Consider the set  of points  which minimize the real valued function

Which of the following statements is true about the set S?

Let  and  be the two eigenvectors corresponding to distinct eigenvalues of a  real symmetric matrix. Which one of the following statements is true?

Let , and . Then, the system of linear equations  has

Let  and let I can be identity matrix. Then  is equal to

Consider discrete random variables  and  with probabilities as follows:

Given , the expected value of  is

Which one of the following statements is true about the small signal voltage gain of a MOSFET based single stage amplifier?

Assuming ideal op-amps, the circuit represents a

The I-V characteristics of the element between the nodes X and Y is best depicted by

A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, R, will behave as a

Consider a discrete-time linear time-invariant (LTI) system , where

Let

where  is the discrete-time unit impulse function. For an input signal , the output  is

Consider a continuous-time signal

where  is the continuous-time unit step function. Let  be the continuous time unit impulse function. The value of  is

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

The Nyquist plot of a strictly stable  having the numerator polynomial as  encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a

Which one of the following figures represents the radial electric field distribution  caused by a spherical cloud of electrons with a volume charge density,  for  (both  are positive and  is the radial distance) and  for  ?

The operating region of the developed torque   and speed () of an induction motor drive is given by the shaded region OQRE in the figure. The load torque  characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time?

The input voltage  and current  of a converter are given by,

where, . The input power factor of the converter is closest to

Instrument(s) required to synchronize an alternator to the grid is/are

The open-loop transfer function of the system shown in the figure, is

For , which of the following real axis point(s) is/are on the root locus?

A continuous time periodic signal x(t)  is

If  is the period of , then  __________ (round off to the nearest integer).

The maximum percentage error in the equivalent resistance of two parallel-connected resistors of  and  with each having a maximum  error is _________ % (round off to nearest integer value).

Consider a distribution feeder, with  ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is ________ (round off to three decimal places).

The bus impedance matrix of a 3-bus system (in pu) is

A symmetrical fault (through a fault impedance of  ) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1 , during the fault is __________ pu (round off to three decimal places).

In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of 0.4 in a switching cycle with  and . The power delivered by the current source, in W, is __________ (round off to the nearest integer).

The induced emf in a  pole, 3-phase star connected synchronous motor is considered to be equal and in phase with the terminal voltage under no load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of  mechanical with respect to the terminal voltage phasor. If the synchronous reactance is , and stator resistance is negligible, then the motor armature current magnitude, in ampere, during loaded condition is closest to, _________ (round off to two decimal places).

Let  and  be continuous random variables with probability density functions  and , respectively. Further, let  and

Which one of the following options is correct?

A Boolean function is given as

The simplified form of this function is represented by

In the circuit,  is an ideal current source. The transistors  and  are assumed to be biased in saturation, wherein  is the input signal and  is fixed DC voltage. Both transistors have a small signal resistance of  and trans-conductance of . The small signal output impedance of this circuit is

In the circuit, shown below, if the values of R and C are very large, the form of the

output voltage for a very high frequency square wave input, is best represented by

Let continuous-time signals  and  be

Consider the convolution . Then  is

Let . Then the closed-loop system shown in the figure below, is

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system . The output is observed to be the continuous-time unit step signal . Which one of the following statements is true?

The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is "". The primary to secondary turns ratio is . If , then the relationship between  and  will be

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume linear magnetic circuit. The external resistance, in , that must be connected in series with the armature to reduce the speed of the motor by half, is closest to

A 3-phase,  pole, 50 Hz star connected induction motor has the following parameters referred to the stator:

Stator resistance, magnetizing reactance and core loss of the motor are neglected. The motor is run with constant  control from a drive. For maximum starting torque, the voltage and frequency output, respectively, from the drive, is closest to,

The 3-phase modulating waveforms  and , used in sinusoidal PWM in a Voltage Source Inverter (VSI) are

where  is the fundamental frequency. The modulating waveforms are compared with a 10 kHz triangular carrier whose magnitude varies between +1 and -1. The VSI has a DC link voltage of 600 V and feeds a star connected motor. The per phase fundamental RMS motor voltage, in volts, is closest to

 feeds an ideal inductor  through an ideal SCR with firing angle . If , then the peak of the inductor current, in ampere, is closest to

In the following circuit, the average voltage

where  is the firing angle. If the power dissipated in the resistor is 64 W, then the closest value of  in degrees is

In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at F very close to circuit breaker 1. The circuit breakers open to isolate the line. The fault self-clears. The circuit breakers reclose and restore the line. Which one of the following diagrams best indicates the rotor accelerating and decelerating areas?

An air filled cylindrical capacitor (capacitance ) of length , with  and  as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity  is inserted inside  of the annular region as shown in Fig. (ii). The value of  for which the capacitance of the capacitor in Fig. (ii), becomes  is

Let  be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of , the divergence of the radial vector field  is independent of  ?

Consider two coupled circuits, having self-inductances  and , that carry nonzero currents  and , respectively. The mutual inductance between the circuits is  with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of  ?

Let . The rate of change of the real valued function,

at the origin in the direction of the point  is __________ (round off to the nearest integer).

Consider ordinary differential equations given by

with initial conditions  and .

If , then at  __________ (round off to the nearest integer).

Let  be a clockwise oriented closed curve in the complex plane defined by . Further, let  be a complex function, where . Then, __________ (round off to the nearest integer).

The op-amps in the following circuit are ideal. The voltage gain of the circuit is ________ (round off to the nearest integer).

The switch (S) closes at . The time, in sec, the capacitor takes to charge to 50 V is ________ (round off to one decimal place).

In an experiment to measure the active power drawn by a single-phase RL Load connected to an AC source through a  resistor, three voltmeters are connected as shown in the figure below. The voltmeter readings are as follows: . Assuming perfect resistors and ideal voltmeters, the Load-active power measured in this experiment, in W, is __________ (round off to one decimal place).

In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage  for unit change in the resistance , in , is __________ (round off to two decimal places).

The steady state capacitor current of a conventional DC-DC buck converter, working in CCM, is shown in one switching cycle. If the input voltage is 30 V, the value of the inductor used, in mH, is ________ (round off to one decimal place).

An ideal low pass filter has frequency response given by

Let  be its time domain representation. Then  __________ (round off to the nearest integer).

Consider the state-space model

where  are the state, input and output, respectively. The matrices  are given below

The sum of the magnitudes of the poles is __________ (round off to nearest integer).

Using shunt capacitors, the power factor of a 3 -phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be corrected to 0.85 pf lag. The line current of the capacitor bank, in A, is _________  (round off to one decimal place).

Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of , the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of  is __________ (round off to the nearest integer).

A controller  of the form  is to be designed for the plant  as shown in the figure. The value of  that yields a phase margin of  at the gain cross-over frequency of  is ___________ (round off to one decimal place).