For a given vector , the vector normal to the plane defined by  is

For the block diagram shown in the figure, the transfer function  is

In the Nyquist plot of the open-loop transfer function

Corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

Consider a unity-gain negative feedback system consisting of the plant (s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are

The following columns present various modes of induction machine operation and the ranges of slip

The correct matching between the elements in column A with those of column B is

A 10-pole, , single phase induction motor runs at  while driving rated load. The frequency of induced rotor currents due to backward field is

A continuous-time system that is initially at rest is described by

where  is the input voltage and  is the output voltage. The impulse response of the system is

The Fourier transform  of the signal  is given by

Which one of the following statements is true?

The Z-transform of a discrete signal  is

Which one of the following statements is true?

For the three-bus power system shown in the figure, the trip signals to the circuit breakers  to  are provided by overcurrent relays  to , respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the  -  loads with isolation of minimum portion of the network using minimum number of directional relays is

The expressions of fuel cost of two thermal generating units as a function of the respective power generation  and  are given as:

where  is a constant. For a given value of , optimal dispatch requires the total load of  to be shared as  and . With the load remaining unchanged, the value of  is increased by  and optimal dispatch is carried out. The changes in  and the total cost of generation,  in Rs/hour will be as follows:

The four stator conductors  and  of a rotating machine are carrying  currents of the same value, the directions of which are shown in the figure (i). The rotor coils  -  ' and  -  ' are formed by connecting the back ends of conductors '  ' and '  ' and '  ' and '  ', respectively, as shown in figure (ii). The e.m.f. induced in coil  -  ' and coil  -  are denoted by  and , respectively. If the rotor is rotated at uniform angular speed  in the clockwise direction then which of the following correctly describes the  and  ?

fig. (i) cross-section view fig. (ii) rotor winding connection diagram

The chopper circuit shown in figure (i) feeds power to a 5 A DC constant current source. The switching frequency of the chopper is . All the components can be assumed to be ideal. The gate signals of switches  and  are shown in figure (ii). Average voltage across the 5 A current source is

Fig. (i)

Fig. (ii)

In the figure, the vectors  and  are related as:  by a transformation matrix A. The correct choice of  is

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation .

The  is estimated by randomly drawing out 10,000 numbers of samples . The estimates  are computed in the following two ways.

A semiconductor switch needs to block voltage  of only one polarity  during OFF state as shown in figure (i) and carry current in both directions during ON state as shown in figure (ii). Which of the following switch combination(s) will realize the same?

Fig. (i)

Fig. (ii)

Which of the following statement(s) is/are true?

The bus admittance  matrix of a 3-bus power system is given below.

Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

The value of parameters of the circuit shown in the figure are :

For time , the circuit is at steady state with the switch '  ' in closed condition. If the switch is opened at , the value of the voltage across the inductor  at in Volts is ________ (Round off to 1 decimal place).

A separately excited DC motor rated  A, 1500 RPM drives a constant torque load at rated speed operating from  supply drawing rated current. The armature resistance is 1.2Ω . If the supply voltage drops by  with field current unaltered then the resultant speed of the motor in RPM is __________ (Round off to the nearest integer).

For the signals  shown in the figure,  is maximum at . Then  in seconds is __________ (Round off to the nearest integer).

For the circuit shown in the figure,  and . The voltage  in Volts is __________ (Round off to 1 decimal place).

A  line of length  has the following parameters:

Resistance,

Inductance, ;

Capacitance,

The line is represented by the nominal-  model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by  and , respectively) maintained at , the phase angle difference  between  and  required for maximum possible active power to be delivered to the receiving end, in degree is ________ (Round off to 2 decimal places).

In the following differential equation, the numerically obtained value of , at , is __________ (Round off to 2 decimal places).

Three points in the -y plane are  and . The value of the slope of the best fit straight line in the least square sense is __________ (Round off to 2 decimal places).

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes  and . All the components are ideal and the breakdown voltage of the Zener is . Which of the following statements is true?

Consider a lead compensator of the form

The frequency at which this compensator produces maximum phase lead is . At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of , is . The values of , respectively, are

A 3-phase, star-connected, balanced load is supplied from a 3-phase,  (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is  and the line current is  (rms), then the power factor of the load per phase is

An 8-bit ADC converts analog voltage in the range of 0 to  to the corresponding digital code as per the conversion characteristics shown in figure. For , which of the following digital output, given in hex, is true?

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude  p.u. and angle of . A variable current source,  is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at

1.05 p.u. and the phase angle of the source current, , where  is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as

Bus 1 Slack Bus

Consider the following equation in a 2-D real-space.

Which of the following statement(s) is/are true.

In the figure, the electric field  and the magnetic field  point to  and  directions, respectively, and have constant magnitudes. A positive charge '  ' is released from rest at the origin. Which of the following statement(s) is/are true.

All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?

The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).

Consider the state-space description of an LTI system with matrices

For the input, , the value of  for which the steady-state output of the system will be zero, is __________ (Round off to the nearest integer).

A three-phase synchronous motor with synchronous impedance of  per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per unit is _________(Round off to 2 decimal places).

A three phase , 6-pole,  squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the supply voltage and frequency are reduced by , the resultant speed of the motor in RPM (neglecting the stator leakage impedance and rotational losses) is _________ (Round off to the nearest integer).

The period of the discrete-time signal  described by the equation below is  __________ (Round off to the nearest integer).

The discrete-time Fourier transform of a signal  is  . Consider that  is a periodic signal of period  such that

Note that . The magnitude of the Fourier series coefficient  is __________ (Round off to 3 decimal places).

For the circuit shown, if , the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals  at time  is __________ (Round off to 2 decimal places).

The admittance parameters of the passive resistive two-port network shown in the figure are :

The power delivered to the load resistor  in Watt is ________ (Round off to 2 decimal places).

When the winding  of the single-phase, , two winding transformer is supplied from an AC current source of frequency , the rated voltage of  (rms),  is obtained at the open-circuited terminals . The cross sectional area of the core is  and the average core length traversed by the mutual flux is . The maximum allowable flux density in the core is  and the relative permeability of the core material is 5000. The leakage impedance of the winding  and winding  at  are and , respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is _________ (Round off to 1 decimal place).

The circuit shown in the figure is initially in the steady state with the switch  in open condition and  in closed condition. The switch  is closed and  is opened simultaneously at the instant , where . The minimum value of  in milliseconds, such that there is no transient in the voltage across the  capacitor, is (Round off to 2 decimal places).

The circuit shown in the figure has reached steady state with thyristor '' in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned  at . The duration in microseconds for which the thyristor would conduct, before it turns off, is ___ (Round off to 2 decimal places).

Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence  of initial logic states, which will not change with clock, is

In a given 8-bit general purpose micro-controller there are following flags. C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity (0 for even, 1 for odd)  and  are the two general purpose registers of the micro-controller. After execution of the following instructions, the decimal equivalent of the binary sequence of the flag pattern [CAOP] will be

MOV RO,

MOV R1, +0x46

ADD R0, R1

The single phase rectifier consisting of three thyristors  and a diode  feed power to a  constant current load.  and  are fired at α=60°  and  is fired at α=240° . The reference for  is the positive zero crossing of . The average voltage  across the load in volts is ________ (Round off to 2 decimal places).

The Zener diode in circuit has a breakdown voltage of . The current gain  of the transistor in the active region in 99. Ignore base-emitter voltage drop . The current through the 20Ω resistance in milliamperes is _________ (Round off to 2 decimal places).

The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a  -  transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases '  ' and '  ' at bus 1 , neglecting all pre-fault currents, the magnitude of the fault current (from phase '  ' to '  ') in p.u. is _______ (Round off to 2 decimal places).

Fig. (i) : Single-line diagram of the power system

Fig. (iii) : Negative-sequence network Fig. (ii) : Positive-sequence network

Fig. (iv) : Zero-sequence network

An infinite surface of linear current density  exists on the  plane, as shown in the figure. The magnitude of the magnetic field intensity  at a point  due to the surface current in Ampere/meter is __________ (Round off to 2 decimal places).

The closed curve shown in the figure is described by , where ;

. The magnitude of the line integral of the vector field  around the closed curve is __________ (Round off to 2 decimal places).

A signal  is sampled at  and then passed through an ideal low pass filter having cut-off frequency of . The maximum frequency present in the filtered signal in  is __________ (Round off to the nearest integer).

A balanced delta connected load consisting of the series connection of one resistor (R=15Ω) and a capacitor  in each phase is connected to three-phase,  supply terminals through a line having an inductance of  per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals  in Volts is ________ (Round off to the nearest integer).

A quadratic function of two variables is given as

The magnitude of the maximum rate of change of the function at the point  is ________ (Round off to the nearest integer).