# GATE Ee Scholarship Test

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Questions: 130 | Attempts: 3,484

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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 poles of the closed-loop transfer function as the gain, K, varies. In an overdamped system, the poles are real and distinct. From the given answer choices, if zero < K < 1 or K > 5, it indicates that the gain is either very small or very large. In both cases, the system will be overdamped, resulting in real and distinct poles. 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 shows the frequency response of the system. Since the Nyquist plot does not cross the negative real axis (right half of the s-plane), it indicates that there are no poles in the right half of the s-plane. The number of roots of the system characteristic equation in the right half of the s-plane is therefore 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 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 to ensure that the system operates properly and does not exhibit unstable behavior such as oscillations or diverging outputs. Therefore, it is necessary for the value of K to be within the range of zero to one for the system to be stable.

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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 the system's response decays after a disturbance. It is determined by the coefficients of the transfer function. In this case, the transfer function has the form (s + a) / (ks^2 + s + 6), where a = 6. The damping ratio is given by the formula ζ = 1 / (2√(k)), where k is the coefficient of the s^2 term in the denominator. Comparing this formula to the given transfer function, we can see that k = 1/6. Therefore, the value of k that corresponds to a damping ratio of 0.5 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 compensate for a system. When a PD controller is implemented, it can amplify the noise present in the system. This means that the compensated system will have higher noise amplification compared to the uncompensated system. Noise amplification refers to the increase in the magnitude of the noise signal. Therefore, the correct answer is higher noise amplification.

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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 on any single toss of an unbiased coin is 0.5. Since the coin is tossed an infinite number of times, we can use the concept of geometric probability to calculate the probability of getting the fourth head on the tenth toss. The probability of getting three tails followed by a head is (0.5)^3 * 0.5 = 0.5^4 = 0.0625. However, the fourth head can occur in different positions within the ten tosses, so we need to multiply this probability by the number of different positions, which is 10 choose 4 = 210. Therefore, the probability is 0.0625 * 210 = 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 given expression z = xyln(xy) represents the product of xy and the natural logarithm of xy. Therefore, the correct answer is C, indicating that the value of z is equal to the product of xy and the natural logarithm of xy.

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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. Zero is not a positive whole number, -1 is a negative whole number, and 3.14 is a decimal number. Therefore, the correct answer is 1.

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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 − 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)

C. Y(t) = (t + 4) x(t − 1)
Explanation
A causal system is a system where the output at any given time depends only on the present and past values of the input. In the given options, the only description that corresponds to a causal system is y(t) = (t + 4) x(t − 1). This is because the output y(t) is a function of the input x(t-1), which is a past value of the input. The other options involve future values of the input, which violates the causality property.

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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.

(16/3) Ω

• B.

(8/3) Ω

• C.

(8/3 + 12j) Ω

• D.

None of the above

B. (8/3) Ω
Explanation
The equivalent impedance seen across terminals A, B can be calculated by finding the total impedance of the circuit. In this circuit, there are two resistors in parallel, each with a resistance of 4Ω. The total resistance of the parallel combination is 2Ω. Additionally, there is a 6Ω resistor in series with the parallel combination. Therefore, the total impedance is 2Ω + 6Ω = 8Ω. However, since the question asks for the equivalent impedance in the form of a complex number, the answer is (8/3) Ω.

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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

A. 6 A
Explanation
According to Ohm's law, the current flowing through a resistor is equal to the voltage applied across it divided by the resistance. In this case, the voltage applied is 24 V and the resistance is 4 Ω. Therefore, the current flowing through the resistor can be calculated as 24 V / 4 Ω = 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 of a system where the output is directly proportional to the input. In the context of superposition theorem, it states that the response of a linear circuit to multiple independent sources can be calculated by considering the individual responses to each source separately and then adding them together. This principle is only applicable to linear circuits, where the relationship between voltage and current remains constant.

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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

A. 4 kΩ
Explanation
In a circuit, the power absorbed by a resistor is maximum when the resistance of the resistor is equal to the internal resistance of the source. In this case, the internal resistance is not given, so we can assume it to be negligible. Therefore, the resistance that will absorb the maximum power is the one with the same value as the load resistance, which is 4 kΩ.

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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

B. Only (ii)
Explanation
Passive elements are electrical components that do not generate or produce electrical energy on their own. Instead, they consume or receive energy from an external source, or they store energy temporarily. Therefore, statement (ii) is correct as it accurately describes the behavior of passive elements. Statement (i), on the other hand, is incorrect as 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 linear element is one that follows Ohm's law, which states that the current passing through it is directly proportional to the voltage applied across it. A resistor is a passive electronic component that obeys Ohm's law, making it a linear element. In contrast, a voltage source and a current source are active elements that do not follow Ohm's law, and therefore, they are not linear elements. The option "none" is incorrect because a resistor is indeed a linear element.

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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 can be found by considering the individual contributions of each independent source in the network separately, while all other independent sources are turned off. This allows for simplification of complex networks and makes it easier to analyze and calculate the response. Therefore, the superposition theorem is applicable to all linear networks, regardless of the presence of dependent sources.

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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 losses in the source due to internal resistance, wire resistance, or other factors. These losses cause a drop in voltage between the source and the terminal, resulting in the terminal voltage being lower than the source voltage. Therefore, it is not possible for the terminal voltage to be higher than the source voltage in a practical voltage source.

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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 total capacitance is the sum of the individual capacitances. In this case, the capacitance values of the three capacitors are 1 F, 2 F, and 3 F. Adding these values together gives a total capacitance of 6 F. Therefore, the equivalent capacitance value when the capacitors are connected in parallel is 6 F.

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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)

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 relates the voltage across a resistor to the current flowing through it, while KCL states that the sum of currents entering a node is equal to the sum of currents leaving the node. By using these principles, the nodal method allows us to analyze and solve complex electrical circuits.

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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
To determine Thevenin's resistance of a circuit, all sources must be replaced by their internal resistances. This is because Thevenin's resistance is calculated by looking at 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 us to determine the Thevenin's resistance accurately. Open circuiting or short circuiting the sources would not give the correct value for Thevenin's resistance.

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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

B. 0.5 sec
Explanation
When a resistor and an inductor are connected in parallel, the total resistance of the circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances. In this case, the total resistance is 1/(1/4 + 1/2) = 2/3 Ω. The time constant of an RL circuit in parallel is given by the product of the total resistance and the inductance. Therefore, the time constant of the circuit is (2/3) * 2 = 4/3 sec, which is approximately equal to 0.5 sec.

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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

B. 4/7 Ω
Explanation
When resistors are connected in series, their resistances add up to give the equivalent resistance. In this case, the resistors R1, R2, and R3 are connected in series, so the equivalent resistance is 1 Ω + 2 Ω + 4 Ω = 7 Ω. Therefore, the correct answer is 7/4 Ω.

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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

C. 2 Ω
Explanation
When a DC source with internal resistance 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 Ω, so the load resistor should also be 2 Ω to maximize power transfer.

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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 the flow of current without any resistance. An inductor stores energy in the form of a magnetic field, and in a steady state, the current through the inductor remains constant. As a result, the inductor acts like a short circuit, allowing the current to flow through it easily.

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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 essential for the operation of electrical circuits. Voltage, on the other hand, represents the electrical potential difference between two points in a circuit. Energy and power are related to the amount of work done or the rate at which work is done, respectively, and are not directly related to the 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 reactance of the inductor and the capacitor cancel out each other, resulting in a purely resistive circuit. In a purely resistive circuit, the current is only limited by the resistance, and therefore, it reaches its maximum value.

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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
Two electrical elements are said to be in parallel only when the voltages across these elements are the same. In a parallel circuit, the voltage across each element is equal because they are connected across the same two points. This is different from a series circuit where the voltage across each element may be different. 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 does not involve the flow of electric charge or the presence of an electric field. Voltage is the electric potential difference between two points, current is the flow of electric charge, and power is the rate at which work is done or energy is transferred in an electrical circuit. However, distance is a physical quantity that measures the separation between two points and is not directly related to electricity.

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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

D. 20 V
Explanation
The voltage in a circuit can be calculated by multiplying the current flowing through the circuit by the resistance. In this case, the current is 4 A and the resistance is 5Ω. So, the voltage can be calculated as 4 A * 5Ω = 20 V. Therefore, the correct answer is 20 V.

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• Current Version
• Oct 26, 2023
Quiz Edited by
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• Jul 16, 2015
Quiz Created by
Anil