state where the current is constant, the inductor effectively short circuits the circuit.Rate this question:
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- 46.
_______ is defined as the time rate of flow of charge.
- A.
Voltage
- B.
Current
- C.
Energy
- D.
Power
Correct Answer
B. CurrentExplanation
Current is defined as the time rate of flow of charge. It represents the movement of electric charge in a circuit. The unit of current is the Ampere (A), and it is measured using an ammeter. Voltage, on the other hand, is the potential difference between two points in a circuit, and it represents the driving force for the current. Energy and power are related to the amount of work done or the rate at which work is done in a circuit, but they are not directly related to the flow of charge. Therefore, the correct answer is current.Rate this question:
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- 47.
At resonant frequency, the current flowing through series R-L-C circuit is
- A.
Zero
- B.
Minimum
- C.
Maximum
- D.
None
Correct Answer
C. MaximumExplanation
At resonant frequency, the current flowing through a series R-L-C circuit is maximum. This is because at resonant frequency, the reactance of the inductor and capacitor cancel each other out, resulting in a purely resistive circuit. In a purely resistive circuit, the impedance is minimum, allowing maximum current to flow through the circuit.Rate this question:
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- 48.
Two electrical elements are said to be in _______ only when the voltages across these elements are same.
- A.
Series
- B.
Parallel
- C.
Both (A) & (B)
- D.
None
Correct Answer
B. ParallelExplanation
When two electrical elements are said to be in parallel, it means that they are connected side by side, allowing the current to flow through both elements simultaneously. In this configuration, the voltage across both elements is the same, as they are connected to the same points in the circuit. Therefore, the correct answer is "Parallel".Rate this question:
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- 49.
Which of the following is not an electrical quantity?
- A.
Voltage
- B.
Current
- C.
Distance
- D.
Power
Correct Answer
C. DistanceExplanation
Distance is not an electrical quantity because it does not involve the flow of electrons or the presence of electric charges. Voltage, current, and power are all electrical quantities that are used to describe different aspects of the behavior and characteristics of electric circuits. Distance, on the other hand, is a physical quantity that measures the spatial separation between two points and is not directly related to electricity.Rate this question:
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- 50.
The value of voltage source for a circuit carrying 4 A of current through 5Ω resistor
- A.
2.5 V
- B.
5 V
- C.
10 V
- D.
20 V
Correct Answer
D. 20 VExplanation
The voltage across a resistor can be calculated using Ohm's Law, which states that voltage (V) is equal to current (I) multiplied by resistance (R). In this case, the current is given as 4 A and the resistance is given as 5 Ω. Therefore, the voltage across the resistor is 4 A * 5 Ω = 20 V.Rate this question:
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.png "In the circuit of figure, the equivalent impedance seen across terminals A, B is")
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