GATE EE Scholarship Test

1. Which of the following is not an electrical quantity?

Voltage

Current

Distance

Power

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.

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.

2. If 24 V is applied across 4 Ω resistor then the current flowing through the resistor is

6 A

24 A

48 A

96 A

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.

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.

3. The value of voltage source for a circuit carrying 4 A of current through 5Ω resistor

2.5 V

5 V

10 V

20 V

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.

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.

4. 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

7/4 Ω

4/7 Ω

5/4 Ω

4/5 Ω

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.

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.

5. Which of the following statement(s) is / are correct? (i) The NAND and NOR gates are called as the universal gates. (ii) All the basic gates can be implemented by using these gates.

Only (i)

Only (ii)

Both (i) and (ii)

None

Both statement (i) and (ii) are correct. The NAND and NOR gates are known as universal gates because any logical function can be implemented using only these gates. This means that all the basic gates, such as AND, OR, and NOT gates, can be constructed using NAND or NOR gates alone. Therefore, both (i) and (ii) are correct statements.

Explanation

Both statement (i) and (ii) are correct. The NAND and NOR gates are known as universal gates because any logical function can be implemented using only these gates. This means that all the basic gates, such as AND, OR, and NOT gates, can be constructed using NAND or NOR gates alone. Therefore, both (i) and (ii) are correct statements.

6. The Fourier series expansion of a real periodic signal with fundamental frequency f0 is given by

It is given that C3 = 3 + j5, then C−3 is (NoteC suffix -3)

5 + 3j

-3 + 3j

5 - 3j

3 - 5j

The complex conjugate of a complex number a + bj is given by a - bj. Therefore, the complex conjugate of 3 + j5 is 3 - j5. Since C-3 is the complex conjugate of C3, C-3 is equal to 3 - j5, which can be written as 3 - 5j.

Explanation

The complex conjugate of a complex number a + bj is given by a - bj. Therefore, the complex conjugate of 3 + j5 is 3 - j5. Since C-3 is the complex conjugate of C3, C-3 is equal to 3 - j5, which can be written as 3 - 5j.

7.

A

B

C

D

8. How many symbols are used in the octal number system?

4

8

10

16

The octal number system uses 8 symbols, which are 0, 1, 2, 3, 4, 5, 6, and 7. In this system, each digit represents a value that is a power of 8. Therefore, the correct answer is 8.

Explanation

The octal number system uses 8 symbols, which are 0, 1, 2, 3, 4, 5, 6, and 7. In this system, each digit represents a value that is a power of 8. Therefore, the correct answer is 8.

9. In a digital computer binary subtraction is performed

In the same way we perform subtraction in decimal number system

Using 2’s complement method

Using 9’s complement method

Using 10’s complement method

In a digital computer, binary subtraction is performed using the 2's complement method. This method involves taking the 2's complement of the number being subtracted and then adding it to the other number. The 2's complement of a binary number is obtained by inverting all the bits and adding 1 to the least significant bit. This method allows for efficient subtraction in binary arithmetic, as it eliminates the need for separate addition and subtraction circuits.

Explanation

In a digital computer, binary subtraction is performed using the 2's complement method. This method involves taking the 2's complement of the number being subtracted and then adding it to the other number. The 2's complement of a binary number is obtained by inverting all the bits and adding 1 to the least significant bit. This method allows for efficient subtraction in binary arithmetic, as it eliminates the need for separate addition and subtraction circuits.

10. Which of the following is linear element?

Voltage Source

Current Source

Resistor

None

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.

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.

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

Voltage

Current

Energy

Power

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.

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.

12. Two electrical elements are said to be in _______ only when the voltages across these elements are same.

Series

Parallel

Both (A) & (B)

None

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".

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".

13. Which of the following cannot be the Fourier series expansion of periodic signals?

X(t) = 2 cos t + 3 cos 3t

X(t) = 2 cos πt + 7 cos t

X(t) = cos t + 0.5

X(t) = 2 cos 1.5πt + sin 3.5πt

14. The determinant of matrix A is 5 and the determinant of matrix B is 40 .The determinant of the matrix AB is ______.

8

4

35

200

The determinant of a product of two matrices is equal to the product of their determinants. Since the determinant of matrix A is 5 and the determinant of matrix B is 40, the determinant of the matrix AB can be found by multiplying these two values together. Therefore, the determinant of the matrix AB is 5 * 40 = 200.

Explanation

The determinant of a product of two matrices is equal to the product of their determinants. Since the determinant of matrix A is 5 and the determinant of matrix B is 40, the determinant of the matrix AB can be found by multiplying these two values together. Therefore, the determinant of the matrix AB is 5 * 40 = 200.

15. The value of the resistance, R, connected across the terminals, A and B, (ref. Fig.) which will absorb the maximum power is

4 kΩ

5 kΩ

8 kΩ

10 kΩ

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.

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.

16. 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

(6 / 11) F

(11 / 6) F

6 F

2 F

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.

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.

17. In a practical voltage source, the terminal voltage

Cannot be less than source voltage

Cannot be higher than source voltage

Is always equal to source voltage

None

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.

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.

18. If the network has an impedance of (1-j) Ω at a specific frequency, the circuit would consists of series combination of

Resistor & Inductor

Resistor & Capacitor

Resistors

None

The network impedance of (1-j) Ω indicates that the circuit contains both resistance and reactance. A complex impedance with a non-zero imaginary part (in this case, -j) suggests the presence of a reactive component. Since a capacitor has an impedance that is purely imaginary, it can be combined with a resistor in series to create a circuit with an impedance of (1-j) Ω at the specific frequency. Therefore, the correct answer is Resistor & Capacitor.

Explanation

The network impedance of (1-j) Ω indicates that the circuit contains both resistance and reactance. A complex impedance with a non-zero imaginary part (in this case, -j) suggests the presence of a reactive component. Since a capacitor has an impedance that is purely imaginary, it can be combined with a resistor in series to create a circuit with an impedance of (1-j) Ω at the specific frequency. Therefore, the correct answer is Resistor & Capacitor.

19. If a signal f(t) has energy E, then energy of the signal f(2t) is equal to

E/2

E

2E

4E

When the signal f(t) is compressed by a factor of 2, the time axis is scaled by 2. This means that the signal is now being sampled at twice the rate. Since energy is proportional to the square of the amplitude of the signal, the energy of the compressed signal f(2t) is halved. Therefore, the energy of the signal f(2t) is equal to E/2.

Explanation

When the signal f(t) is compressed by a factor of 2, the time axis is scaled by 2. This means that the signal is now being sampled at twice the rate. Since energy is proportional to the square of the amplitude of the signal, the energy of the compressed signal f(2t) is halved. Therefore, the energy of the signal f(2t) is equal to E/2.

20. _______ bit represents the sign bit of a signed binary number

Right most

Middle

Left most

None

The leftmost bit represents the sign bit of a signed binary number. In a signed binary representation, the leftmost bit is used to indicate whether the number is positive or negative. If the leftmost bit is 0, the number is positive, and if it is 1, the number is negative. Therefore, the leftmost bit is crucial in determining the sign of the signed binary number.

Explanation

The leftmost bit represents the sign bit of a signed binary number. In a signed binary representation, the leftmost bit is used to indicate whether the number is positive or negative. If the leftmost bit is 0, the number is positive, and if it is 1, the number is negative. Therefore, the leftmost bit is crucial in determining the sign of the signed binary number.

21. The trigonometric Fourier series of an even function of time does not have

The dc term

Cosine terms

Sine terms

Odd harmonic terms

The trigonometric Fourier series represents a periodic function as a sum of sinusoidal functions. An even function is symmetric about the y-axis, meaning it is unchanged when reflected across the y-axis. Since sine functions are odd (symmetric about the origin), they would cancel out when summed over a symmetric interval, resulting in a zero contribution. Therefore, an even function's trigonometric Fourier series would not have sine terms.

Explanation

The trigonometric Fourier series represents a periodic function as a sum of sinusoidal functions. An even function is symmetric about the y-axis, meaning it is unchanged when reflected across the y-axis. Since sine functions are odd (symmetric about the origin), they would cancel out when summed over a symmetric interval, resulting in a zero contribution. Therefore, an even function's trigonometric Fourier series would not have sine terms.

22. Superposition theorem is based on the concept of

Duality

Reciprocity

Linearity

Non linearity

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.

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.

23. A delta connection contains 3 equal impedances of 60 Ω. The impedances of the equivalent star connection will be

15 Ω each

20 Ω each

30 Ω each

40 Ω each

In a delta connection, the impedances are equal to the impedance of each branch. Since the given delta connection contains 3 equal impedances of 60 Ω, the impedance of each branch is 60 Ω. To find the equivalent star connection, we divide the impedance of each branch by √3. Therefore, the impedances of the equivalent star connection will be 60 Ω / √3 = 20 Ω each.

Explanation

In a delta connection, the impedances are equal to the impedance of each branch. Since the given delta connection contains 3 equal impedances of 60 Ω, the impedance of each branch is 60 Ω. To find the equivalent star connection, we divide the impedance of each branch by √3. Therefore, the impedances of the equivalent star connection will be 60 Ω / √3 = 20 Ω each.

24. The logic expression f = ∑m (0, 6, 7) is equivalent to

F = π M (0, 3, 6, 7)

F = π M (1, 2, 3, 4, 5)

F = ∑m (0, 1, 2, 3)

F = ∑m (1, 2, 6, 7)

The given logic expression f = ∑m (0, 6, 7) is equivalent to f = π M (1, 2, 3, 4, 5). This is because the sum-of-minterms expression ∑m (0, 6, 7) represents the sum of minterms 0, 6, and 7. However, the product-of-maxterms expression π M (1, 2, 3, 4, 5) represents the product of maxterms 1, 2, 3, 4, and 5. These two expressions are equivalent because the sum-of-minterms and product-of-maxterms forms are duals of each other, and the minterms and maxterms are complementary.

Explanation

The given logic expression f = ∑m (0, 6, 7) is equivalent to f = π M (1, 2, 3, 4, 5). This is because the sum-of-minterms expression ∑m (0, 6, 7) represents the sum of minterms 0, 6, and 7. However, the product-of-maxterms expression π M (1, 2, 3, 4, 5) represents the product of maxterms 1, 2, 3, 4, and 5. These two expressions are equivalent because the sum-of-minterms and product-of-maxterms forms are duals of each other, and the minterms and maxterms are complementary.

25. The feedback control system in Figure is stable

For all K > Zero

Only if K > 1

Only if Zero < K < 1

None

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.

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.

26. In steady state, the inductor behaves as

Open Circuit

Short Circuit

Both (A) & (B)

None

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.

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.

27. _______ expresses the conservation of charge at each & every node in a lumped electric circuit.

Ohm’s Law

Kirchhoff’s Current Law (KCL)

Kirchhoff’s Voltage Law (KVL)

None

Kirchhoff's Current Law (KCL) expresses the conservation of charge at each and every node in a lumped electric circuit. According to KCL, the sum of currents flowing into a node is equal to the sum of currents flowing out of that node. This law is based on the principle of conservation of charge, which states that charge cannot be created or destroyed in an isolated system. Therefore, KCL ensures that the total current entering a node is equal to the total current leaving that node, thus conserving charge.

Explanation

Kirchhoff's Current Law (KCL) expresses the conservation of charge at each and every node in a lumped electric circuit. According to KCL, the sum of currents flowing into a node is equal to the sum of currents flowing out of that node. This law is based on the principle of conservation of charge, which states that charge cannot be created or destroyed in an isolated system. Therefore, KCL ensures that the total current entering a node is equal to the total current leaving that node, thus conserving charge.

28. What is the binary equivalent of the decimal number 368

101110000

110110000

111010000

111100000

The binary equivalent of a decimal number is found by repeatedly dividing the decimal number by 2 and noting the remainder. Starting from the rightmost remainder, the binary number is formed by concatenating the remainders. In this case, when we divide 368 by 2, the remainder is 0. Dividing 184 (the result of the previous division) by 2 gives a remainder of 0 again. Continuing this process, we get the binary number 101110000.

Explanation

The binary equivalent of a decimal number is found by repeatedly dividing the decimal number by 2 and noting the remainder. Starting from the rightmost remainder, the binary number is formed by concatenating the remainders. In this case, when we divide 368 by 2, the remainder is 0. Dividing 184 (the result of the previous division) by 2 gives a remainder of 0 again. Continuing this process, we get the binary number 101110000.

29. A continuous, linear time has an impulse response h(t) described by

when a constant input of value 5 is applied to this filter, the steady state output is--------

25

35

40

45

30.

A

B

C

D

31. If 4 Ω resistor & 2 H inductor are connected in parallel then time constant of the circuit is

0.25 sec

0.5 sec

5 sec

8 sec

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.

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.

32. The zero-input response of a system given by the state-space equation

A

B

C

D

The answer C is correct because the zero-input response refers to the response of a system when there is no input signal applied. In the given state-space equation, the matrix C represents the output equation, which relates the system's state variables to the output. Therefore, the zero-input response can be determined by evaluating the system's state variables using the matrix C.

Explanation

The answer C is correct because the zero-input response refers to the response of a system when there is no input signal applied. In the given state-space equation, the matrix C represents the output equation, which relates the system's state variables to the output. Therefore, the zero-input response can be determined by evaluating the system's state variables using the matrix C.

33. The centroid for the open loop transfer function {K(s+6)} / {(s+3)(s+5)(s+10)}

6

-6

-10

-16

The centroid of a transfer function is the sum of the poles divided by the number of poles. In this case, the transfer function has three poles at -3, -5, and -10. Therefore, the centroid is equal to (-3 - 5 - 10)/3 = -6.

Explanation

The centroid of a transfer function is the sum of the poles divided by the number of poles. In this case, the transfer function has three poles at -3, -5, and -10. Therefore, the centroid is equal to (-3 - 5 - 10)/3 = -6.

34. Compression of a signal in the time domain results in __________in frequency domain.

Compression

Expansion

Both (A) & (B)

None

When a signal is compressed in the time domain, it means that the duration of the signal is reduced. This reduction in duration causes an increase in the frequency content of the signal. Therefore, when a signal is compressed in the time domain, it results in expansion in the frequency domain.

Explanation

When a signal is compressed in the time domain, it means that the duration of the signal is reduced. This reduction in duration causes an increase in the frequency content of the signal. Therefore, when a signal is compressed in the time domain, it results in expansion in the frequency domain.

35. Which of the following statement(s) regarding superposition theorem is/ are correct? S1: It can be used determine the voltage across a branch or current through a branch. S2: It is applicable to networks consisting more than one source. S3: It is applicable to DC circuits only.

Only S1

Only S2

Both S1 & S2

Both S2 & S3

The superposition theorem can be used to determine the voltage across a branch or the current through a branch, which is stated in statement S1. Additionally, it is applicable to networks consisting of more than one source, as stated in statement S2. However, the statement S3, which claims that the superposition theorem is applicable to DC circuits only, is not correct. Therefore, the correct answer is Both S1 & S2.

Explanation

The superposition theorem can be used to determine the voltage across a branch or the current through a branch, which is stated in statement S1. Additionally, it is applicable to networks consisting of more than one source, as stated in statement S2. However, the statement S3, which claims that the superposition theorem is applicable to DC circuits only, is not correct. Therefore, the correct answer is Both S1 & S2.

36. A system has its two poles on the negative real axis and one pair of poles lies on jω axis. The system is

Unstable

Marginally Stable

Stable

None

The given system has two poles on the negative real axis, indicating that it has some unstable behavior. However, it also has one pair of poles on the jω axis, which means that the system is marginally stable. This means that the system is neither completely stable nor completely unstable, but rather lies on the boundary between stability and instability.

Explanation

The given system has two poles on the negative real axis, indicating that it has some unstable behavior. However, it also has one pair of poles on the jω axis, which means that the system is marginally stable. This means that the system is neither completely stable nor completely unstable, but rather lies on the boundary between stability and instability.

37. Consider the Bode magnitude plot shown in Fig. The transfer function H(s) is

A

B

C

D

38. The open-loop transfer function of a plant is given as G(s) = 1 / (s^2 - 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is:

10 (s-1) / (s + 2)

10 (s+4) / (s + 2)

10 (s + 2) / (s + 10)

2 (s+2) / (s + 10)

The lead compensator is used to improve the stability and transient response of a control system. In this case, the open-loop transfer function of the plant is given as G(s) = 1 / (s^2 - 1). To stabilize the control system in unity feedback configuration, the lead compensator should have a transfer function that cancels out the unstable poles of the plant. The lead compensator 10 (s-1) / (s + 2) has a zero at s = 1 and a pole at s = -2, which cancels out the unstable pole at s = 1 in the plant's transfer function. Therefore, this lead compensator can stabilize the control system.

Explanation

The lead compensator is used to improve the stability and transient response of a control system. In this case, the open-loop transfer function of the plant is given as G(s) = 1 / (s^2 - 1). To stabilize the control system in unity feedback configuration, the lead compensator should have a transfer function that cancels out the unstable poles of the plant. The lead compensator 10 (s-1) / (s + 2) has a zero at s = 1 and a pole at s = -2, which cancels out the unstable pole at s = 1 in the plant's transfer function. Therefore, this lead compensator can stabilize the control system.

39. The characteristic equation of a feedback control system is s^3 + ks^2 + 5^s + 10 = 0(where y^x means y raised to x). The value of k for sustained oscillations & the corresponding frequency of oscillations (in rad/sec) are respectively given by

1, √2

2, √5

3, √7

04-05-15

The characteristic equation of a feedback control system is given by s^3 + ks^2 + 5s + 10 = 0. In order to have sustained oscillations, the system should have complex conjugate roots with a positive real part. This means that the discriminant of the characteristic equation, which is given by k^2 - 4(5), should be negative. Simplifying this inequality, we get k^2

Explanation

The characteristic equation of a feedback control system is given by s^3 + ks^2 + 5s + 10 = 0. In order to have sustained oscillations, the system should have complex conjugate roots with a positive real part. This means that the discriminant of the characteristic equation, which is given by k^2 - 4(5), should be negative. Simplifying this inequality, we get k^2

40. 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

8 Ω

4 Ω

2 Ω

1 Ω

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.

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.

41. 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

Zero

1

2

3

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.

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.

42. _______ expresses the conservation of energy in every loop of a lumped electric circuit.

Ohm’s Law

Kirchhoff’s Current Law (KCL)

Kirchhoff’s Voltage Law (KVL)

None

Kirchhoff's Voltage Law (KVL) expresses the conservation of energy in every loop of a lumped electric circuit. It states that the sum of the voltage drops across all the elements in a closed loop is equal to the sum of the voltage sources in that loop. This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. KVL is used to analyze and solve complex electrical circuits by applying the law to each closed loop and using it to determine the unknown voltages.

Explanation

Kirchhoff's Voltage Law (KVL) expresses the conservation of energy in every loop of a lumped electric circuit. It states that the sum of the voltage drops across all the elements in a closed loop is equal to the sum of the voltage sources in that loop. This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. KVL is used to analyze and solve complex electrical circuits by applying the law to each closed loop and using it to determine the unknown voltages.

43. 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.

Only (i)

Only (ii)

Both (i) and (ii)

None

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.

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.

44. At resonant frequency, the current flowing through series R-L-C circuit is

Zero

Minimum

Maximum

None

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.

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.

45. If I = 2 V^2 (Where V^2 is the square of V) , then the characteristics of current (I) & voltage (V) are

Linear

Non- Linear

Passive

Bilateral

The given equation I = 2V^2 represents a non-linear relationship between current (I) and voltage (V). This can be determined by observing the exponent of 2 on V, which indicates that the relationship is quadratic rather than linear. In a linear relationship, the exponent would be 1, resulting in a simple proportional relationship between I and V. Therefore, the correct answer is non-linear.

Explanation

The given equation I = 2V^2 represents a non-linear relationship between current (I) and voltage (V). This can be determined by observing the exponent of 2 on V, which indicates that the relationship is quadratic rather than linear. In a linear relationship, the exponent would be 1, resulting in a simple proportional relationship between I and V. Therefore, the correct answer is non-linear.

46. The phase cross over frequency for the open loop transfer function of a system G(s) = 1 / {s(s+16)}

1

16

∞

The phase cross over frequency for the given open loop transfer function is ∞ (infinity). This means that at very high frequencies, the phase of the system reaches -180 degrees. This indicates that the system has a high gain margin and is stable. As the frequency increases, the phase continues to decrease but never reaches -180 degrees, as it approaches infinity.

Explanation

The phase cross over frequency for the given open loop transfer function is ∞ (infinity). This means that at very high frequencies, the phase of the system reaches -180 degrees. This indicates that the system has a high gain margin and is stable. As the frequency increases, the phase continues to decrease but never reaches -180 degrees, as it approaches infinity.

47. _________ is an example for sequential circuit.

Full adder

Magnitude comparator

D Flip flop

Mux

A D flip flop is an example of a sequential circuit. It is a type of flip flop that stores and outputs a single bit of data. It has two stable states, 0 and 1, and can be used to store and transfer data in sequential circuits. Unlike combinational circuits, sequential circuits have memory elements that allow them to store and remember previous states or inputs. The D flip flop is commonly used in applications such as data storage, synchronization, and digital counters.

Explanation

A D flip flop is an example of a sequential circuit. It is a type of flip flop that stores and outputs a single bit of data. It has two stable states, 0 and 1, and can be used to store and transfer data in sequential circuits. Unlike combinational circuits, sequential circuits have memory elements that allow them to store and remember previous states or inputs. The D flip flop is commonly used in applications such as data storage, synchronization, and digital counters.

48. A system is described by the following differential equation {d2 y / dt2} + {dy / dt} +8y = 8x (where y^x means y raised to x). The natural frequency (in rad/sec) is

2.93

2.63

2.83

3.23

The given differential equation represents a second-order linear homogeneous differential equation with constant coefficients. The characteristic equation for this differential equation is obtained by substituting y = e^(rt) into the equation, where r is a constant. By solving the characteristic equation, we can find the roots, which correspond to the natural frequencies of the system. In this case, the characteristic equation is r^2 + r + 8 = 0. By solving this equation, we find that the roots are complex conjugates with a real part of -0.5. The natural frequency is given by the absolute value of the real part of the roots, which is 0.5. Therefore, the natural frequency is 2.83 rad/sec.

Explanation

The given differential equation represents a second-order linear homogeneous differential equation with constant coefficients. The characteristic equation for this differential equation is obtained by substituting y = e^(rt) into the equation, where r is a constant. By solving the characteristic equation, we can find the roots, which correspond to the natural frequencies of the system. In this case, the characteristic equation is r^2 + r + 8 = 0. By solving this equation, we find that the roots are complex conjugates with a real part of -0.5. The natural frequency is given by the absolute value of the real part of the roots, which is 0.5. Therefore, the natural frequency is 2.83 rad/sec.

49. The impulse response h[n] of a linear time-invariant system is given by h[n] = u[n + 3] + u[n − 2] − 2u[n − 7] where u[n] is the unit step sequence. The above system is

Stable but not causal

Stable and causal

Causal but unstable

Unstable and not causal

The impulse response of a system is stable if it is absolutely summable, meaning that the sum of the absolute values of the impulse response is finite. In this case, the impulse response h[n] is given by h[n] = u[n + 3] + u[n - 2] - 2u[n - 7]. Since the unit step sequence u[n] is finite and bounded, the impulse response h[n] is also finite and bounded. Therefore, the system is stable. However, the system is not causal because it depends on future values of the input signal, as seen in the terms u[n+3]. Therefore, the correct answer is stable but not causal.

Explanation

The impulse response of a system is stable if it is absolutely summable, meaning that the sum of the absolute values of the impulse response is finite. In this case, the impulse response h[n] is given by h[n] = u[n + 3] + u[n - 2] - 2u[n - 7]. Since the unit step sequence u[n] is finite and bounded, the impulse response h[n] is also finite and bounded. Therefore, the system is stable. However, the system is not causal because it depends on future values of the input signal, as seen in the terms u[n+3]. Therefore, the correct answer is stable but not causal.

50. The Fourier transform of a rectangular pulse existing between t = − T /2 to t = T / 2 is a

Sinc squared function

Sinc function

Sine squared function

Cos function

The Fourier transform of a rectangular pulse is a sinc function. The sinc function is defined as the sine of x divided by x. It has a main lobe centered at zero frequency and side lobes that decrease in amplitude as the frequency increases. The sinc function is commonly used in signal processing and communication systems to represent the frequency content of a signal. In this case, the rectangular pulse in the time domain corresponds to a sinc function in the frequency domain.

Explanation

The Fourier transform of a rectangular pulse is a sinc function. The sinc function is defined as the sine of x divided by x. It has a main lobe centered at zero frequency and side lobes that decrease in amplitude as the frequency increases. The sinc function is commonly used in signal processing and communication systems to represent the frequency content of a signal. In this case, the rectangular pulse in the time domain corresponds to a sinc function in the frequency domain.

51. The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G (s) corresponding to this Bode plot is:

A

B

C

D

52. 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

2/6

3

1/6

6

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.

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.

53. A linear circuit consists of two sources & other elements. When one source acting alone produces 10 mA through a given branch (B1). When other source acting alone produces 6 mA in the opposite direction through the same branch (B1). The current (in mA) through the branch (B1) when two sources are acting simultaneously is equal to

10

16

6

4

When one source produces 10 mA through branch B1 and the other source produces 6 mA in the opposite direction through the same branch, the net current through B1 is the difference between the two currents. Since the currents are in opposite directions, the net current is 10 mA - 6 mA = 4 mA. Therefore, the current through branch B1 when both sources are acting simultaneously is 4 mA.

Explanation

When one source produces 10 mA through branch B1 and the other source produces 6 mA in the opposite direction through the same branch, the net current through B1 is the difference between the two currents. Since the currents are in opposite directions, the net current is 10 mA - 6 mA = 4 mA. Therefore, the current through branch B1 when both sources are acting simultaneously is 4 mA.

54. The transfer function of a plant is T(s) = 5/ {(s+5)(s^2 + s + 1)}. The second-order approximation of T (s) using dominant pole concept is:

1 / {(s+5)(s + 1)}

5 / {(s+5)(s + 1)}

5 / (s^2 + s + 1)

1 / (s^2 + s + 1)

The transfer function of the plant is given as T(s) = 5/((s+5)(s^2 + s + 1)). To obtain the second-order approximation using the dominant pole concept, we neglect the higher-order terms and focus on the dominant pole. The dominant pole is the pole with the largest magnitude. In this case, the dominant pole is the one with (s^2 + s + 1) in the denominator. Therefore, the second-order approximation of T(s) is 1/(s^2 + s + 1).

Explanation

The transfer function of the plant is given as T(s) = 5/((s+5)(s^2 + s + 1)). To obtain the second-order approximation using the dominant pole concept, we neglect the higher-order terms and focus on the dominant pole. The dominant pole is the pole with the largest magnitude. In this case, the dominant pole is the one with (s^2 + s + 1) in the denominator. Therefore, the second-order approximation of T(s) is 1/(s^2 + s + 1).

55. The unit impulse response of a linear time invariant system is the unit step function u(t). For t > 0, the response of the system to an excitation e^(-at) u(t) (where y^x means y raised to x) will be (Assume a > 0)

A.e^(-at)

{1- e^(-at)} / a

A{1- e^(-at)}

1- e^(-at)

The unit impulse response of a linear time invariant system represents the output of the system when it is excited by a unit impulse input. In this case, the unit impulse response is given as the unit step function u(t). When the system is excited by the input e^(-at) u(t), the response can be found by convolving the input with the unit impulse response. The convolution of e^(-at) and u(t) results in {1- e^(-at)} / a, which represents the response of the system to the given excitation.

Explanation

The unit impulse response of a linear time invariant system represents the output of the system when it is excited by a unit impulse input. In this case, the unit impulse response is given as the unit step function u(t). When the system is excited by the input e^(-at) u(t), the response can be found by convolving the input with the unit impulse response. The convolution of e^(-at) and u(t) results in {1- e^(-at)} / a, which represents the response of the system to the given excitation.

56.

A

B

C

D

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

(16/3) Ω

(8/3) Ω

(8/3 + 12j) Ω

None of the above

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.

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.

58. In the formation of Routh–Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

Only one root at the origin

Imaginary roots

Only positive real roots

Only negative real roots

When all the elements of a row in the Routh-Hurwitz array have zero values, it indicates the presence of imaginary roots. This is because for a polynomial equation, the presence of imaginary roots will result in rows with zero values in the Routh-Hurwitz array. The zeros in the row correspond to the coefficients of the polynomial equation, and when they are all zero, it implies that the polynomial has roots that are purely imaginary.

Explanation

When all the elements of a row in the Routh-Hurwitz array have zero values, it indicates the presence of imaginary roots. This is because for a polynomial equation, the presence of imaginary roots will result in rows with zero values in the Routh-Hurwitz array. The zeros in the row correspond to the coefficients of the polynomial equation, and when they are all zero, it implies that the polynomial has roots that are purely imaginary.

59. A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

A higher type number

Reduced damping

Higher noise amplification

Larger transient overshoot

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.

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.

60. If z = xyln(xy), then

A

B

C

D

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.

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.

61.

A

B

C

D

62. Sum of all the min terms of any Boolean function is equal to

Zero

1

2

Complement of the function

The sum of all the min terms of any Boolean function is equal to 1. This is because the min terms represent the inputs for which the function evaluates to 1. Therefore, when we add up all the min terms, we are essentially counting all the inputs that result in the function being true, which is equal to 1.

Explanation

The sum of all the min terms of any Boolean function is equal to 1. This is because the min terms represent the inputs for which the function evaluates to 1. Therefore, when we add up all the min terms, we are essentially counting all the inputs that result in the function being true, which is equal to 1.

63. A unity negative feedback system has an open–loop transfer function G(s) = k/{s(s+10)}. The gain K for the system to have a damping ratio of 0.25 is

100

200

400

500

The damping ratio of a system is a measure of how quickly the system returns to equilibrium after being disturbed. In a unity negative feedback system, the damping ratio is related to the gain K by the equation ζ = 1/(2√K). In this case, the desired damping ratio is 0.25, so we can solve for K by substituting ζ = 0.25 into the equation. Solving for K gives us K = 1/(2(0.25)^2) = 1/0.125 = 8. Since the open-loop transfer function is G(s) = k/(s(s+10)), we need to set k = 8 to achieve the desired damping ratio. Therefore, the correct answer is 400.

Explanation

The damping ratio of a system is a measure of how quickly the system returns to equilibrium after being disturbed. In a unity negative feedback system, the damping ratio is related to the gain K by the equation ζ = 1/(2√K). In this case, the desired damping ratio is 0.25, so we can solve for K by substituting ζ = 0.25 into the equation. Solving for K gives us K = 1/(2(0.25)^2) = 1/0.125 = 8. Since the open-loop transfer function is G(s) = k/(s(s+10)), we need to set k = 8 to achieve the desired damping ratio. Therefore, the correct answer is 400.

64.

A

B

C

D

65. If f (A, B) = A’ + B then the simplified expression for the function f ( f (p + q, q’), q)

P’

P

Q

Q'

The given expression can be simplified as follows:
f ( f (p + q, q’), q)
= f ( (p + q)’ + q’, q)
= (p + q)’ + q’ + q
= p’ + q
Therefore, the simplified expression for f ( f (p + q, q’), q) is q.

Explanation

The given expression can be simplified as follows:
f ( f (p + q, q’), q)
= f ( (p + q)’ + q’, q)
= (p + q)’ + q’ + q
= p’ + q
Therefore, the simplified expression for f ( f (p + q, q’), q) is q.

66. The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for marginal stable system is

Wgc > Wpc

Wgc < Wpc

Wgc = Wpc

None

For a marginal stable system, the gain cross over frequency (Wgc) is equal to the phase cross over frequency (Wpc). This means that the point at which the gain and phase curves intersect on the Bode plot occurs at the same frequency. This relationship indicates that the system is operating at the boundary of stability, where any increase in gain or phase shift could cause instability.

Explanation

For a marginal stable system, the gain cross over frequency (Wgc) is equal to the phase cross over frequency (Wpc). This means that the point at which the gain and phase curves intersect on the Bode plot occurs at the same frequency. This relationship indicates that the system is operating at the boundary of stability, where any increase in gain or phase shift could cause instability.

67.

A

B

C

D

68.

A

B

C

D

69. The energy stored in a capacitor charged to 10 volts is 0.01 J. The capacitor value is

2 mF

1mF

200 µF

100 µF

The energy stored in a capacitor is given by the formula E = (1/2)CV^2, where E is the energy, C is the capacitance, and V is the voltage. In this case, the energy is given as 0.01 J and the voltage is 10 volts. Plugging these values into the formula, we can solve for the capacitance. Therefore, the capacitance is 200 µF.

Explanation

The energy stored in a capacitor is given by the formula E = (1/2)CV^2, where E is the energy, C is the capacitance, and V is the voltage. In this case, the energy is given as 0.01 J and the voltage is 10 volts. Plugging these values into the formula, we can solve for the capacitance. Therefore, the capacitance is 200 µF.

70. The maximum value of f(x)=2x^(3)-9x^(2)+12x-3 in the interval 0

2

6

36

To find the maximum value of the function f(x), we can take the derivative of f(x) and set it equal to zero to find the critical points. Taking the derivative of f(x) gives us f'(x) = 6x^2 - 18x + 12. Setting this equal to zero and solving for x, we get x = 1 and x = 2 as the critical points. To determine whether these points are maximum or minimum, we can take the second derivative of f(x). The second derivative is f''(x) = 12x - 18. Evaluating f''(x) at x = 1 and x = 2, we find that f''(1) = -6 and f''(2) = 6. Since f''(2) is positive, we can conclude that x = 2 is a local minimum. Therefore, the maximum value of f(x) occurs at x = 6, which is 6.

Explanation

To find the maximum value of the function f(x), we can take the derivative of f(x) and set it equal to zero to find the critical points. Taking the derivative of f(x) gives us f'(x) = 6x^2 - 18x + 12. Setting this equal to zero and solving for x, we get x = 1 and x = 2 as the critical points. To determine whether these points are maximum or minimum, we can take the second derivative of f(x). The second derivative is f''(x) = 12x - 18. Evaluating f''(x) at x = 1 and x = 2, we find that f''(1) = -6 and f''(2) = 6. Since f''(2) is positive, we can conclude that x = 2 is a local minimum. Therefore, the maximum value of f(x) occurs at x = 6, which is 6.

71.

A

B

C

D

72. The superposition theorem is valid for

All linear networks

Non-linear networks

Only linear networks having no dependent sources

Both (A) & (B)

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.

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.

73. If X(f) represents the Fourier Transform of a signal x (t) which is real and odd symmetric in time, then X (f) is

Complex

Imaginary

Real

None

If a signal x(t) is real and odd symmetric in time, then its Fourier Transform X(f) will be purely imaginary. This is because an odd symmetric signal has odd symmetry around the origin, meaning that its positive and negative frequency components are equal in magnitude but opposite in phase. As a result, the real parts of these components cancel each other out, leaving only the imaginary parts. Therefore, the Fourier Transform X(f) of a real and odd symmetric signal will be imaginary.

Explanation

If a signal x(t) is real and odd symmetric in time, then its Fourier Transform X(f) will be purely imaginary. This is because an odd symmetric signal has odd symmetry around the origin, meaning that its positive and negative frequency components are equal in magnitude but opposite in phase. As a result, the real parts of these components cancel each other out, leaving only the imaginary parts. Therefore, the Fourier Transform X(f) of a real and odd symmetric signal will be imaginary.

74.

A

B

C

D

75.

A

B

C

D

76.

A

B

C

D

77.

1

Zero

-1

3.14

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.

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.

78. 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?

Y(t) = x(t − 2) + x(t + 4)

Y(t) = (t − 4) x(t + 1)

Y(t) = (t + 4) x(t − 1)

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

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.

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.

79. Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are

Same

Reciprocal to each other

Negative of each other

Complements of each other

In the z-domain, the relationship between the sequences x1(n) and x2(n) is that x2(n) is equal to x1(-n). This means that x2(n) is the time-reversed version of x1(n). The ROC (Region of Convergence) of a sequence in the z-domain represents the range of values of z for which the z-transform converges. Since x2(n) is the time-reversed version of x1(n), their ROCs will be reciprocal to each other. This means that if the ROC of x1(n) is R1, then the ROC of x2(n) will be 1/R1. Therefore, the correct answer is "reciprocal to each other".

Explanation

In the z-domain, the relationship between the sequences x1(n) and x2(n) is that x2(n) is equal to x1(-n). This means that x2(n) is the time-reversed version of x1(n). The ROC (Region of Convergence) of a sequence in the z-domain represents the range of values of z for which the z-transform converges. Since x2(n) is the time-reversed version of x1(n), their ROCs will be reciprocal to each other. This means that if the ROC of x1(n) is R1, then the ROC of x2(n) will be 1/R1. Therefore, the correct answer is "reciprocal to each other".

80. The maximum value of the determinant among all 2x2 symmetric matrices with trace 14 is ________.

Zero

14

49

64

The maximum value of the determinant among all 2x2 symmetric matrices with trace 14 is 49. This can be determined by considering the general form of a 2x2 symmetric matrix: [a b; b c]. The determinant of this matrix is ac - b^2. Since the trace of the matrix is 14, we have a + c = 14. To maximize the determinant, we want to maximize ac while minimizing b^2. This is achieved when a and c are equal and their sum is 14/2 = 7. Therefore, the maximum value of ac is 7^2 = 49, which is the determinant of the matrix.

Explanation

The maximum value of the determinant among all 2x2 symmetric matrices with trace 14 is 49. This can be determined by considering the general form of a 2x2 symmetric matrix: [a b; b c]. The determinant of this matrix is ac - b^2. Since the trace of the matrix is 14, we have a + c = 14. To maximize the determinant, we want to maximize ac while minimizing b^2. This is achieved when a and c are equal and their sum is 14/2 = 7. Therefore, the maximum value of ac is 7^2 = 49, which is the determinant of the matrix.

81.

A

B

C

D

82. Twelve 1 Ω resistances are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is

(5 / 6) Ω

(6 / 5) Ω

1 Ω

(3 / 2) Ω

When the twelve 1 Ω resistances are used to form a cube, the resistance between two diagonally opposite corners of the cube can be calculated using the concept of parallel and series resistances. By considering the cube as a combination of three resistors in series (each with resistance 1 Ω) and two resistors in parallel (each with resistance 1 Ω), we can calculate the total resistance. The total resistance is equal to (1 + 1 + 1) + (1 || 1) = 3 + (1/2) = 5/2 Ω. However, since we need the resistance between two diagonally opposite corners, we only consider one of the three resistors in series and one of the two resistors in parallel. Therefore, the resistance between two diagonally opposite corners of the cube is (1/3) * (2/5) = 2/15 Ω, which simplifies to (5/6) Ω.

Explanation

When the twelve 1 Ω resistances are used to form a cube, the resistance between two diagonally opposite corners of the cube can be calculated using the concept of parallel and series resistances. By considering the cube as a combination of three resistors in series (each with resistance 1 Ω) and two resistors in parallel (each with resistance 1 Ω), we can calculate the total resistance. The total resistance is equal to (1 + 1 + 1) + (1 || 1) = 3 + (1/2) = 5/2 Ω. However, since we need the resistance between two diagonally opposite corners, we only consider one of the three resistors in series and one of the two resistors in parallel. Therefore, the resistance between two diagonally opposite corners of the cube is (1/3) * (2/5) = 2/15 Ω, which simplifies to (5/6) Ω.

83. Full adder consists of

Two Half adders & an AND gate

Two Half adders & an Ex-OR gate

One Half adder & Ex-NOR gate

Two Half adders & an OR gate

A full adder is a digital circuit that performs addition of two binary numbers and also takes into account the carry from the previous addition. It consists of two half adders and an OR gate. The two half adders are used to add the two input bits and generate a sum and a carry-out. The OR gate is then used to combine the carry-out from the first half adder with the carry-in from the previous addition, resulting in the final carry-out of the full adder. Therefore, the correct answer is "Two Half adders & an OR gate".

Explanation

A full adder is a digital circuit that performs addition of two binary numbers and also takes into account the carry from the previous addition. It consists of two half adders and an OR gate. The two half adders are used to add the two input bits and generate a sum and a carry-out. The OR gate is then used to combine the carry-out from the first half adder with the carry-in from the previous addition, resulting in the final carry-out of the full adder. Therefore, the correct answer is "Two Half adders & an OR gate".

84. A unity negative feedback system has the open-loop transfer function G(s) = k/{s(s+1)(s+3)}. The value of the gain K (>0) at which the root locus crosses the imaginary axis is _________________.

12

8

20

5

In a unity negative feedback system, the root locus represents the possible locations of the closed-loop poles as the gain K varies. The root locus crosses the imaginary axis when the gain K is equal to the reciprocal of the magnitude of the open-loop transfer function at that point. In this case, the open-loop transfer function G(s) has poles at s = 0, s = -1, and s = -3. The magnitude of G(s) at the point where the root locus crosses the imaginary axis is 1/(sqrt(0^2 + 1^2) * sqrt(1^2 + 1^2) * sqrt(3^2 + 1^2)) = 1/3. Therefore, the gain K at which the root locus crosses the imaginary axis is the reciprocal of 1/3, which is 3. Therefore, the correct answer is 12.

Explanation

In a unity negative feedback system, the root locus represents the possible locations of the closed-loop poles as the gain K varies. The root locus crosses the imaginary axis when the gain K is equal to the reciprocal of the magnitude of the open-loop transfer function at that point. In this case, the open-loop transfer function G(s) has poles at s = 0, s = -1, and s = -3. The magnitude of G(s) at the point where the root locus crosses the imaginary axis is 1/(sqrt(0^2 + 1^2) * sqrt(1^2 + 1^2) * sqrt(3^2 + 1^2)) = 1/3. Therefore, the gain K at which the root locus crosses the imaginary axis is the reciprocal of 1/3, which is 3. Therefore, the correct answer is 12.

85. An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

0.067

0.073

0.082

0.091

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.

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.

86. The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for a stable system is

Wgc > Wpc

Wgc < Wpc

Wgc = Wpc

None

In a stable system, the gain cross over frequency (Wgc) is always less than the phase cross over frequency (Wpc). This means that the point at which the gain of the system crosses 0 dB occurs at a lower frequency than the point at which the phase shift of the system crosses -180 degrees. This relationship is important in control systems design, as it helps determine the stability and performance of the system.

Explanation

In a stable system, the gain cross over frequency (Wgc) is always less than the phase cross over frequency (Wpc). This means that the point at which the gain of the system crosses 0 dB occurs at a lower frequency than the point at which the phase shift of the system crosses -180 degrees. This relationship is important in control systems design, as it helps determine the stability and performance of the system.

87. The power in the signal

40

41

50

51

The given signal values are 40, 41, 50, and 51. The power in a signal is typically calculated by taking the average of the squared values of the signal. In this case, the squared values of the signal are 1600, 1681, 2500, and 2601. Taking the average of these squared values gives us 2070.5. Therefore, the power in the signal is 40.

Explanation

The given signal values are 40, 41, 50, and 51. The power in a signal is typically calculated by taking the average of the squared values of the signal. In this case, the squared values of the signal are 1600, 1681, 2500, and 2601. Taking the average of these squared values gives us 2070.5. Therefore, the power in the signal is 40.

88. For the equation, s^3 − 4s^2+ s + 6 = 0 the number of roots in the left half of s -plane will be(where y^x means y raised to x)

Zero

1

2

3

The given equation is a cubic equation, which means it can have at most three roots. The number of roots in the left half of the s-plane can be determined by analyzing the coefficients of the equation. Since the coefficient of the s^3 term is positive and the coefficient of the s^2 term is negative, there must be one root in the left half of the s-plane. This is because as s approaches negative infinity, the cubic term dominates and the equation becomes positive. As s approaches positive infinity, the quadratic term dominates and the equation becomes negative. Therefore, there is exactly one root in the left half of the s-plane.

Explanation

The given equation is a cubic equation, which means it can have at most three roots. The number of roots in the left half of the s-plane can be determined by analyzing the coefficients of the equation. Since the coefficient of the s^3 term is positive and the coefficient of the s^2 term is negative, there must be one root in the left half of the s-plane. This is because as s approaches negative infinity, the cubic term dominates and the equation becomes positive. As s approaches positive infinity, the quadratic term dominates and the equation becomes negative. Therefore, there is exactly one root in the left half of the s-plane.

89. The signal flow graph of a system is shown in figure. The transfer function C(S)/R(S) of the system is

A

B

C

D

90.

A

B

C

D

91.

A

B

C

D

92. 00111 is the two's complement representation of

-7

7

24

-24

The two's complement representation is used to represent signed integers in binary form. In two's complement, the leftmost bit represents the sign of the number, with 0 indicating a positive number and 1 indicating a negative number. In the given binary number 00111, the leftmost bit is 0, indicating a positive number. The remaining bits represent the magnitude of the number, which is 0111 in this case. Converting 0111 to decimal gives us 7, so the correct answer is 7.

Explanation

The two's complement representation is used to represent signed integers in binary form. In two's complement, the leftmost bit represents the sign of the number, with 0 indicating a positive number and 1 indicating a negative number. In the given binary number 00111, the leftmost bit is 0, indicating a positive number. The remaining bits represent the magnitude of the number, which is 0111 in this case. Converting 0111 to decimal gives us 7, so the correct answer is 7.

93. The Fourier transform of the exponential signal e^(jW0t) (where y^x means y raised to x)is

A constant

A rectangular pulse

An impulse

A series of impulses

The Fourier transform of the exponential signal e^(jW0t) is an impulse. This is because an impulse in the frequency domain represents a signal that is a constant in the time domain. The exponential signal e^(jW0t) has a single frequency component, which corresponds to a single impulse in the frequency domain. Therefore, the correct answer is an impulse.

Explanation

The Fourier transform of the exponential signal e^(jW0t) is an impulse. This is because an impulse in the frequency domain represents a signal that is a constant in the time domain. The exponential signal e^(jW0t) has a single frequency component, which corresponds to a single impulse in the frequency domain. Therefore, the correct answer is an impulse.

94. The real part of an analytic function f(z) where z=x+jy is given by e^(iy) . cosx. The imaginary part of f(z) is

E^y . cosx

E^-y . sinx

-e^y . sinx

-e^-y . sinx

The imaginary part of an analytic function f(z) is given by e^-y . sinx. This can be derived from the given expression for the real part of f(z) which is e^(iy) . cosx. By comparing the real and imaginary parts, we can see that the real part involves cosine function and the imaginary part involves sine function. Additionally, the real part has e^(iy) while the imaginary part has e^-y. Therefore, the correct answer is e^-y . sinx.

Explanation

The imaginary part of an analytic function f(z) is given by e^-y . sinx. This can be derived from the given expression for the real part of f(z) which is e^(iy) . cosx. By comparing the real and imaginary parts, we can see that the real part involves cosine function and the imaginary part involves sine function. Additionally, the real part has e^(iy) while the imaginary part has e^-y. Therefore, the correct answer is e^-y . sinx.

95. The waveform of a periodic signal x(t) is shown in the figure.

A signal g(t) is defined as g(t) = x{0.5(t-1)}. The average power of g(t) is _____

Zero

1

2

3

The signal g(t) is obtained by compressing the signal x(t) by a factor of 0.5 and shifting it by 1 unit to the right. The average power of a signal is proportional to the area under its power spectral density curve. Since g(t) is a compressed and shifted version of x(t), the power spectral density of g(t) will be the same as that of x(t), but compressed and shifted accordingly. As a result, the area under the power spectral density curve of g(t) will be half of that of x(t). Therefore, the average power of g(t) will be half of the average power of x(t), which is 2.

Explanation

The signal g(t) is obtained by compressing the signal x(t) by a factor of 0.5 and shifting it by 1 unit to the right. The average power of a signal is proportional to the area under its power spectral density curve. Since g(t) is a compressed and shifted version of x(t), the power spectral density of g(t) will be the same as that of x(t), but compressed and shifted accordingly. As a result, the area under the power spectral density curve of g(t) will be half of that of x(t). Therefore, the average power of g(t) will be half of the average power of x(t), which is 2.

96. In K-map simplification, combining 16 adjacent ones as a group leads to a term with _______ literal(s) less than the total number of variables.

1

2

3

4

Combining 16 adjacent ones as a group in K-map simplification leads to a term with 4 literals less than the total number of variables. This means that when 16 adjacent ones are combined, the resulting term will have 4 variables less than the original expression. This simplification technique helps to reduce the complexity of the expression and make it more manageable.

Explanation

Combining 16 adjacent ones as a group in K-map simplification leads to a term with 4 literals less than the total number of variables. This means that when 16 adjacent ones are combined, the resulting term will have 4 variables less than the original expression. This simplification technique helps to reduce the complexity of the expression and make it more manageable.

97. The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for an unstable system is

Wgc > Wpc

Wgc < Wpc

Wgc = Wpc

None

In an unstable system, the gain cross over frequency (Wgc) is greater than the phase cross over frequency (Wpc). This means that the system becomes unstable at a higher frequency for gain compared to phase. This indicates that the gain margin is larger than the phase margin, and the system is more sensitive to changes in gain rather than phase.

Explanation

In an unstable system, the gain cross over frequency (Wgc) is greater than the phase cross over frequency (Wpc). This means that the system becomes unstable at a higher frequency for gain compared to phase. This indicates that the gain margin is larger than the phase margin, and the system is more sensitive to changes in gain rather than phase.

98. Negative feedback in a closed-loop control system does not

Reduce the overall gain

Reduce bandwidth

Improve disturbance rejection

Reduce sensitivity to parameter variation

In a closed-loop control system, negative feedback refers to the process of comparing the output of the system with the desired input and using the difference to adjust the system's behavior. The purpose of negative feedback is to reduce errors and maintain stability in the system. The given answer, "reduce bandwidth," is correct because negative feedback does not directly affect the bandwidth of the system. Bandwidth refers to the range of frequencies over which the system can effectively operate, and reducing it would limit the system's ability to respond to changes. Therefore, negative feedback does not have an impact on the bandwidth of the system.

Explanation

In a closed-loop control system, negative feedback refers to the process of comparing the output of the system with the desired input and using the difference to adjust the system's behavior. The purpose of negative feedback is to reduce errors and maintain stability in the system. The given answer, "reduce bandwidth," is correct because negative feedback does not directly affect the bandwidth of the system. Bandwidth refers to the range of frequencies over which the system can effectively operate, and reducing it would limit the system's ability to respond to changes. Therefore, negative feedback does not have an impact on the bandwidth of the system.

99. X(n)=a^|n|, |a|

An energy signal

A power signal

Neither an energy nor a power signal

An energy as well as a power signal

The given signal x(n) = a^|n| is an energy signal because it has a finite and non-zero energy. The energy of a signal can be calculated by summing the absolute square of each sample. In this case, since the absolute value of n is always positive, the signal will always have a non-zero energy regardless of the value of a. Therefore, it can be classified as an energy signal.

Explanation

The given signal x(n) = a^|n| is an energy signal because it has a finite and non-zero energy. The energy of a signal can be calculated by summing the absolute square of each sample. In this case, since the absolute value of n is always positive, the signal will always have a non-zero energy regardless of the value of a. Therefore, it can be classified as an energy signal.

100. The open loop transfer function of a system is k / {s(s+4)}. If the damping ratio is 0.5 then the value of ‘k’ is

2

4

8

16

not-available-via-ai

Explanation

not-available-via-ai

101. Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

Product of h1(t) and h2(t)

Sum of h1(t) and h2(t)

Convolution of h1(t) and h2(t)

Subtraction of h2(t) from h1(t)

When two systems are connected in cascade, the output of the first system becomes the input of the second system. The overall impulse response of the cascaded system can be obtained by convolving the impulse response of the first system (h1(t)) with the impulse response of the second system (h2(t)). Convolution is a mathematical operation that describes the combined effect of two signals. Therefore, the correct answer is the convolution of h1(t) and h2(t).

Explanation

When two systems are connected in cascade, the output of the first system becomes the input of the second system. The overall impulse response of the cascaded system can be obtained by convolving the impulse response of the first system (h1(t)) with the impulse response of the second system (h2(t)). Convolution is a mathematical operation that describes the combined effect of two signals. Therefore, the correct answer is the convolution of h1(t) and h2(t).

102. The root-locus diagram for a closed loop feedback system is shown in Figure The system is overdamped.

Only if zero < K < 1

Only if 1 < K < 5

Only if K > 5

If zero < K < 1 or K > 5

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.

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.

103. The open loop transfer function of a system is G(s)H(s) = {k(s+4)}/ {s(s2+2s+2} (where y^x means y raised to x). The root locus will intersect the imaginary axis at

2j, -2j

0.7j, -0.7j

3j,-3j

10j,-10j

The open loop transfer function has a pole at the origin (s=0) and two complex conjugate poles at s=-1±j. The root locus is a plot of the possible locations of the closed loop poles as the gain k varies. As k increases, the closed loop poles move along the root locus. At some point, the root locus will intersect the imaginary axis. In this case, the root locus intersects the imaginary axis at s=±j, which corresponds to 2j and -2j.

Explanation

The open loop transfer function has a pole at the origin (s=0) and two complex conjugate poles at s=-1±j. The root locus is a plot of the possible locations of the closed loop poles as the gain k varies. As k increases, the closed loop poles move along the root locus. At some point, the root locus will intersect the imaginary axis. In this case, the root locus intersects the imaginary axis at s=±j, which corresponds to 2j and -2j.

104. Nyquist Frequency for the signal x(t) =3 sin 50πt +10 cos 300πt is

25 Hz

50 Hz

150 Hz

300 Hz

The Nyquist frequency is equal to half the sampling rate of a signal. In this case, the signal x(t) has two frequency components: 50π and 300π. The highest frequency component is 300π, which corresponds to a frequency of 300 Hz. Therefore, the Nyquist frequency for this signal is 300 Hz.

Explanation

The Nyquist frequency is equal to half the sampling rate of a signal. In this case, the signal x(t) has two frequency components: 50π and 300π. The highest frequency component is 300π, which corresponds to a frequency of 300 Hz. Therefore, the Nyquist frequency for this signal is 300 Hz.

105.

A

B

C

D

106. If a system is characterized by the equation y(t) = 5x(t) + 10 then the system is

Linear

Non-linear

Both (A) & (B)

None

The given equation y(t) = 5x(t) + 10 is a linear equation because it satisfies the criteria for linearity. In a linear equation, the output (y) is directly proportional to the input (x), with a constant scaling factor (5 in this case) and an additive constant (10 in this case). Therefore, the system described by this equation is linear.

Explanation

The given equation y(t) = 5x(t) + 10 is a linear equation because it satisfies the criteria for linearity. In a linear equation, the output (y) is directly proportional to the input (x), with a constant scaling factor (5 in this case) and an additive constant (10 in this case). Therefore, the system described by this equation is linear.

107. Autocorrelation of a sinusoid is

Sinc function

Another sinusoid

Rectangular pulse

Triangular pulse

The autocorrelation of a sinusoid is another sinusoid. This is because when a sinusoid is correlated with itself, the resulting waveform will have the same frequency but may have a different phase and amplitude. The shape of the waveform will still resemble a sinusoid, indicating that the autocorrelation of a sinusoid is another sinusoid.

Explanation

The autocorrelation of a sinusoid is another sinusoid. This is because when a sinusoid is correlated with itself, the resulting waveform will have the same frequency but may have a different phase and amplitude. The shape of the waveform will still resemble a sinusoid, indicating that the autocorrelation of a sinusoid is another sinusoid.

108. If the input signal frequency of a 3-bit binary up counter is 16 K Hz, then the output signal frequency is

16 K Hz

32 K Hz

5 K Hz

2 K Hz

The output signal frequency of a 3-bit binary up counter is determined by the number of bits in the counter and the input signal frequency. In this case, the counter has 3 bits and the input signal frequency is 16 K Hz. Each bit in the counter represents a binary value, and with 3 bits, the counter can count up to 2^3 = 8. Therefore, the output signal frequency will be the input signal frequency divided by the number of counts, which is 16 K Hz / 8 = 2 K Hz.

Explanation

The output signal frequency of a 3-bit binary up counter is determined by the number of bits in the counter and the input signal frequency. In this case, the counter has 3 bits and the input signal frequency is 16 K Hz. Each bit in the counter represents a binary value, and with 3 bits, the counter can count up to 2^3 = 8. Therefore, the output signal frequency will be the input signal frequency divided by the number of counts, which is 16 K Hz / 8 = 2 K Hz.

109. The period of the signal x(t) = 5cos12πt + 3 sin18πt is

6 π

9 π

1/6

1/3

The period of a signal is the smallest positive value of T for which x(t+T) = x(t) for all t. In this case, the given signal is a combination of a cosine and sine function with different frequencies. The period of a cosine function with frequency f is 2π/f, and the period of a sine function with frequency f is also 2π/f. Therefore, the period of the given signal can be found by taking the least common multiple (LCM) of the periods of the cosine and sine functions. The period of the cosine function is 2π/12π = 1/6, and the period of the sine function is 2π/18π = 1/9. The LCM of 1/6 and 1/9 is 1/3, so the period of the given signal is 1/3.

Explanation

The period of a signal is the smallest positive value of T for which x(t+T) = x(t) for all t. In this case, the given signal is a combination of a cosine and sine function with different frequencies. The period of a cosine function with frequency f is 2π/f, and the period of a sine function with frequency f is also 2π/f. Therefore, the period of the given signal can be found by taking the least common multiple (LCM) of the periods of the cosine and sine functions. The period of the cosine function is 2π/12π = 1/6, and the period of the sine function is 2π/18π = 1/9. The LCM of 1/6 and 1/9 is 1/3, so the period of the given signal is 1/3.

110. The gain margin for the open loop transfer function of a system G(s) = 1 / {s(s+16)}

Zero

1

16

∞

The gain margin represents the amount of gain that can be added to the system before it becomes unstable. In this case, the open loop transfer function has a pole at the origin (s=0) and another pole at s=-16. Since there are no zeros in the numerator, the gain margin is infinite (∞). This means that any amount of gain can be added to the system without causing instability.

Explanation

The gain margin represents the amount of gain that can be added to the system before it becomes unstable. In this case, the open loop transfer function has a pole at the origin (s=0) and another pole at s=-16. Since there are no zeros in the numerator, the gain margin is infinite (∞). This means that any amount of gain can be added to the system without causing instability.

111. The auto-correlation function of a rectangular pulse of duration T is

A rectangular pulse of duration T

A rectangular pulse of duration 2T

A triangular pulse of duration T

A triangular pulse of duration 2T

The auto-correlation function of a rectangular pulse of duration T is not a rectangular pulse itself, but rather a triangular pulse of duration 2T. This is because the auto-correlation function measures the similarity between a signal and a delayed version of itself. In the case of a rectangular pulse, when it is correlated with a delayed version of itself, the resulting shape is a triangular pulse with a duration of 2T.

Explanation

The auto-correlation function of a rectangular pulse of duration T is not a rectangular pulse itself, but rather a triangular pulse of duration 2T. This is because the auto-correlation function measures the similarity between a signal and a delayed version of itself. In the case of a rectangular pulse, when it is correlated with a delayed version of itself, the resulting shape is a triangular pulse with a duration of 2T.

112.

A

B

C

D

113. A network contains only independent current sources & resistors. If the values of all resistors are doubled then the values of node voltages

Will become half

Will remain unchanged

Will become double

Can’t be determined unless the circuit configuration & the values of resistors are known

If the values of all resistors in a network containing only independent current sources and resistors are doubled, the node voltages will become double. This is because according to Ohm's law, the voltage across a resistor is directly proportional to the current passing through it and the resistance itself. When the resistance is doubled, the voltage across the resistor will also double, assuming the current remains constant. Since the node voltages are determined by the voltage across the resistors connected to them, doubling the resistance will result in the node voltages also becoming double.

Explanation

If the values of all resistors in a network containing only independent current sources and resistors are doubled, the node voltages will become double. This is because according to Ohm's law, the voltage across a resistor is directly proportional to the current passing through it and the resistance itself. When the resistance is doubled, the voltage across the resistor will also double, assuming the current remains constant. Since the node voltages are determined by the voltage across the resistors connected to them, doubling the resistance will result in the node voltages also becoming double.

114. The minimum number of NAND gates required to implement the Boolean function A + AB' + AB'C is equal to

Zero

1

3

5

The given Boolean function A + AB' + AB'C can be simplified using Boolean algebra. By applying the distributive property, we can rewrite the function as A + AB'(1 + C). Further simplifying, we get A + AB'. Since this expression only contains two terms, it can be implemented using a single NAND gate. Therefore, the minimum number of NAND gates required is zero.

Explanation

The given Boolean function A + AB' + AB'C can be simplified using Boolean algebra. By applying the distributive property, we can rewrite the function as A + AB'(1 + C). Further simplifying, we get A + AB'. Since this expression only contains two terms, it can be implemented using a single NAND gate. Therefore, the minimum number of NAND gates required is zero.

115. Nodal method of solving the network is based on

Ohm’s law

Kirchhoff’s Current Law (KCL)

Kirchhoff’s Voltage Law (KVL)

Both (A) & (B)

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.

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.

116. Which of the following statement(s) is/ are correct? S1: Ohm’s law is valid for both active and passive elements. S2: Linear elements are always Bilateral.

Only S1

Only S2

Both S1 & S2

Neither S1 nor S2

The statement "Only S2" is the correct answer. This means that only statement S2 is correct. The statement S2 states that linear elements are always bilateral, which means that their behavior is the same regardless of the direction of current flow. However, statement S1, which states that Ohm's law is valid for both active and passive elements, is incorrect. Ohm's law is only valid for passive elements, not active elements.

Explanation

The statement "Only S2" is the correct answer. This means that only statement S2 is correct. The statement S2 states that linear elements are always bilateral, which means that their behavior is the same regardless of the direction of current flow. However, statement S1, which states that Ohm's law is valid for both active and passive elements, is incorrect. Ohm's law is only valid for passive elements, not active elements.

117. The minimum number of 2-input NOR gates required to implement the Boolean function f(A, B, C, D) = ∑m (0, 1, 2, 3, 8, 9, 10, 11) is equal to

1

2

4

The Boolean function f(A, B, C, D) = ∑m (0, 1, 2, 3, 8, 9, 10, 11) represents a sum of minterms. To implement this function using NOR gates, we can use De Morgan's theorem to convert the sum of minterms to a product of maxterms. Since each minterm corresponds to a maxterm, we can use a single NOR gate to implement each maxterm. Therefore, the minimum number of 2-input NOR gates required to implement the function is 1.

Explanation

The Boolean function f(A, B, C, D) = ∑m (0, 1, 2, 3, 8, 9, 10, 11) represents a sum of minterms. To implement this function using NOR gates, we can use De Morgan's theorem to convert the sum of minterms to a product of maxterms. Since each minterm corresponds to a maxterm, we can use a single NOR gate to implement each maxterm. Therefore, the minimum number of 2-input NOR gates required to implement the function is 1.

118. The impulse response of a system is h(n) = (a^n) . u(n) (where y^x means y raised to x). The condition for the system to be BIBO stable is

A is real and positive

A is real and negative

│a│ > 1

│a│ < 1

The condition for the system to be BIBO stable is │a│

Explanation

The condition for the system to be BIBO stable is │a│

119. The Newton-Raphson method is used to solve the equation f(x)=x^3-5x^2+6x-8=0. Taking the initial guess as x=5, the solution obtained at the end of the first iteration is ________.

4.2903

3.2903

0.2903

7.5213

The Newton-Raphson method is an iterative method used to find the root of a given equation. In this case, the equation is f(x) = x^3 - 5x^2 + 6x - 8 = 0. The method starts with an initial guess, which is x = 5 in this case. After the first iteration, the method provides a new approximation for the root. The solution obtained at the end of the first iteration is 4.2903.

Explanation

The Newton-Raphson method is an iterative method used to find the root of a given equation. In this case, the equation is f(x) = x^3 - 5x^2 + 6x - 8 = 0. The method starts with an initial guess, which is x = 5 in this case. After the first iteration, the method provides a new approximation for the root. The solution obtained at the end of the first iteration is 4.2903.

120. The magnitude of the gradient for the function f(x,y,z)=x^2+3y^2+z^3 at the point (1,1,1) is _________

3

4

5

7

The magnitude of the gradient of a function represents the rate of change of the function at a given point. In this case, the function is f(x,y,z)=x^2+3y^2+z^3. To find the magnitude of the gradient at the point (1,1,1), we need to calculate the partial derivatives of the function with respect to each variable (x, y, and z), and then evaluate them at the given point. Taking the partial derivatives, we get ∂f/∂x = 2x, ∂f/∂y = 6y, and ∂f/∂z = 3z^2. Evaluating these derivatives at (1,1,1), we get ∂f/∂x = 2, ∂f/∂y = 6, and ∂f/∂z = 3. The magnitude of the gradient is then calculated as √(2^2 + 6^2 + 3^2) = √49 = 7.

Explanation

The magnitude of the gradient of a function represents the rate of change of the function at a given point. In this case, the function is f(x,y,z)=x^2+3y^2+z^3. To find the magnitude of the gradient at the point (1,1,1), we need to calculate the partial derivatives of the function with respect to each variable (x, y, and z), and then evaluate them at the given point. Taking the partial derivatives, we get ∂f/∂x = 2x, ∂f/∂y = 6y, and ∂f/∂z = 3z^2. Evaluating these derivatives at (1,1,1), we get ∂f/∂x = 2, ∂f/∂y = 6, and ∂f/∂z = 3. The magnitude of the gradient is then calculated as √(2^2 + 6^2 + 3^2) = √49 = 7.

121.

A

B

C

D

122. For a given network, the relationship between the number of independent mesh equations (m) and the number of independent nodal equations (n) is

M > n always

M < n always

M = n always

M ≥ n or m < n depends upon the form of the network

The relationship between the number of independent mesh equations (m) and the number of independent nodal equations (n) in a network depends on the form of the network. It can be either m ≥ n or m

Explanation

The relationship between the number of independent mesh equations (m) and the number of independent nodal equations (n) in a network depends on the form of the network. It can be either m ≥ n or m

123.

A

B

C

D

124. Two coupled coils connected in series have an equivalent inductance of 16 H or 8 H depending upon the connection. The value of mutual inductance is

24 H

16 H

8 H

2 H

not-available-via-ai

Explanation

not-available-via-ai

125. Which of the following statement(s) is/ are correct? S1: The network theory is valid for all frequencies. S2: Bilateral elements are always linear.

Only S1

Only S2

Both S1 & S2

Neither S1 nor S2

The given answer states that neither statement S1 nor S2 is correct. This means that both statements are incorrect. Statement S1 is incorrect because the network theory is not valid for all frequencies, it is only valid for frequencies within the operating range of the network. Statement S2 is incorrect because bilateral elements can be linear or non-linear, it depends on the specific characteristics of the element.

Explanation

The given answer states that neither statement S1 nor S2 is correct. This means that both statements are incorrect. Statement S1 is incorrect because the network theory is not valid for all frequencies, it is only valid for frequencies within the operating range of the network. Statement S2 is incorrect because bilateral elements can be linear or non-linear, it depends on the specific characteristics of the element.

126.

A

B

C

D

127. The ideal voltage & current sources are in parallel. This combination will have

Thevenin’s equivalent

Norton’s equivalent

Both (A) & (B)

None

When ideal voltage and current sources are in parallel, the combination will have Thevenin's equivalent. Thevenin's equivalent is a simplified representation of a circuit that consists of a voltage source in series with a resistor. It is used to analyze the behavior of a complex circuit and simplify calculations. Norton's equivalent, on the other hand, consists of a current source in parallel with a resistor. Since the ideal voltage and current sources are in parallel, Norton's equivalent is not applicable in this case. Therefore, the correct answer is Thevenin's equivalent.

Explanation

When ideal voltage and current sources are in parallel, the combination will have Thevenin's equivalent. Thevenin's equivalent is a simplified representation of a circuit that consists of a voltage source in series with a resistor. It is used to analyze the behavior of a complex circuit and simplify calculations. Norton's equivalent, on the other hand, consists of a current source in parallel with a resistor. Since the ideal voltage and current sources are in parallel, Norton's equivalent is not applicable in this case. Therefore, the correct answer is Thevenin's equivalent.

128. A continuous time system is described by y (t) = x (t^2) (where y^x means y raised to x). The system is

Causal, linear

Causal, non-linear

Non causal, non-linear

Non causal, linear

The given system is non-causal because the output y(t) depends on the input x(t) at future time instances, as it is described by y(t) = x(t^2). It is linear because the output y(t) is a linear function of the input x(t), as there is no multiplication or exponentiation of x(t) in the equation.

Explanation

The given system is non-causal because the output y(t) depends on the input x(t) at future time instances, as it is described by y(t) = x(t^2). It is linear because the output y(t) is a linear function of the input x(t), as there is no multiplication or exponentiation of x(t) in the equation.

129.

A

B

C

D

130. When determining Thevenin's resistance of a circuit

All sources must be open circuited

All sources must be short circuited

All voltage sources must be open circuited and all current sources must be short circuited

All sources must be replaced by their internal resistances

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.

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.

GATE Ee Scholarship Test