Consider the infinite-length, discrete-time sequence , where  is an integer. The region of convergence of its Z-transform  is given by: (Note:  is a complex variable)

Let  be any continuous-time periodic signal with period . It is sampled uniformly with a sampling period  where , resulting in the discrete sequence , where  is an integer.

Which one of the following statements is correct about  ?

The Laplace transform of the step response of a system is given by

The rise time is defined as the time taken for the response to go from 0.1 to 0.9 of its final value. The settling time is defined as the time taken for the response to reach 0.98 of its final value.

For this system, the rise time (  ), settling time (  ), and time constant (  ), all expressed in seconds, are

Consider the following differential equation:

Which one of the following options is correct?

A uniform ring charge of radius  carries a total charge . Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength  kept at the center of the ring?

( is the permittivity of the medium)

A positive point charge with velocity  enters a region having electric field  and magnetic field . Which one of the following statements is correct for the force on the charge as it enters the region?

A , single-phase two-winding transformer is configured as a  autotransformer.

What will be the rating of the autotransformer?

Consider a power system with  buses, of which  are generator buses and the remaining  are load buses (where there is no generation).

Assume that there are no reactive power-limit violations at the generator buses.

What is the size of the Jacobian matrix in the Newton-Raphson load flow method?

The initial three-phase voltage phasors (, and ) at a bus of a power network are as shown in Case-1. Due to a disturbance, the bus voltage phasors changed in phase by a small angle , and the magnitudes remained the same as depicted in Case-2.

Which one of the following statements is correct about the zero sequence components?

A certain application requires power at a frequency of 16.67 Hz, while the available grid frequency is 50 Hz. A 3-phase synchronous motor connected to the 50 Hz, 3-phase grid, driving a synchronous generator, is used for this application.

Which one of the following combinations is a suitable choice for the number of poles in the motor and generator, respectively?

Which one of the following options is correct regarding the typical double-squirrel-cage structure used in induction motors?

The figure shows the single-line diagram of a synchronous generator delivering  of power at unity power factor to an infinite bus.

 denotes the stator current phasor. If the field excitation is increased, which one of the following options correctly describes its effect on the stator current, power factor, and load angle of the machine?

A circuit with ideal elements is shown.

Which one of the following options correctly identifies all the linear elements in the circuit?

For the circuit shown, which one of the following options correctly identifies the Thevenin's equivalent parameters between nodes Y and Z?

Refer to the four circuits shown.

Which one of the following options for , and  makes all of them realizable?

A single-phase voltage source  delivers a current,  A to a load.

The load power factor, correct up to two decimal places, is:

The figure shows a straight-line approximation for the forward characteristics of a power diode. A continuous on-state current of 15 A is flowing through the diode.

What is the power loss in the diode?

Consider the circuit shown in Figure (a). A gate pulse  is applied between time instants  and . After , during the MOSFET turn OFF process, it experiences a voltage overshoot.

Based on the  waveforms shown in Figure (b), which one of the following options is correct?

The asymptotic Bode magnitude plot of a system is shown

Which one of the following options best represents the transfer function of the system?

Two  matrices  and  have a common eigenvalue 2, and the same corresponding nonzero eigenvector.

Which of the following options is/are correct?

(Note:  is the  identity matrix.)

A  single-phase transformer is designed for use in India and rated 100 VA at 50 Hz . Later, this unit is shipped to the USA where it is used as a  transformer at 60 Hz .

Which of the following statements is/are correct?

Given that , the integral  over the unit sphere  centered at the origin evaluates to

(Round off to one decimal place)

In the linear regulator circuit shown, the base to emitter voltage  of the BJT is 0.6 V . The Zener diode clamps the base voltage to 5.4 V. Ignore the biasing current of the Zener diode and BJT.

The maximum possible efficiency of the regulator circuit is  %

(Round off to one decimal place)

Consider the circuit shown. Assume that the diode  is ideal. The supply voltage , and . The peak diode current (in amperes) is

(Round off to one decimal place)

 is an  skew-symmetric matrix with real-valued entries, and  is an -dimensional column vector with real-valued entries such that .

The quantity  evaluates to

(Answer in integer)

A time-limited waveform  is specified as follows:

A new waveform  is constructed from  as follows:

The sum of the coefficients of the third harmonics of the sine and cosine terms in the trigonometric Fourier series expansion of  is .

What is the value of ?

In the circuit shown, the open loop gain of the operational amplifier is .

What is the voltage gain of the circuit? (Round off to two decimal places)

Three single-phase  transformers are connected to form a three-phase transformer bank with connections as shown.

Considering  phase sequence, the vector group of the transformer is:

In the circuit shown, the phase currents are

Given that the CTs are ideal with no saturation, and the turns ratio of the Main CT is  and that of the Auxiliary Transformer  is  on every phase, the value of , rounded off to three decimal places, is:

The operating characteristic of a reactance relay is given by  , where  is the reactance calculated by the relay. Its operating characteristic in the admittance plane (G - B plane, where G and B denote conductance and susceptance, respectively, expressed in \(\scriptstyle \mho\)) is given by:

A three-phase two-winding transformer has a voltage transformation ratio , where  is the primary side voltage in p.u., and  is the secondary side voltage in p.u.  and  represent the currents injected into the primary and secondary sides of the transformer, respectively. The admittance corresponding to the leakage impedance of the transformer referred to the secondary is  p.u. Neglect the magnetizing branch.

The Y bus representation of this transformer is:

An electrical component has voltage drop , when the current through it is .

What is the average power dissipated over a half cycle corresponding to  ?

The electrical network shown has an independent voltage source (10 V) and a current source ( ).

The voltage across the capacitor at time instants (in seconds) , and , respectively, is:

The terminal voltage and current of a linear electrical network shown in Figure (a) are given in the table.

The correct choice for the parameters () of the Norton equivalent circuit shown in Figure (b) is:

The digital circuit shown has 3 inputs , and ).

The simplified logical expression for the output (OUT) is:

The MOSFET switches shown in the circuit are ideal.

Which of the following is the correct option for Boolean logical expression of the output (OUT), and the maximum possible power (P) consumed by the circuit?

Consider the single-phase voltage source inverter circuit feeding an inductive load . Assume that the power MOSFET switches are ideal.  and are switched on during the first \(\scriptstyle 10\mu S\), and  and  are switched on during the next \(\scriptstyle 10\mu S\) in a switching cycle. The switches in the same leg are thus switched in a complementary fashion. Neglect the dead time. The waveform of the inductor current (  ) in the steady state is triangular with a peak value of 5 A as shown.

The rms value of the current through the switch  is:

Consider the boost converter circuit shown. Assume that the semiconductor devices are ideal. In steady state, the inductor current rises linearly from 0 A to 6 A in the first  and then falls linearly from 6 A to 0 A in the next  of every switching cycle as shown. The load resistance  is  and the capacitance  is .

Neglect the ripple in the output voltage. What is the input voltage  ?

Which one of the following statements is ALWAYS correct about a collection of  column vectors, each having  real-valued entries?

Consider the second-order differential equation

with initial conditions         

The solution is given by

The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two nonintersecting regions with areas  and  within the loop are subjected to magnetic fields  , and , respectively.

What is the expression for the induced rms voltage in loop A?

A system is characterized by the following state equation and output equation (  : input,  : state vector,  : output)

What are the values of  and  for which the poles of the transfer function are at  and  ?

A system is represented in state-space form as follows:

( : input,  : state vector,  : output)

Consider the new state vector

What is the state-space representation of the system in terms of the new state vector ?

For the balanced 3-phase transmission line shown, consider the following cases:

Case-1:  p.u., p.u., p.u. and

Case-2:  p.u.,  p.u.,  p.u. and

Which of the following statements is/are correct about real power loss and reactive power loss in the line?

Consider an  orthogonal matrix  with real entries and each column having unit Euclidean norm.

Which of the following statements is/are correct?

Consider the system of linear equations: , where  is an  matrix, and  and  are -dimensional column vectors.

Suppose this system of equations has a unique solution. Which of the following statements is/are correct?

The resistance values of the Wheatstone bridge shown are: . The battery voltage . The battery has an internal resistance of  and the Galvanometer (G) has a resistance of .

The value of the resistance S for balanced condition is   (Answer in integer)

A system with two generators G1 and G2 (without generator limits) is shown.

The total load on the system is 1184 MW. The expressions for the cost of generation ( and ) and real power loss () are as follows:

When the generators are operating at their optimal generation, meeting the total load requirement, the real power loss in the system is  MW (Round off to one decimal place)

Consider the Lagrange multiplier  for optimal generation.

A balanced three-phase supply is given to a -pole, , wound rotor induction motor with Y-connected stator and rotor windings. The motor is driving a constant torque load. With shorted sliprings, the machine runs at 1476 rpm.

When an external non-inductive resistance of  per phase is connected in series in the rotor circuit, the steady-state speed drops to 1404 rpm.

Neglecting rotational losses, the actual per phase rotor winding resistance is           

(Round off to two decimal places)

Consider the two-port network shown. For maximum power transfer to the resistive load , the value of  should be   (Round off to two decimal places)

Consider the circuit shown. Assume that the diode () is ideal.

Given , and  , the average value of the current through the diode is  A

(Round off to two decimal places)

The magnitude of the contour integral

over the contour  is

(Round off to two decimal places)

Note:  is a complex variable and

A uniform spherical volume charge distribution of radius 2 m, centered at the origin, has a strength of . A point charge of strength  is moved from (  ) to (  ) in Cartesian coordinate system. The relative permittivity of the medium is 1 and the coordinate values are in meters.

The work done during the process is  

(Round off to two decimal places)

Let X and Y be two real-valued random variables with

, and , where E denotes the expectation operator.

The value of  that minimizes   is

(Round off to one decimal place)

The integral  evaluates to (Round off to two decimal places)