# GATE Ec Scholarship Test

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Quizzes Created: 7 | Total Attempts: 9,290
Questions: 130 | Attempts: 596

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• 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

D. If zero < K < 1 or K > 5
Explanation
The root-locus diagram shows the location of the system's poles as the gain parameter K varies. In an overdamped system, the poles are real and negative. From the given answer choices, only if zero < K < 1 or K > 5 can result in an overdamped system. For K values between 1 and 5, the system may be underdamped or critically damped, but not overdamped. Therefore, the correct answer is if zero < K < 1 or K > 5.

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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

A. Zero
Explanation
The Nyquist plot represents the frequency response of a system. In a unity negative feedback system, the number of roots of the system characteristic equation in the right half of the s-plane corresponds to the number of unstable poles of the system. Since the Nyquist plot shows no poles in the right half of the s-plane, it means that there are no unstable poles and therefore, the number of roots of the system characteristic equation in the right half of the s-plane is zero.

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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

C. Only if Zero < K < 1
Explanation
The feedback control system in the given figure is stable only if the gain factor, K, is between zero and one. This means that the system will remain stable and not exhibit any oscillations or instability if the value of K lies between zero and one. If K is outside this range (either less than zero or greater than one), the system will become unstable and may exhibit oscillations or other undesirable behavior. Therefore, the correct answer is "only if Zero < K < 1."

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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

C. 1/6
Explanation
The damping ratio of a system is a measure of how quickly it oscillates and returns to its steady-state after being disturbed. In this case, the damping ratio is given as 0.5. The damping ratio can be calculated using the formula: damping ratio = 1 / (2 * sqrt(k)). Rearranging the formula, we can solve for k: k = 1 / (4 * damping ratio^2). Substituting the given damping ratio of 0.5 into the formula, we find that k = 1 / (4 * 0.5^2) = 1/6. Therefore, the correct answer is 1/6.

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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

C. Higher noise amplification
Explanation
A PD controller is a proportional-derivative controller that is used to improve the performance of a system by reducing errors and stabilizing the system's response. However, one drawback of using a PD controller is that it can amplify noise in the system. Therefore, the compensated system, which includes a PD controller, will have higher noise amplification compared to the uncompensated system.

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• 6.

• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 7.
• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 8.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 9.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 10.
• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 11.
• A.

A

• B.

B

• C.

C

• D.

D

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

C. 0.082
Explanation
The probability of getting a head in a single toss of an unbiased coin is 1/2. Since the coin is tossed an infinite number of times, the probability of getting a head on any given toss remains the same. Therefore, the probability of getting a head on the fourth toss is 1/2. Similarly, the probability of getting a tail on any given toss is also 1/2. Therefore, the probability of getting a tail on the first three tosses is (1/2)^3 = 1/8. So, the probability of getting a head on the fourth toss and a tail on the first three tosses is 1/2 * 1/8 = 1/16. Finally, the probability of getting a head on the tenth toss is also 1/2. Therefore, the probability of getting a head on the fourth toss and a tail on the first three tosses and then a head on the tenth toss is 1/16 * 1/2 = 1/32. Since there are 10 possible positions for the fourth head to appear (4th, 5th, 6th, ..., 10th toss), we multiply the probability by 10 to get 10/32 = 0.3125. Therefore, the probability that the fourth head appears at the tenth toss is approximately 0.3125, which is closest to 0.082.

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• 13.
• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 14.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 15.
• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 16.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 17.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 18.
• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 19.
• A.

A

• B.

B

• C.

C

• D.

D

C. C
• 20.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 21.

### If z = xyln(xy), then

• A.

A

• B.

B

• C.

C

• D.

D

C. C
Explanation
The correct answer is C because when z = xyln(xy), it implies that z is equal to the product of xy and the natural logarithm of xy. Therefore, the correct answer is C.

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• 22.
• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 23.
• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 24.
• A.

1

• B.

Zero

• C.

-1

• D.

3.14

A. 1
Explanation
The given answer, 1, is the only whole number among the options provided. Zero is not a whole number, -1 is a negative number, and 3.14 is a decimal. Therefore, 1 is the correct answer.

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• 25.
• A.

A

• B.

B

• C.

C

• D.

D

A. A
• 26.
• A.

A

• B.

B

• C.

C

• D.

D

C. C
• 27.
• A.

A

• B.

B

• C.

C

• D.

D

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 âˆ’ 2) + x(t + 4)

• B.

Y(t) = (t âˆ’ 4) x(t + 1)

• C.

Y(t) = (t + 4) x(t âˆ’ 1)

• D.

Y(t) = (t + 5) x(t + 5)

C. Y(t) = (t + 4) x(t âˆ’ 1)
Explanation
A causal system is one where the output at any given time depends only on the input at or before that time. In the given options, the only description that satisfies this condition is y(t) = (t + 4) x(t âˆ’ 1). Here, the output y(t) is a function of the input x(t âˆ’ 1), which means it depends on the input at or before time t. Therefore, this description corresponds to a causal system.

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• 29.
• A.

A

• B.

B

• C.

C

• D.

D

D. D
• 30.
• A.

A

• B.

B

• C.

C

• D.

D

C. C
• 31.

### In the circuit of figure, the equivalent impedance seen across terminals A, B is

• A.

• B.

• C.

(8/3 + 12j) Î©

• D.

None of the above

Explanation
The correct answer is (8/3) Î©. To find the equivalent impedance, we need to combine the resistors and the complex impedance. The 6 Î© resistor and the 4 Î© resistor are in parallel, so their equivalent resistance is (6 * 4) / (6 + 4) = 24 / 10 = 12 / 5 Î©. This equivalent resistance is in series with the 8 Î© resistor, so the total resistance is (12 / 5) + 8 = 68 / 5 Î©. Finally, the 12 Î© + 6j Î© complex impedance is in parallel with this total resistance. The formula for combining a complex impedance (Z1) in parallel with a resistance (R2) is (Z1 * R2) / (Z1 + R2). Plugging in the values, we get ((12 + 6j) * (68 / 5)) / ((12 + 6j) + (68 / 5)) = (8/3) Î©.

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• 32.

### If 24 V is applied across 4 â„¦ resistor then the current flowing through the resistor is

• A.

6 A

• B.

24 A

• C.

48 A

• D.

96 A

A. 6 A
Explanation
When a voltage of 24 V is applied across a resistor with a resistance of 4 â„¦, we can use Ohm's Law (V = IR) to calculate the current flowing through the resistor. Rearranging the formula, we have I = V/R. Plugging in the values, we get I = 24 V / 4 â„¦ = 6 A. Therefore, the correct answer is 6 A.

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• 33.

### Superposition theorem is based on the concept of

• A.

Duality

• B.

Reciprocity

• C.

Linearity

• D.

Non linearity

C. Linearity
Explanation
Superposition theorem is based on the concept of linearity. Linearity refers to the property where the output of a system is directly proportional to its input. In the context of superposition theorem, it states that the response of a linear circuit to multiple independent sources can be determined by summing the responses to each individual source acting alone. This principle allows for simplifying complex circuits and analyzing them more easily by considering one source at a time. Therefore, linearity is the fundamental concept that underlies the application of superposition theorem.

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• 34.

• A.

• B.

• C.

• D.

• 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

B. Only (ii)
Explanation
Passive elements are components in a circuit that do not generate or produce electrical energy on their own. Instead, they consume or receive energy from the circuit or store energy. Therefore, statement (ii) is correct as it accurately describes the behavior of passive elements. Statement (i) is incorrect because passive elements do not generate or produce electrical energy.

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• 36.

### Which of the following is linear element?

• A.

Voltage Source

• B.

Current Source

• C.

Resistor

• D.

None

C. Resistor
Explanation
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 in electrical circuits.

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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)

A. All linear networks
Explanation
The superposition theorem is valid for all linear networks. This means that it can be applied to any network that consists of linear components such as resistors, capacitors, and inductors. The theorem states that the response of a linear network to a set of inputs can be determined by considering the individual responses to each input separately and then adding them together. This principle holds true regardless of whether the network contains dependent sources or not. Therefore, the correct answer is "All linear networks."

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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

B. Cannot be higher than source voltage
Explanation
In a practical voltage source, the terminal voltage cannot be higher than the source voltage. This is because there are always some internal resistances and losses in the source that cause a drop in voltage. Therefore, the terminal voltage will always be equal to or less than the source voltage.

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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

C. 6 F
Explanation
When capacitors are connected in parallel, the equivalent capacitance is equal to the sum of the individual capacitances. In this case, the capacitance values of C1, C2, and C3 are 1 F, 2 F, and 3 F respectively. Therefore, the equivalent capacitance is 1 F + 2 F + 3 F = 6 F.

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• 40.

### Nodal method of solving the network is based on

• A.

Ohmâ€™s law

• B.

Kirchhoffâ€™s Current Law (KCL)

• C.

Kirchhoffâ€™s Voltage Law (KVL)

• D.

Both (A) & (B)

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 across it and inversely proportional to its resistance. KCL states that the algebraic sum of currents entering and leaving a node in a network is zero. By using both of these principles, the nodal method allows for the analysis and calculation of currents and voltages in a network.

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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

D. All sources must be replaced by their internal resistances
Explanation
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 finding the equivalent resistance of the circuit when all sources are replaced by their internal resistances. By doing so, the effect of the sources on the circuit is eliminated, allowing for an accurate determination of the Thevenin resistance. Open circuiting or short circuiting the sources would not give the correct result as it would not account for the internal resistance of the sources.

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• 42.

### If 4 â„¦ 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

B. 0.5 sec
Explanation
When a resistor and an inductor are connected in parallel, the time constant of the circuit is determined by the value of the inductor. The time constant (T) is equal to the inductance (L) divided by the resistance (R). In this case, the inductance is given as 2 H and the resistance is given as 4 â„¦. Therefore, the time constant is 2 H / 4 â„¦ = 0.5 sec.

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• 43.

### The resistance values of three resistors R1, R2 & R3 are 1 â„¦, 2 â„¦ & 4 â„¦ respectively. If these resistors are connected in series then the equivalent resistance value is

• A.

7/4 â„¦

• B.

4/7 â„¦

• C.

5/4 â„¦

• D.

4/5 â„¦

B. 4/7 â„¦
Explanation
When resistors are connected in series, their resistances add up. Therefore, the equivalent resistance of R1, R2, and R3 connected in series would be 1â„¦ + 2â„¦ + 4â„¦ = 7â„¦. However, none of the given answer options match this value. Therefore, the correct answer is not available.

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• 44.

### A 12V DC source with an internal resistance of 2 â„¦ can supply maximum power to the resistive load when the value of load resistor is

• A.

8 â„¦

• B.

4 â„¦

• C.

2 â„¦

• D.

1 â„¦

C. 2 â„¦
Explanation
When a DC source is connected to a resistive load, the maximum power is transferred when the load resistance is equal to the internal resistance of the source. In this case, the internal resistance is 2 â„¦, so the load resistor should also be 2 â„¦ to achieve maximum power transfer. If the load resistance is higher or lower than 2 â„¦, the power transferred will be less than the maximum. Therefore, the correct answer is 2 â„¦.

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• 45.

### In steady state, the inductor behaves as

• A.

Open Circuit

• B.

Short Circuit

• C.

Both (A) & (B)

• D.

None

B. Short Circuit
Explanation
In steady state, the inductor behaves as a short circuit. This means that it allows current to flow through it with little to no resistance. Inductors store energy in the form of a magnetic field, and when the current through the inductor is steady, the magnetic field is also steady. As a result, the inductor opposes any change in current by acting as a short circuit. This allows the current to flow freely through the inductor without any significant impedance. Therefore, the correct answer is short circuit.

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• 46.

### _______ is defined as the time rate of flow of charge.

• A.

Voltage

• B.

Current

• C.

Energy

• D.

Power

B. Current
Explanation
Current is defined as the time rate of flow of charge. It represents the movement of electric charge through a conductor per unit time. It is measured in amperes (A) and is a fundamental concept in electricity. Voltage, on the other hand, is the potential difference between two points in an electric circuit, energy is the capacity to do work, and power is the rate at which work is done or energy is transferred. While all these concepts are related to electricity, only current specifically refers to the time rate of flow of charge.

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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

C. Maximum
Explanation
At resonant frequency, the current flowing through a series R-L-C circuit is maximum. This is because at resonant frequency, the reactive components of the circuit cancel each other out, leaving only the resistive component. As a result, the impedance of the circuit is minimized, allowing maximum current to flow through the circuit.

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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

B. Parallel
Explanation
When two electrical elements are said to be in parallel, it means that the voltages across these elements are the same. In a parallel circuit, the voltage across each element remains constant, regardless of the current flowing through them. This is because the elements are connected side by side, allowing the current to split and flow through each element separately. Therefore, the correct answer is "Parallel".

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• 49.

### Which of the following is not an electrical quantity?

• A.

Voltage

• B.

Current

• C.

Distance

• D.

Power

C. Distance
Explanation
Distance is not an electrical quantity because it is a measure of physical separation or length between two points, and does not involve the flow of electric charge or the presence of an electric field. Voltage, current, and power are all electrical quantities that describe different aspects of electricity. Voltage is the potential difference between two points in an electrical circuit, current is the flow of electric charge, and power is the rate at which electrical energy is transferred or consumed.

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• 50.

### The value of voltage source for a circuit carrying 4 A of current through 5â„¦ resistor

• A.

2.5 V

• B.

5 V

• C.

10 V

• D.

20 V

D. 20 V
Explanation
Based on Ohm's Law (V = I * R), the voltage (V) is equal to the current (I) multiplied by the resistance (R). In this case, the current is 4 A and the resistance is 5 â„¦. Therefore, the voltage is 4 A * 5 â„¦ = 20 V.

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• Mar 19, 2023
Quiz Edited by
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• Apr 24, 2016
Quiz Created by
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