TS PGECET 2024 Electrical Engineering Question Paper with Answer Key PDF

Question 1:

If \( \lambda_1, \lambda_2, \lambda_3 \) are the eigenvalues of the matrix , then the values of \[ (\lambda_1 + \lambda_2 + \lambda_3) \ and \ (\lambda_1 \cdot \lambda_2 \cdot \lambda_3) \] are respectively

• (A) 1 and 3
• (B) -3 and 4
• (C) 4 and 12
• (D) 2 and -12

If \( A = \begin{pmatrix} 2024 & 2021
2023 & 2022 \end{pmatrix} \), then the value of \[ \left| A^{2024} - A^{2023} \right| \]
is

• (A) 2024
• (B) 1
• (C) 0
• (D) 2023

Among the following, Rolle's theorem is not applicable for

• (A) \( f(x) = x^3 - 4x \) in \([-2, 2]\)
• (B) \( f(x) = |x| \) in \([-1, 1]\)
• (C) \( f(x) = (x-a)^m (x-b)^n \) in \([a, b], m, n > 0\)
• (D) \( f(x) = x^2 - 3x + 2 \) in \([1, 2]\)

If the function \( u = \sin^{-1} \left( \frac{x^3 + y^3}{x + y} \right) \), then \[ x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \]
is

• (A) \( 2 \tan u \)
• (B) \( 3 \csc u \)
• (C) \( 3 \sin u \)
• (D) \( 2 \cos u \)

The integrating factor of \[ \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \]
is

• (A) \( \sin x \)
• (B) \( \cos x \)
• (C) \( \cot x \)
• (D) \( \tan x \)

Particular integral of \[ \frac{dy}{dx} + y = e^{x} \]
is

• (A) \( e^x \)
• (B) \( x e^x \)
• (C) \( e^{-x} e^x \)
• (D) \( e^{e^x} \)

The value of the integral \[ \int_C \frac{2e^z}{(z-4)(z-2)} \, dz \]
where \( C: |z| = 3 \) is

• (A) \( -\pi i e^2 \)
• (B) \( -2 \pi i e^2 \)
• (C) \( 2 \pi i e^2 \)
• (D) \( \pi i e^2 \)

If \[ f(x) = \begin{cases} -\pi, & -\pi < x < 0
x, & 0 < x < \pi \end{cases} \]
then the constant term of the Fourier series is

• (A) \( \frac{\pi}{2} \)
• (B) \( -\pi \)
• (C) \( \frac{\pi}{2} \)
• (D) \( \frac{\pi}{4} \)

Newton-Raphson iterative formula for finding \[ \frac{1}{\sqrt{N}}, (N > 0) \]
is

• (A) \( x_{n+1} = x_n (2 - N x_n) \)
• (B) \( x_{n+1} = \frac{1}{2} \left( x_n + \frac{N}{x_n} \right) \)
• (C) \( x_{n+1} = \frac{1}{2} \left( x_n + \frac{1}{N x_n} \right) \)

The mean and variance of a random variable \( X \) having a Binomial distribution are 4 and 2 respectively, then \( P(X=1) \) is

• (A) \( \frac{1}{32} \)
• (B) \( \frac{1}{8} \)
• (C) \( \frac{1}{16} \)
• (D) \( \frac{1}{4} \)

A 1-\(\phi\), RC series circuit has \( R = 5\, \Omega \) and \( C = 10\, \mu F \). If the angular frequency of current is 20000 rad/sec, then the applied voltage

• (A) Lags the current by \( \pi/4 \) radians
• (B) Leads the current by \( \pi/4 \) radians
• (C) Lags the current by \( \pi/2 \) radians
• (D) Leads the current by \( \pi/2 \) radians

A source voltage of 100 V dc is applied across a RLC series circuit. Under steady-state conditions, voltages across each element is

• (A) \( V_R = 100V, V_L = 0, V_C = 0 \)
• (B) \( V_R = 100V, V_L = -100V, V_C = 100V \)
• (C) \( V_R = 0, V_L = 100V, V_C = -100V \)
• (D) \( V_R = 0, V_L = 0, V_C = -100V \)

The equivalent inductance of two equal inductances when connected in series aiding is 14 H and when connected in series opposing is 6 H. What is the coefficient of coupling?

• (A) 0.5
• (B) 0.8
• (C) 0.4
• (D) 1.0

Certain resistors connected in parallel and the equivalent resistance is \( X \). If one of the resistances is removed the equivalent resistance is \( Y \). What is the conductance value of removed resistance?

• (A) \( \frac{XY}{Y-X} \)
• (B) \( \frac{XY}{X-Y} \)
• (C) \( \frac{X-Y}{XY} \)
• (D) \( \frac{Y-X}{XY} \)

For an input voltage \( v = 10 \sin 1000t \), the Thevenin's impedance at the terminals X and Y for the following circuit is

• (A) \( 0.5 + j0.5 \)
• (B) \( 0.5 - j0.5 \)
• (C) \( 1.0 + j1 \)
• (D) \( 1.0 - j1 \)

A signal of \( v = 5 + 10 \sin \omega t \) is applied across a \( 2\, \Omega \) resistor. The power dissipated in the resistor is

• (A) \( 75\, W \)
• (B) \( 37.5\, W \)
• (C) \( 62.5\, W \)
• (D) \( 125\, W \)

Three impedances \( 6 + j(10/3)\, \Omega \) each are connected in delta. The per-phase impedance of equivalent star circuit will be

• (A) \( 18 + j(10/9)\, \Omega \)
• (B) \( 2 + j(10/3)\, \Omega \)
• (C) \( 2 + j(10/9)\, \Omega \)
• (D) \( 18 + j10\, \Omega \)

The \( h \) parameters of the following circuit is

• (A) \( h = \begin{bmatrix} 0 & 1
  1 & -1 \end{bmatrix} \)
• (B) \( h = \begin{bmatrix} 0 & -1
  -1 & 1 \end{bmatrix} \)
• (C) \( h = \begin{bmatrix} 0 & -1
  1 & 1 \end{bmatrix} \)
• (D) \( h = \begin{bmatrix} 0 & 1
  -1 & 1 \end{bmatrix} \)

The \( Z \) parameter \( Z_{21} \) of the following circuit is

• (A) \( Z_2 \)
• (B) \( Z_1 \)
• (C) \( Z_1 + Z_2 \)
• (D) \( -Z_2 \)

In a 3-\(\phi\) star connected balanced circuit, if angle between phase voltage \( V_p \) and phase current is \( \theta \) (leading), then the wattmeter readings in two wattmeter method are:

• (A) \( \sqrt{3} V_p I_p \cos(30^\circ + \theta) \) and \( \sqrt{3} V_p I_p \cos(60^\circ - \theta) \)
• (B) \( 3 V_p I_p \cos(30^\circ + \theta) \) and \( 3 V_p I_p \cos(60^\circ - \theta) \)
• (C) \( V_p I_p \cos(30^\circ + \theta) \) and \( V_p I_p \cos(30^\circ - \theta) \)
• (D) \( \sqrt{3} V_p I_p \cos(30^\circ + \theta) \) and \( \sqrt{3} V_p I_p \cos(30^\circ - \theta) \)

Choose the correct statement of Reciprocity theorem in single source network:

• (A) The ratio of response to excitation is invariant to an interchange of the positions of the excitation and response, if the excitation is a current source, the response should be a voltage source.
• (B) The ratio of response to excitation is invariant to an interchange of the positions of the excitation and response, if the excitation is a voltage source, the response should be a voltage source.
• (C) The ratio of response to excitation is invariant to an interchange of the positions of the excitation and response, if the excitation is a current source, the response should be a current source.
• (D) None of these

If BW is bandwidth, \( \omega_r \) is resonant frequency and Q is quality factor of a resonant circuit, then Selectivity is defined as:

• (A) \( \frac{\omega_r}{Q} \)
• (B) \( Q \)
• (C) \( \frac{\omega_r}{BW} \)
• (D) \( BW \)

The response of a 1-\(\phi\) R-L series circuit is \( i(t) = Ae^{-\frac{R}{L}t} + I_m \sin(\omega t - \theta) \). Then the supply voltage should be:

• (A) \( V_m \sin(\omega t + \varphi) \)
• (B) \( V_m \sin(\omega t - \varphi) \)
• (C) \( V_m \sin(\omega t) \)
• (D) \( V_m \sin(\omega t) + Exponential source \)

Point charges \( Q_1 = 1nC \) and \( Q_2 = 2nC \) are at a distance apart. Which of the following statement is incorrect?

• (A) The force on \( Q_1 \) is repulsive
• (B) The force on \( Q_2 \) is the same in magnitude on \( Q_1 \)
• (C) As the distance between them decreases, the force on \( Q_1 \) increases linearly
• (D) The force on \( Q_2 \) is along the line joining them

If \( \vec{D} = \epsilon \vec{E} \) and \( \vec{V} = \sigma \vec{E} \) in a given material, the material is said to be:

• (A) Linear and Isotropic
• (B) Linear and homogeneous
• (C) Isotropic only
• (D) Isotropic and homogeneous

Two identical coaxial circular coils carry the same current 1 amp but in opposite directions. The magnitude of the magnetic field \( B \) at a point on the axis midway between the coils is

• (A) \( Zero \)
• (B) The same as that produced by one coil
• (C) Twice that produced by one coil
• (D) Half that produced by one coil

Magnetic dipole moment is ______ of the loop, its direction is normal to the loop

• (A) the sum of current and area
• (B) the product of current and volume
• (C) the sum of current and volume
• (D) the product of current and area

\( \nabla \cdot \vec{B} = 0 \), shows that

• (A) Electrostatic fields have no sources or sinks
• (B) Magnetostatic fields have no sources or sinks
• (C) Electrostatic fields have two sources and two sinks
• (D) Magnetostatic fields have two sources and one sink

The reciprocal of reluctance is

• (A) permeability
• (B) permittivity
• (C) permeance
• (D) conductance

The magnetization \( M \), in amperes per meter is

• (A) Magnetic dipole moment per unit volume
• (B) Volume/unit Magnetic dipole moment
• (C) Magnetic dipole moment per unit area
• (D) Magnetic dipole moment per unit length

The slip-speed of a 3-\(\phi\), cage, 50 Hz, induction motor is 20 rpm at no-load. If slip-speed is doubled due to load, then the electrical equivalent of mechanical load will

• (A) remain same
• (B) be exactly doubled
• (C) be more than doubled
• (D) be less than halved

The time period of rotor current of a 3-\(\phi\), 4-pole, 50 Hz, induction motor is 200 ms. Then slip speed of the motor is

• (A) 1425 rpm
• (B) 1350 rpm
• (C) 75 rpm
• (D) 150 rpm

The current and power factor of a 3–\(\phi\) induction motor at no-load are respectively

• (A) 1 to 2% of rated current and 0.2 lagging
• (B) 30 to 40% of rated current and 0.2 lagging
• (C) 2 to 6% of rated current and 0.8 lagging
• (D) 30 to 40% of rated current and 0.8 lagging

A 3-\(\phi\), 400 V, 50 Hz, 4 pole induction motor has rotor resistance and standstill reactance of 0.08 Ω and 0.4 Ω respectively. What is its approximate speed at maximum torque?

• (A) 600 rpm
• (B) 750 rpm
• (C) 150 rpm
• (D) 335 rpm

The external rotor resistance of a 3-\(\phi\) induction motor is increased more than the resistance required to get maximum starting torque. Then maximum torque occurs in \underline{\hspace{2cm of Torque (y-axis) – Speed (x-axis) characteristic plot.

• (A) Second Quadrant
• (B) Third Quadrant
• (C) Fourth Quadrant
• (D) First Quadrant

A 1-\(\phi\), 230 V, 50 Hz transformer is operated at 230 V, 60 Hz. Then its

• (A) Eddy current loss will remain same and Hysteresis loss will increase
• (B) Eddy current loss will remain same and Hysteresis loss will decrease
• (C) Eddy current loss will decrease and Hysteresis loss will remain same
• (D) Eddy current loss will increase and Hysteresis loss will also increase

Indicate a correct choice on currents during open circuit (OC) and short circuit (SC) tests of transformer

• (A) OC test at rated current \& SC test at rated current
• (B) OC test at rated current \& SC test at no-load current
• (C) OC test at no-load current \& SC test at no-load current
• (D) OC test at rated voltage \& SC test at rated current

A 11kV/3.3kV, 100 MVA, 3-phase transformer has equivalent impedance seen from LV side of (1.2 + j4.8) Ω. The per unit impedance of the transformer is

• (A) 0.5 + j2
• (B) 1 + j4
• (C) 2 + j8
• (D) 0.25 + j1

If R and X are equivalent resistance and equivalent reactance of a transformer respectively, then at maximum voltage regulation, the power factor is

• (A) R/\( \sqrt{X^2 - R^2} \) leading
• (B) R/\( \sqrt{X^2 - R^2} \) lagging
• (C) R/\( \sqrt{X^2 + R^2} \) lagging
• (D) R/\( \sqrt{X^2 + R^2} \) leading

On two sides of a 3-\(\phi\) star / delta transformer the

• (A) Voltages differ by 60° and currents differ by 30°
• (B) Voltages differ by 30° and currents differ by 60°
• (C) Both voltages and currents differ by 60°
• (D) Both voltages and currents differ by 30°

The input of a 98% efficiency, 2000 rpm separately excited dc motor is 5 kW. The torque output is

• (A) 28.1 Nm
• (B) 23.9 Nm
• (C) 20.3 Nm
• (D) 19.1 Nm

The speed of a d.c. series motor at an armature current of 10 A is 800 rpm. If load torque is proportional to square of speed, then at 5 A the speed will be

• (A) 4000 rpm
• (B) 200 rpm
• (C) 1600 rpm
• (D) 3200 rpm

If \( R_1, R_2, R_3, R_4, R_5 \) are resistances of each of five sections of starter of d.c. shunt motor, then these resistances are

• (A) not in Geometric progression
• (B) in Geometric progression
• (C) in Arithmetic progression
• (D) in Harmonic progression

Dummy coils are used in wave wound d.c. machines to reduce

• (A) Hysteresis losses
• (B) Mechanical imbalance on armature
• (C) Frictional losses
• (D) Mechanical imbalance on iron frame

Choose a wrong choice on d.c. machine regarding compoles or compensating winding

• (A) Compoles neutralize reactance voltage
• (B) Compensated winding is connected in series with armature
• (C) Compole winding neutralize de-magnetizing effect of armature reaction
• (D) Compensating winding neutralize cross-magnetizing effect of armature reaction

Swinburne’s test measures the following on a 200 V, 15 kW dc shunt motor:
Input current = 7 A; Field current = 2 A. Estimate field copper loss and iron \& frictional losses. Assume \( R_a = 0.04 \Omega \)

• (A) 400 W, 998 W respectively
• (B) 999 W, 400 W respectively
• (C) 400 W, 999 W respectively
• (D) 998 W, 400 W respectively

If short pitch angle of a 3-\(\phi\), 2 pole synchronous machine is \(30^\circ\), then pitch factor is

• (A) \( \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2}} \)
• (B) \( \frac{\sqrt{2} + \sqrt{3}}{2} \)
• (C) \( \frac{\sqrt{2} - \sqrt{3}}{2} \)
• (D) \( \frac{\sqrt{2} + \sqrt{3}}{2} \)

Speed of 3-\(\phi\) synchronous motor can be controlled by varying frequency at constant torque at

• (A) Variable voltage and constant current
• (B) Variable voltage and variable current
• (C) Constant voltage and constant current
• (D) Constant voltage and variable current

If voltage of a d.c. servo-motor increases, then the Torque-speed characteristic and slope respectively are

• (A) Linear, negative
• (B) Linear, positive
• (C) Non-Linear, negative
• (D) Non-Linear, positive

The step angle of a stepper motor is given by

• (A) \( \frac{180^\circ}{No. of stator phases \times No. of rotor teeth} \)
• (B) \( \frac{360^\circ}{No. of stator phases \times No. of rotor teeth} \)
• (C) \( \frac{360^\circ}{No. of stator teeth \times No. of rotor teeth} \)
• (D) \( \frac{180^\circ}{No. of stator teeth \times No. of rotor teeth} \)

Choose the correct one:

Whenever a short circuit takes place at a bus with higher short circuit capacity,

• (A) current flows in the bus
• (B) current flows in the bus
• (C) current flows in the bus
• (D) current flows in the bus

_____ is a voltage restrained directional relay.

• (A) Reactance
• (B) Over current
• (C) Mho
• (D) Impedance

A travelling wave of 500/1/55 means a crest value of

• (A) \(500\,kV\) with rise time of 1 ms and fall time of 55 ms
• (B) \(500\,kV\) with rise time of 1 \(\mu\)s and fall time of 55 ms
• (C) \(500\,kV\) with rise time of 1 \(\mu\)s and fall time of 55 \(\mu\)s
• (D) \(500\,kV\) with rise time of 1 ms and fall time of 55 \(\mu\)s

The quantities to be obtained at slack bus with usual notations are

• (A) \(Q,\, \delta\)
• (B) \(P,\, |V|\)
• (C) \(P,\, Q\)
• (D) \(|V|,\, \delta\)

Choose the correct one:

• (A) Ybus matrix and Zbus matrix are sparse
• (B) Jacobian matrix and Zbus matrix are not sparse
• (C) Ybus matrix and Jacobian matrix are sparse
• (D) Ybus matrix sparse and Jacobian matrix is not sparse

Typical values of time constants of a load frequency control system in case of thermal power generation system are related as (Tsg: speed governor, Tps: power system, Tt: turbine)

• (A) \(T_{sg} < T_{t} \ll T_{ps}\)
• (B) \(T_{sg} < T_{ps} < T_{t}\)
• (C) \(T_{sg} = T_{t} = T_{ps}\)
• (D) \(T_{sg} > T_{ps} \gg T_{t}\)

\rule{0pt}{4ex} ____ fault analysis is used to calculate the rupturing capacity of circuit breakers

• (A) Single line to Ground
• (B) Double line
• (C) Three phases
• (D) Double line to Ground

By using bundle conductor ______

• (A) The self GMD is decreased, the inductance is reduced, the surge impedance is reduced
• (B) The self GMD is increased, the inductance is reduced, the surge impedance is reduced
• (C) The self GMD is increased, the inductance is increased, the surge impedance is reduced
• (D) The self GMD is increased, the inductance is reduced, the surge impedance is increased

The typical values of voltage regulation and efficiency of a medium transmission line respectively are

• (A) 92% and 94%
• (B) 6% and 18%
• (C) 6% and 94%
• (D) 92% and 6%

In case of a transmission line, the corona ______

• (A) Reduces the magnitude of high voltage steep fronted waves due to lightning or switching
• (B) Increases the magnitude of high voltage steep fronted waves due to lightning or switching
• (C) First reduces and then decreases the magnitude of high voltage steep fronted waves due to lightning or switching
• (D) First reduces and then increases the magnitude of high voltage steep fronted waves due to lightning or switching

In case of overhead lines, normally ______ insulators are used at road crossings

• (A) Strain type
• (B) Pin type
• (C) Suspension type
• (D) Both Pin type and Suspension Type

In case of voltage control of a power system network, for the same voltage both the reactive power capacity of a shunt capacitor is _____ that of a series capacitor.

• (A) Smaller than
• (B) Higher than
• (C) 0.75 times
• (D) Equal to

Choose the correct one:
The zero sequence voltages are single phase voltages and they give rotating field in ___ space

• (A) space
• (B) give an alternating field
• (C) give an alternating field in space
• (D) space

Short circuit MVA of a 3-phase alternator is ______

• (A) Directly proportional to \( Z_{pu} \)
• (B) Inversely proportional to square of \( Z_{pu} \)
• (C) Inversely proportional to \( Z_{pu} \)
• (D) Directly proportional to square of \( Z_{pu} \)

The steady state stability limit of a power system can be increased by

• (A) Decreasing the excitation of a generator
• (B) Increasing the reactance
• (C) Reducing the reactance
• (D) Using shunt reactors

The line trap unit employed in carrier current relaying offers

• (A) High impedance to 50 Hz power frequency signals
• (B) High impedance to carrier frequency signals
• (C) Low impedance to carrier frequency signals
• (D) Low impedance to 50 Hz power frequency signals

The order of the lightning discharge current is

• (A) 100000 A
• (B) 100 A
• (C) 1 A
• (D) 1 μA

Consider the following statements:

1. By using bundled conductors in an overhead line, the corona loss is reduced

2. By using bundled conductors, the inductance of transmission line increases and capacitance reduces

3. Corona loss causes interference in adjoining communication lines

Which of these statements are correct?

• (A) 1 and 2
• (B) 2 and 3
• (C) 1 and 3
• (D) 1, 2 and 3

The maximum reactive power generation of a generator is limited because of

• (A) Stability limit of the machine
• (B) Overheating of the rotor
• (C) Flame instability of a boiler
• (D) Over heating of the stator windings

A stranded conductor is expressed as 19/1 where the first number corresponds to ........ and the second number corresponds to ........

• (A) Number of strands, radius of each strand
• (B) Number of strands, diameter of each strand
• (C) SWG of each strand, radius of each strand
• (D) SWG of each strand, diameter of each strand

For open loop system, the sensitivity of overall transfer function for a small change in forward path transfer function \( G(s) \) is

• (A) 1
• (B) 0
• (C) −1
• (D) ∞

If \( R(s) \) is input signal, \( C(s) \) is output signal and \( G(s)H(s) \) is feedback signal, then the steady-state error is given by

• (A) \( \lim_{s \to 0} \frac{SR(s)}{1 + sG(s)H(s)} \)
• (B) \( \lim_{s \to 0} \frac{SR(s)}{1 + G(s)H(s)} \)
• (C) \( \lim_{s \to 0} \frac{R(s)}{1 + G(s)H(s)} \)
• (D) \( \lim_{s \to 0} \frac{sR(s)}{1 + G(s)H(s)} \)

If the phase angle at gain cross-over frequency of a system is -116°, then the phase margin will be

• (A) −64°
• (B) 116°
• (C) 64°
• (D) −116°

For the given transfer function \( G(s) = \frac{5(s+4)}{(1+4s)(1+0.25s)} \), for large values of \( \omega \), the slope of the transfer function on the Bode plot is

• (A) −20 dB/decade
• (B) −40 dB/decade
• (C) 40 dB/decade
• (D) +20 dB/decade

A unity feedback system has open loop transfer function \( \frac{1}{(s^2 + 5)} \), then the closed loop transfer function is

• (A) \( \frac{1}{s^2 + 5} \)
• (B) \( \frac{1}{(5^2 + s)} \)
• (C) \( \frac{1}{(s^2 + 5s + 1)} \)
• (D) \( \frac{s}{(s^2 + 5)} \)

The value of \( k \), where root locus cuts the jω axis in plotting root locus, is calculated by

• (A) taking \( \frac{dK}{ds} = 0 \)
• (B) where the first asymptote cuts the jω axis
• (C) Bode Plot
• (D) Routh-Hurwitz method

A system has the following characteristic polynomial equation and it has three sign changes in the first column of Routh array. Choose correct choice for the number of roots on right and left side of s-plane.
\[ s^4 + 3s^3 + 10s^2 + 5s + 10 = 0 \]

• (A) 3 roots on right side \& 2 roots on left side
• (B) 2 roots on right side \& 3 roots on left side
• (C) 4 roots on right side \& 1 root on left side
• (D) 1 root on right side \& 4 roots on left side

Choose the correct combination of the following:

(a) At break-away point the root locus breaks from real axis into complex plane

(b) At break-away point the root locus breaks from imaginary axis into complex plane

(c) At break-in point the root locus enters the real axis from the complex plane

(d) At break-in point the root locus enters the imaginary axis from the complex plane

• (A) (a), (b), and (c) are true
• (B) (b) and (c) are true
• (C) (b) and (d) are true
• (D) (a) and (d) are true

The transfer function of the following system is

• (A) \(\frac{C(s)}{R(s)} = \frac{G - H_1}{1 + GH_2}\)
• (B) \(\frac{C(s)}{R(s)} = \frac{G + H_1}{1 - GH_2}\)
• (C) \(\frac{C(s)}{R(s)} = \frac{G + H_1}{1 + GH_2}\)
• (D) \(\frac{C(s)}{R(s)} = \frac{G - H_1}{1 - GH_2}\)

Find the frequency of sustained oscillations for the following system when \( K = 48 \):
\[ G(s)H(s) = \frac{K}{s(s^2 + 7s + 4)} \]

• (A) \( \sqrt{6} \ rad/sec \)
• (B) \( 2 \ rad/sec \)
• (C) \( \sqrt{2} \ rad/sec \)
• (D) \( \sqrt{8} \ rad/sec \)

Find gain of the following open loop system having phase cross-over frequency of 1.732 rad/sec.
\[ G(s)H(s) = \frac{1}{s(1+s)} \]

• (A) \( \sqrt{1/8} \)
• (B) \( 3/\sqrt{10} \)
• (C) \( 1/4 \)
• (D) \( 8 \)

A state-space system is given by \[ \dot{x} = \begin{bmatrix}1 & -2
3 & -4\end{bmatrix}x + \begin{bmatrix}1
0\end{bmatrix}u, \quad y = \begin{bmatrix}1 & 2\end{bmatrix}x \]
The controllability matrix [CM] is

• (A) \( [CM] = \begin{bmatrix}1 & 2
  0 & 2\end{bmatrix} \)
• (B) \( [CM] = \begin{bmatrix}1 & -2
  0 & 1\end{bmatrix} \)
• (C) \( [CM] = \begin{bmatrix}0 & 1
  1 & 0\end{bmatrix} \)
• (D) \( [CM] = \begin{bmatrix}1 & 1
  0 & 1\end{bmatrix} \)

The transfer function of the following signal flow graph is \( \frac{x_3(s)}{x_1(s)} \):

• (A) \(\frac{(a - b)(c + d)}{1 - ab}\)
• (B) \(\frac{ac + bc}{1 - cd}\)
• (C) \(\frac{ac + ad}{1 - cd}\)
• (D) \(\frac{(a - b)(c + d)}{1 - cd}\)

The transfer function of an RLC series circuit when input voltage is fed to \( R, L \) and output voltage is across \( C \) is:

• (A) \( \frac{1}{s^2LC + sRL + 1} \)
• (B) \( \frac{1}{s^2RL + sLC + 1} \)
• (C) \( \frac{1}{s^2RC + sLC + 1} \)
• (D) \( \frac{1}{s^2LC + sRC + 1} \)

The following statements refer to the pole-zero configuration for compensator networks:

I. In lag network, pole is nearer to origin

II. In lag network, zero is nearer to origin

III. In lead network, zero is nearer to origin

IV. In lead network, pole is nearer to origin


Choose the correct combination:

• (A) Only I is correct
• (B) Only III is correct
• (C) Only I \& II are correct
• (D) Only III \& IV are correct

A 50 V reading in a 0 – 150 V range Voltmeter has an error of 1.25 V. Find the % error of full-scale reading.

• (A) \( 0.833% \)
• (B) \( 1.25% \)
• (C) \( 3.75% \)
• (D) \( 1.875% \)

A 4½ digit digital voltmeter would display a reading of 0.6794 V in 10 V range as:

• (A) 0.6790 V
• (B) 00.679 V
• (C) 0.6794 V
• (D) 000.67 V

With fixed dimensions of Cathode Ray Tube (C.R.T), the ratio of electrostatic deflection sensitivity to magnetic deflection sensitivity, if the accelerating voltage is 10 kV, is:

• (A) 50 : 1
• (B) 1 : 50
• (C) 1 : 100
• (D) 100 : 1

A dc ammeter has a multiplication factor of 8 and its shunt current is 17.5 A, then the current through ammeter is:

• (A) 1.875 A
• (B) 2.0 A
• (C) 1.94 A
• (D) 2.5 A

A 200 V, 50 Hz, 1-phase energy meter makes 960 revolutions to supply a load of 0.8 pf for 2 hrs.
If motor constant is 160 rev/kWh, then load current is:

• (A) 1.875 A
• (B) 15 A
• (C) 18.75 A
• (D) 37.5 A

If \( I_p, I_m, I_s \) are magnetising, primary and secondary currents of current transformer, then
approximate phase angle \( \theta \) in degrees between \( I_p \) and reversed \( I_s \) is:

• (A) \( \theta = \frac{180}{\pi} \times \left( \frac{I_m}{I_s} \right) \)
• (B) \( \theta = \frac{180}{\pi} \times \left( \frac{I_p}{I_s} \right) \)
• (C) \( \theta = \frac{180}{\pi} \times \left( \frac{I_s}{I_m} \right) \)
• (D) \( \theta = \frac{180}{\pi} \times \left( \frac{I_s}{I_p} \right) \)

Match the following quantities of mechanical transducer with their operation:

(a) Manometer         (i) Force to displacement

(b) Hydrometer        (ii) Velocity to pressure

(c) Accelerometer   (iii) Specific gravity to displacement

(d) Load cell            (iv) Pressure to displacement
 

• (A) (a)–(iv); (b)–(iii); (c)–(ii); (d)–(i)
• (B) (a)–(ii); (b)–(iii); (c)–(iv); (d)–(i)
• (C) (a)–(iv); (b)–(ii); (c)–(iii); (d)–(i)
• (D) (a)–(iv); (b)–(i); (c)–(ii); (d)–(iii)

The output of an LVDT is ±2 mV when core moves through a distance of 0.5 mm.
The sensitivity is:

• (A) 0.25 mm/mV
• (B) 4 mV/mm
• (C) 0.25 mm/V
• (D) 4 mm/V

An analog transducer has a resolution of 0.01%. Calculate the number of bits required for A/D conversion.

• (A) 10
• (B) 6
• (C) 14
• (D) 12

A potentiometer is basically a

• (A) deflection type instrument and power consumed in the circuit of unknown source is ideally zero
• (B) null type instrument and power consumed in the circuit of unknown source is high
• (C) deflection type instrument and power consumed in the circuit of unknown source is high
• (D) null type instrument and power consumed in the circuit of unknown source is ideally zero

The V-I characteristic of a FET is shown below. For small signal amplification the device should be biased in the region

• (A) BC
• (B) OA
• (C) AB
• (D) AC

The base current of CE transistor in active region is 15 μA, find \( V_{CE} \), assuming \( \beta = 150 \), \( R_C = 2~k\Omega \) and \( V_{CC} = 12~V \).

• (A) 8.5 V
• (B) 9.0 V
• (C) 9.5 V
• (D) 7.5 V

If an inverting Op-Amp with \( R_f = 50~k\Omega \) and \( R = 200~k\Omega \) is reconfigured as non-inverting Op-Amp, then its voltage gain is

• (A) 4 with phase inversion
• (B) 5 without phase inversion
• (C) 5 with phase inversion
• (D) 4 without phase inversion

The Op-Amp circuit shown below is a (an)

• (A) Anti-log amplifier
• (B) Logarithmic amplifier
• (C) Clamping circuit
• (D) Clipping circuit

The depletion mode MOSFET is also known as

• (A) N-type MOSFET
• (B) P-type MOSFET
• (C) Normally-on MOSFET
• (D) Normally-off MOSFET

When the enable data input \( D = 1 \), select inputs \( S_1 = S_0 = 0 \) in the 1×4 Demultiplexer, then the outputs \( Y_0, Y_1, Y_2, Y_3 \) are

• (A) \( Y_0 = 0, Y_1 = 0, Y_2 = 0, Y_3 = 1 \)
• (B) \( Y_0 = 0, Y_1 = 1, Y_2 = 1, Y_3 = 0 \)
• (C) \( Y_0 = 1, Y_1 = 0, Y_2 = 0, Y_3 = 0 \)
• (D) \( Y_0 = 1, Y_1 = 0, Y_2 = 0, Y_3 = 1 \)

For an 8-bit counter ramp A/D converter driven by 1000 kHz clock, calculate maximum conversion time.

• (A) 1.28 milli seconds
• (B) 0.128 milli seconds
• (C) 0.256 milli seconds
• (D) 2.56 milli seconds

The input frequency of seven cascaded T flip-flops is 512 kHz. What is the time period of the output?

• (A) 13.67 μs
• (B) 250 μs
• (C) 125 μs
• (D) 500 μs

A 4×1 Multiplexer consists of

• (A) 2 NAND & 4 NOT gates
• (B) 2 NOT & 4 NAND gates
• (C) 2 AND & 4 NOT gates
• (D) 2 NOT & 4 AND gates

In 8085 μP, the NOP operation is

• (A) Machine control instruction
• (B) Branch instruction
• (C) Logical instruction
• (D) Arithmetic instruction

A snubber circuit used for protection of a power diode consists of

• (A) Parallel Resistance and Capacitance in parallel with diode
• (B) Parallel Resistance and Capacitance in series with diode
• (C) Series Resistance and Capacitance in parallel with diode
• (D) Series Resistance and Capacitance in series with diode

The sequence of devices in the order of decreasing frequency of operation are

• (A) GTO, MOSFET, IGBT
• (B) MOSFET, IGBT, GTO
• (C) GTO, IGBT, MOSFET
• (D) MOSFET, GTO, IGBT

A 1-\(\phi\) fully controlled bridge rectifier with a highly inductive load is fired at an angle of cos\(^{-1}(0.8)\). Assuming the load current is pure dc, the input power factor is

• (A) 0.64
• (B) 0.72
• (C) 0.80
• (D) 0.50

The instantaneous voltage wave-form of a 3-\(\phi\) fully controlled rectifier with R-L load is more negative and less positive when the firing angle ‘α’ lies between

• (A) 150\(^\circ\) and 180\(^\circ\)
• (B) 60\(^\circ\) and 90\(^\circ\)
• (C) 90\(^\circ\) and 120\(^\circ\)
• (D) 120\(^\circ\) and 150\(^\circ\)

Choose the most correct Voltage vs. Frequency plot of a 3-phase variable speed Induction motor drive at constant flux operation

• (A)
• (B)
• (C)
• (D)

Find rms value of output voltage of a 220 V input Type A chopper for a duty ratio of 0.25, assuming a voltage drop of 2 V across the chopper when it is on.

• (A) 109 V
• (B) 110 V
• (C) 55 V
• (D) 54.5 V

A 230 V supply is excited into a motor controlled by a 220 V, 50 Hz, 1-\(\phi\), full-converter. What is the minimum firing angle when back emf equal to 190 V?

• (A) \( \alpha = \sin^{-1} \left( \frac{19}{22\sqrt{2}} \right) \)
• (B) \( \alpha = \sin^{-1} \left( \frac{19}{20\sqrt{2}} \right) \)
• (C) \( \alpha = \sin^{-1} \left( \frac{10}{11\sqrt{2}} \right) \)
• (D) \( \alpha = \sin^{-1} \left( \frac{1}{\sqrt{2}} \right) \)

A 1-\(\phi\) inverter is fed with an RLC series load of \( R = 1\,\Omega, X_L = 6\,\Omega \) and \( X_C = 7\,\Omega \). Then the phase angle between fundamental current and third harmonic voltage is

• (A) \( -\tan^{-1}(18) \)
• (B) \( -\tan^{-1}\left( \frac{47}{3} \right) \)
• (C) \( +\tan^{-1}(18) \)
• (D) \( +\tan^{-1}\left( \frac{47}{3} \right) \)

A 1-\(\phi\) AC voltage controller feeds a load resistance of \( R \). If firing angles of two switches are off set at \( 180^\circ \), then rms value of input current is

• (A) Equal to half the rms value of load current
• (B) Greater than rms value of load current
• (C) Equal to rms value of load current
• (D) Less than rms value of load current

A 3-\(\phi\) semi-converter drives a dc motor which runs at a rated speed of 1000 rpm at \( 0^\circ \) firing angle. Find the speed of the motor when firing angle is \( 60^\circ \).

• (A) 866 rpm
• (B) 933 rpm
• (C) 1333 rpm
• (D) 750 rpm

The ratio of latching current to holding current of SCR

• (A) is always more than one
• (B) always depends on gate current
• (C) is always less than one
• (D) is always equal to one

Design minimum value of capacitance \( C \) needed for a Buck converter with a frequency \( f = 100 \, kHz \) so that ripple voltage \( V_r \) is less than 1% of output voltage \( V_o \). Assume the duty ratio \( \delta = 0.6 \) and inductor \( L = 25 \, \mu H \).

• (A) 60 \( \mu F \)
• (B) 20 \( \mu F \)
• (C) 40 \( \mu F \)
• (D) 30 \( \mu F \)

The frequency modulation of a 3-\(\phi\) sinusoidal pulse width modulation is an odd multiple of 3. Then the output line voltage contains

• (A) \( 5^{th}, 7^{th}, 9^{th}, 11^{th}, \dots \) harmonics
• (B) \( 3^{rd}, 5^{th}, 7^{th}, 9^{th}, \dots \) harmonics
• (C) \( 5^{th}, 7^{th}, 11^{th}, 13^{th}, \dots \) harmonics
• (D) \( 7^{th}, 11^{th}, 15^{th}, \dots \) harmonics

Which of the following is not a feature of CSI fed AC motor drive?

• (A) Used in high power drives
• (B) Open loop control is not possible
• (C) Feed-back diodes are not required
• (D) Multi-motor operation is possible

Which of the following triggering circuits can be used in feed-back control systems?

• (A) UJT triggering circuit
• (B) R triggering circuit
• (C) RC half-wave triggering circuit
• (D) RC full-wave triggering circuit