GATE Ec Scholarship Test
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The root-locus diagram for a closed loop feedback system is shown in Figure The system is overdamped.
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Only if zero < K < 1
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Only if 1 < K < 5
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Only if K > 5
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If zero < K < 1 or K > 5
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.png "GATE Ec Scholarship Test - Quiz")
About This Quiz
The GATE EC Scholarship Test assesses knowledge in electronics and control systems through questions on root-locus, Nyquist plots, feedback stability, and transfer functions. It evaluates critical engineering concepts vital for advanced studies and professional certification.
Quiz Preview
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A
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B
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C
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D
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A. B -
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A
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B
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C
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D
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A. A -
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A
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B
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C
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D
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A. C -
- 5.
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
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(6 / 11) F
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(11 / 6) F
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6 F
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2 F
Correct Answer
A. 6 FExplanation
When capacitors are connected in parallel, the equivalent capacitance is equal to the sum of the individual capacitances. In this case, the capacitance values of C1, C2, and C3 are 1 F, 2 F, and 3 F respectively. Therefore, the equivalent capacitance is 1 F + 2 F + 3 F = 6 F.Rate this question:
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- 6.
Which of the following is not an electrical quantity?
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Voltage
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Current
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Distance
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Power
Correct Answer
A. DistanceExplanation
Distance is not an electrical quantity because it is a measure of physical separation or length between two points, and does not involve the flow of electric charge or the presence of an electric field. Voltage, current, and power are all electrical quantities that describe different aspects of electricity. Voltage is the potential difference between two points in an electrical circuit, current is the flow of electric charge, and power is the rate at which electrical energy is transferred or consumed.Rate this question:
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- 7.
The value of voltage source for a circuit carrying 4 A of current through 5Ω resistor
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2.5 V
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5 V
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10 V
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20 V
Correct Answer
A. 20 VExplanation
Based on Ohm's Law (V = I * R), the voltage (V) is equal to the current (I) multiplied by the resistance (R). In this case, the current is 4 A and the resistance is 5 Ω. Therefore, the voltage is 4 A * 5 Ω = 20 V.Rate this question:
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- 8.
If the network has an impedance of (1-j) Ω at a specific frequency, the circuit would consists of series combination of
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Resistor & Inductor
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Resistor & Capacitor
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Resistors
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None
Correct Answer
A. Resistor & CapacitorExplanation
The given impedance of (1-j) Ω indicates a combination of resistance and reactance. The presence of the imaginary component (-j) suggests the existence of a reactive element, which can be either an inductor or a capacitor. Since the impedance is not purely imaginary, it implies the presence of a resistance as well. Therefore, the correct answer is a series combination of a resistor and a capacitor.Rate this question:
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- 9.
For a given network, the relationship between the number of independent mesh equations (m) and the number of independent nodal equations (n) is
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M > n always
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M < n always
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M = n always
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M ≥ n or m < n depends upon the form of the network
Correct Answer
A. M ≥ n or m < n depends upon the form of the networkExplanation
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 is not always the case that m is greater than or equal to n, or that m is less than n. The specific structure and connections of the network will determine the relationship between m and n.Rate this question:
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- 10.
Full adder consists of
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Two Half adders & an AND gate
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Two Half adders & an Ex-OR gate
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One Half adder & Ex-NOR gate
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Two Half adders & an OR gate
Correct Answer
A. Two Half adders & an OR gateExplanation
A full adder is a digital circuit that adds three binary digits - two input bits and a carry bit. It consists of two half adders, which add the two input bits and produce a sum and a carry, and an OR gate, which combines the carry outputs of the two half adders to produce the final carry output. Therefore, the correct answer is "Two Half adders & an OR gate".Rate this question:
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- 11.
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:
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A
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B
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C
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D
Correct Answer
A. D -
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If a system is characterized by the equation y(t) = 5x(t) + 10 then the system is
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Linear
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Non-linear
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Both (A) & (B)
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None
Correct Answer
A. Non-linearExplanation
The given equation y(t) = 5x(t) + 10 represents a linear system. In a linear system, the output is directly proportional to the input with a constant scaling factor. In this case, the output y(t) is equal to 5 times the input x(t) plus a constant value of 10. Therefore, the system can be classified as linear.Rate this question:
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- 13.
Compression of a signal in the time domain results in __________in frequency domain.
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Compression
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Expansion
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Both (A) & (B)
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None
Correct Answer
A. ExpansionExplanation
When a signal is compressed in the time domain, it means that the duration of the signal is reduced. This compression causes an increase in the frequency components of the signal in the frequency domain. Therefore, the correct answer is expansion, as the compression in the time domain results in an expansion in the frequency domain.Rate this question:
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- 14.
Autocorrelation of a sinusoid is
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Sinc function
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Another sinusoid
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Rectangular pulse
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Triangular pulse
Correct Answer
A. Another sinusoidExplanation
The autocorrelation of a sinusoid is another sinusoid because when a sinusoidal signal is correlated with itself, it results in a waveform that has the same frequency but possibly a different phase. The autocorrelation function measures the similarity between a signal and a time-shifted version of itself, and in the case of a sinusoid, the resulting waveform will still exhibit the same periodicity and shape as the original sinusoid.Rate this question:
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- 15.
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
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Product of h1(t) and h2(t)
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Sum of h1(t) and h2(t)
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Convolution of h1(t) and h2(t)
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Subtraction of h2(t) from h1(t)
Correct Answer
A. Convolution of h1(t) and h2(t)Explanation
When two systems are connected in cascade, the overall impulse response of the cascaded system is given by the convolution of the impulse responses of the individual systems. Convolution is a mathematical operation that combines the two functions to produce a new function that represents how the output of one system affects the input of the other system. Therefore, the correct answer is the convolution of h1(t) and h2(t).Rate this question:
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- 16.
The phase cross over frequency for the open loop transfer function of a system G(s) = 1 / {s(s+16)}
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1
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16
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∞
Correct Answer
A. ∞Explanation
The phase cross over frequency for a system is the frequency at which the phase of the open loop transfer function becomes -180 degrees. In this case, the open loop transfer function G(s) = 1 / {s(s+16)} has a pole at s = 0 and s = -16. Since there are no zeros in the transfer function, the phase of G(s) will never reach -180 degrees. Therefore, the phase cross over frequency is infinity (∞).Rate this question:
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- 17.
The logic expression f = ∑m (0, 6, 7) is equivalent to
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F = π M (0, 3, 6, 7)
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F = π M (1, 2, 3, 4, 5)
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F = ∑m (0, 1, 2, 3)
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F = ∑m (1, 2, 6, 7)
Correct Answer
A. F = π M (1, 2, 3, 4, 5)Explanation
The given logic expression f = ∑m (0, 6, 7) is equivalent to f = π M (1, 2, 3, 4, 5) because the sum-of-products (SOP) expression ∑m (0, 6, 7) can be simplified using the product-of-sums (POS) expression π M (1, 2, 3, 4, 5). This means that the logic function f can be represented using the POS expression π M (1, 2, 3, 4, 5) instead of the original SOP expression.Rate this question:
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- 18.
_________ is an example for sequential circuit.
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Full adder
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Magnitude comparator
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D Flip flop
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Mux
Correct Answer
A. D Flip flopExplanation
A D flip flop is an example of a sequential circuit because it stores and remembers information based on its previous state. It has two stable states, 0 and 1, and can change its output based on the input and the clock signal. This makes it suitable for applications that require memory and the ability to store and retrieve data. Unlike combinational circuits, sequential circuits have memory elements and can maintain state, making the D flip flop a clear example of a sequential circuit.Rate this question:
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- 19.
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A
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B
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C
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D
Correct Answer
A. A -
- 20.
In a practical voltage source, the terminal voltage
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Cannot be less than source voltage
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Cannot be higher than source voltage
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Is always equal to source voltage
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None
Correct Answer
A. Cannot be higher than source voltageExplanation
In a practical voltage source, the terminal voltage cannot be higher than the source voltage. This is because there are always some internal resistances and losses in the source that cause a drop in voltage. Therefore, the terminal voltage will always be equal to or less than the source voltage.Rate this question:
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- 21.
Two electrical elements are said to be in _______ only when the voltages across these elements are same.
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Series
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Parallel
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Both (A) & (B)
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None
Correct Answer
A. ParallelExplanation
When two electrical elements are said to be in parallel, it means that the voltages across these elements are the same. In a parallel circuit, the voltage across each element remains constant, regardless of the current flowing through them. This is because the elements are connected side by side, allowing the current to split and flow through each element separately. Therefore, the correct answer is "Parallel".Rate this question:
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- 22.
How many symbols are used in the octal number system?
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4
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8
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10
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16
Correct Answer
A. 8Explanation
The octal number system uses 8 symbols, which are 0, 1, 2, 3, 4, 5, 6, and 7. In octal, each digit represents a power of 8, similar to how each digit in decimal represents a power of 10. Therefore, the correct answer is 8.Rate this question:
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- 23.
What is the binary equivalent of the decimal number 368
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101110000
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110110000
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111010000
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111100000
Correct Answer
A. 101110000Explanation
The binary equivalent of a decimal number is obtained by continuously dividing the decimal number by 2 and noting down the remainders in reverse order. In this case, when we divide 368 by 2, we get a quotient of 184 and a remainder of 0. When we divide 184 by 2, we get a quotient of 92 and a remainder of 0. This process continues until we get a quotient of 1. The remainders in reverse order are 0, 0, 0, 0, 0, 0, 1, 1, 1, giving us the binary equivalent of 368 as 101110000.Rate this question:
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- 24.
The maximum value of f(x)=2x^(3)-9x^(2)+12x-3 in the interval 0
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2
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6
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36
Correct Answer
A. 6Explanation
The maximum value of a function occurs at the vertex of its graph. To find the vertex of the function f(x)=2x^(3)-9x^(2)+12x-3, we can use the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic term, linear term, and constant term respectively. In this case, a = 2, b = -9, and c = 12. Plugging these values into the formula, we get x = -(-9) / (2*2) = 9/4. To find the corresponding y-value, we substitute this x-value into the function: f(9/4) = 2(9/4)^(3) - 9(9/4)^(2) + 12(9/4) - 3 = 6. Therefore, the maximum value of f(x) in the given interval is 6.Rate this question:
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- 25.
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
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Zero
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1
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2
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3
Correct Answer
A. ZeroExplanation
The Nyquist plot represents the frequency response of a system. In a unity negative feedback system, the number of roots of the system characteristic equation in the right half of the s-plane corresponds to the number of unstable poles of the system. Since the Nyquist plot shows no poles in the right half of the s-plane, it means that there are no unstable poles and therefore, the number of roots of the system characteristic equation in the right half of the s-plane is zero.Rate this question:
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- 26.
The feedback control system in Figure is stable
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for all K > Zero
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Only if K > 1
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Only if Zero < K < 1
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None
Correct Answer
A. Only if Zero < K < 1Explanation
The feedback control system in the given figure is stable only if the gain factor, K, is between zero and one. This means that the system will remain stable and not exhibit any oscillations or instability if the value of K lies between zero and one. If K is outside this range (either less than zero or greater than one), the system will become unstable and may exhibit oscillations or other undesirable behavior. Therefore, the correct answer is "only if Zero < K < 1."Rate this question:
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- 27.
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A
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B
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C
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D
Correct Answer
A. B -
- 28.
Superposition theorem is based on the concept of
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Duality
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Reciprocity
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Linearity
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Non linearity
Correct Answer
A. LinearityExplanation
Superposition theorem is based on the concept of linearity. Linearity refers to the property where the output of a system is directly proportional to its input. In the context of superposition theorem, it states that the response of a linear circuit to multiple independent sources can be determined by summing the responses to each individual source acting alone. This principle allows for simplifying complex circuits and analyzing them more easily by considering one source at a time. Therefore, linearity is the fundamental concept that underlies the application of superposition theorem.Rate this question:
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- 29.
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.
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Only (i)
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Only (ii)
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Both (i) and (ii)
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None
Correct Answer
A. Only (ii)Explanation
Passive elements are components in a circuit that do not generate or produce electrical energy on their own. Instead, they consume or receive energy from the circuit or store energy. Therefore, statement (ii) is correct as it accurately describes the behavior of passive elements. Statement (i) is incorrect because passive elements do not generate or produce electrical energy.Rate this question:
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- 30.
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
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8 Ω
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4 Ω
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2 Ω
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1 Ω
Correct Answer
A. 2 ΩExplanation
When a DC source is connected to a resistive load, the maximum power is transferred when the load resistance is equal to the internal resistance of the source. In this case, the internal resistance is 2 Ω, so the load resistor should also be 2 Ω to achieve maximum power transfer. If the load resistance is higher or lower than 2 Ω, the power transferred will be less than the maximum. Therefore, the correct answer is 2 Ω.Rate this question:
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- 31.
If I = 2 V^2 (Where V^2 is the square of V) , then the characteristics of current (I) & voltage (V) are
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Linear
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Non- Linear
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Passive
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Bilateral
Correct Answer
A. Non- LinearExplanation
The given equation I = 2V^2 represents a quadratic relationship between current (I) and voltage (V), where the current is proportional to the square of the voltage. In a linear relationship, the current would be directly proportional to the voltage, which is not the case here. Therefore, the characteristics of the current and voltage in this equation are non-linear.Rate this question:
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- 32.
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.
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Only S1
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Only S2
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Both S1 & S2
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Both S2 & S3
Correct Answer
A. Both S1 & S2Explanation
Superposition theorem is a principle used in electrical engineering to analyze linear circuits. It states that the total response in a linear circuit is the sum of the responses caused by each individual source acting alone. S1 is correct because superposition theorem can be used to determine the voltage across a branch or current through a branch by considering one source at a time. S2 is correct because it is applicable to networks consisting of more than one source. However, S3 is incorrect because superposition theorem is applicable to both DC and AC circuits.Rate this question:
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- 33.
A delta connection contains 3 equal impedances of 60 Ω. The impedances of the equivalent star connection will be
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15 Ω each
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20 Ω each
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30 Ω each
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40 Ω each
Correct Answer
A. 20 Ω eachExplanation
In a delta connection, the impedance across each branch is equal to the impedance of the load. Since the delta connection contains 3 equal impedances of 60 Ω, the equivalent star connection will have equal impedances as well. Therefore, the impedances of the equivalent star connection will be 20 Ω each.Rate this question:
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- 34.
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.
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Only (i)
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Only (ii)
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Both (i) and (ii)
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None
Correct Answer
A. Both (i) and (ii)Explanation
The given answer, "both (i) and (ii)", is correct. (i) is correct because NAND and NOR gates are indeed called universal gates as they can be used to implement any other logic gate. (ii) is also correct because all the basic gates, such as AND, OR, and NOT gates, can be implemented using NAND or NOR gates. Therefore, both statements are correct.Rate this question:
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- 35.
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.
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1
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2
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3
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4
Correct Answer
A. 4Explanation
When combining 16 adjacent ones as a group in K-map simplification, it creates a term with 4 literals less than the total number of variables. This means that the resulting term will have 4 variables less than the original expression.Rate this question:
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- 36.
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)
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Zero
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1
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2
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3
Correct Answer
A. 1Explanation
The given equation is a cubic equation. In order to determine the number of roots in the left half of the s-plane, we need to analyze the coefficients of the equation. Since the highest power of s is odd (s^3), there must be at least one real root. However, the equation does not have any imaginary roots (since there are no terms with s^2 or s with imaginary coefficients), so there can only be one real root. Therefore, the number of roots in the left half of the s-plane is 1.Rate this question:
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- 37.
A system has its two poles on the negative real axis and one pair of poles lies on jω axis. The system is
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Unstable
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Marginally Stable
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Stable
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None
Correct Answer
A. Marginally StableExplanation
The given system has two poles on the negative real axis, indicating that it has a stable component. Additionally, it has one pair of poles on the jω axis, which signifies oscillatory behavior. This combination suggests that the system is marginally stable.Rate this question:
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- 38.
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
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100
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200
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400
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500
Correct Answer
A. 400Explanation
In a unity negative feedback system, the damping ratio can be calculated using the formula ζ = 1/2√(1+K). Given that the damping ratio is 0.25, we can substitute this value into the formula and solve for K. By rearranging the formula, we get K = (4ζ^2 - 1). Plugging in ζ = 0.25, we find that K = 400.Rate this question:
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- 39.
The relationship between gain cross over frequency (Wgc) & phase cross over frequency (Wpc) for a stable system is
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Wgc > Wpc
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Wgc < Wpc
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Wgc = Wpc
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None
Correct Answer
A. Wgc < WpcExplanation
For a stable system, the gain cross over frequency (Wgc) is always less than the phase cross over frequency (Wpc). This means that the frequency at which the gain of the system is equal to 1 is always lower than the frequency at which the phase shift of the system is equal to -180 degrees. This relationship ensures stability in the system, as it indicates that the system's gain decreases at a faster rate than its phase shift increases, preventing any instability or oscillations.Rate this question:
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- 40.
The trigonometric Fourier series of an even function of time does not have
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The dc term
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Cosine terms
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Sine terms
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Odd harmonic terms
Correct Answer
A. Sine termsExplanation
An even function is symmetric about the y-axis, meaning that its graph remains unchanged when reflected across the y-axis. Since sine functions are odd functions, they are symmetric about the origin and do not exhibit this symmetry property. Therefore, the trigonometric Fourier series of an even function does not contain sine terms.Rate this question:
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- 41.
If a signal f(t) has energy E, then energy of the signal f(2t) is equal to
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E/2
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E
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2E
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4E
Correct Answer
A. E/2Explanation
When the signal f(t) is multiplied by 2, it causes the signal to compress in the time domain. This compression results in the signal being stretched in the frequency domain. Since energy is proportional to the area under the signal in the time domain, when the signal is compressed by a factor of 2, the area under the signal is also reduced by a factor of 2. Therefore, the energy of the signal f(2t) is equal to E/2.Rate this question:
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- 42.
The Fourier transform of a rectangular pulse existing between t = − T /2 to t = T / 2 is a
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Sinc squared function
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Sinc function
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Sine squared function
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Cos function
Correct Answer
A. Sinc functionExplanation
The Fourier transform of a rectangular pulse existing between t = − T /2 to t = T / 2 is a sinc function. The sinc function is defined as the sine of x divided by x. In the frequency domain, the sinc function represents the spectral content of the rectangular pulse. 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 analyze and manipulate signals.Rate this question:
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- 43.
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
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0.067
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0.073
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0.082
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0.091
Correct Answer
A. 0.082Explanation
The probability of getting a head in a single toss of an unbiased coin is 1/2. Since the coin is tossed an infinite number of times, the probability of getting a head on any given toss remains the same. Therefore, the probability of getting a head on the fourth toss is 1/2. Similarly, the probability of getting a tail on any given toss is also 1/2. Therefore, the probability of getting a tail on the first three tosses is (1/2)^3 = 1/8. So, the probability of getting a head on the fourth toss and a tail on the first three tosses is 1/2 * 1/8 = 1/16. Finally, the probability of getting a head on the tenth toss is also 1/2. Therefore, the probability of getting a head on the fourth toss and a tail on the first three tosses and then a head on the tenth toss is 1/16 * 1/2 = 1/32. Since there are 10 possible positions for the fourth head to appear (4th, 5th, 6th, ..., 10th toss), we multiply the probability by 10 to get 10/32 = 0.3125. Therefore, the probability that the fourth head appears at the tenth toss is approximately 0.3125, which is closest to 0.082.Rate this question:
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- 44.
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1
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Zero
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-1
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3.14
Correct Answer
A. 1Explanation
The given answer, 1, is the only whole number among the options provided. Zero is not a whole number, -1 is a negative number, and 3.14 is a decimal. Therefore, 1 is the correct answer.Rate this question:
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- 45.
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?
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Y(t) = x(t − 2) + x(t + 4)
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Y(t) = (t − 4) x(t + 1)
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Y(t) = (t + 4) x(t − 1)
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Y(t) = (t + 5) x(t + 5)
Correct Answer
A. Y(t) = (t + 4) x(t − 1)Explanation
A causal system is one where the output at any given time depends only on the input at or before that time. In the given options, the only description that satisfies this condition is y(t) = (t + 4) x(t − 1). Here, the output y(t) is a function of the input x(t − 1), which means it depends on the input at or before time t. Therefore, this description corresponds to a causal system.Rate this question:
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- 46.
In the circuit of figure, the equivalent impedance seen across terminals A, B is
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(16/3) Ω
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(8/3) Ω
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(8/3 + 12j) Ω
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None of the above
Correct Answer
A. (8/3) ΩExplanation
The correct answer is (8/3) Ω. To find the equivalent impedance, we need to combine the resistors and the complex impedance. The 6 Ω resistor and the 4 Ω resistor are in parallel, so their equivalent resistance is (6 * 4) / (6 + 4) = 24 / 10 = 12 / 5 Ω. This equivalent resistance is in series with the 8 Ω resistor, so the total resistance is (12 / 5) + 8 = 68 / 5 Ω. Finally, the 12 Ω + 6j Ω complex impedance is in parallel with this total resistance. The formula for combining a complex impedance (Z1) in parallel with a resistance (R2) is (Z1 * R2) / (Z1 + R2). Plugging in the values, we get ((12 + 6j) * (68 / 5)) / ((12 + 6j) + (68 / 5)) = (8/3) Ω.Rate this question:
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- 47.
Which of the following is linear element?
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Voltage Source
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Current Source
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Resistor
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None
Correct Answer
A. ResistorExplanation
A resistor is a linear element because it follows Ohm's law, which states that the current flowing through a resistor is directly proportional to the voltage across it. In other words, the relationship between voltage and current in a resistor is linear. This means that if you double the voltage across a resistor, the current through it will also double. Therefore, a resistor can be considered a linear element in electrical circuits.Rate this question:
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- 48.
The superposition theorem is valid for
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All linear networks
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Non-linear networks
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Only linear networks having no dependent sources
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Both (A) & (B)
Correct Answer
A. All linear networksExplanation
The superposition theorem is valid for all linear networks. This means that it can be applied to any network that consists of linear components such as resistors, capacitors, and inductors. The theorem states that the response of a linear network to a set of inputs can be determined by considering the individual responses to each input separately and then adding them together. This principle holds true regardless of whether the network contains dependent sources or not. Therefore, the correct answer is "All linear networks."Rate this question:
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- 49.
_______ is defined as the time rate of flow of charge.
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Voltage
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Current
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Energy
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Power
Correct Answer
A. CurrentExplanation
Current is defined as the time rate of flow of charge. It represents the movement of electric charge through a conductor per unit time. It is measured in amperes (A) and is a fundamental concept in electricity. Voltage, on the other hand, is the potential difference between two points in an electric circuit, energy is the capacity to do work, and power is the rate at which work is done or energy is transferred. While all these concepts are related to electricity, only current specifically refers to the time rate of flow of charge.Rate this question:
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.png "In the circuit of figure, the equivalent impedance seen across terminals A, B is")
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Mar 19, 2023Quiz Edited by
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Apr 24, 2016Quiz Created by
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