Which one of the following matrices has an inverse?

The number of junctions in the circuit is        

All the elements in the circuit are ideal. The power delivered by the  source in watts is

The circuit shown in the figure with the switch S open, is in steady state. After the switch S is closed, the time constant of the circuit in seconds is        

Suppose signal  is obtained by the time-reversal of signal , i.e., . Which one of the following options is always true for the convolution of  and  ?

If  is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal  is

A three phase,  pole induction motor runs at . The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is

Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here,  is the applied primary voltage,  is the induced primary voltage,  is the open circuit secondary voltage, and  is the induced secondary voltage.

The figure shows the single line diagram of a 4-bus power network. Branches , , and  have impedances , and  per-unit (pu), respectively, where , with  and . The current drawn from each load bus (marked as arrows) is equal to  pu, where . If the network is to operate with minimum loss, the branch that should be opened is

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

Consider the standard second-order system of the form  with the poles  and  having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below:

System 1:  and

System 2:  and

Which one of the following statements is correct?

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are same?

The table lists two instrument transformers and their features:

The correct matching of the two columns is

Simplified form of the Boolean function

 Is

In the circuit, the present value of  is 1. Neglecting the delay in the combinatorial circuit, the values of  and , respectively, after the application of the clock will be

If the following switching devices have similar power ratings, which one of them is the fastest?

A single-phase triac based AC voltage controller feeds a series RL load. The input AC supply is . The values of  and  are  and , respectively. The minimum triggering angle of the triac to obtain controllable output voltage is

Which of the following complex functions is/are analytic on the complex plane?

Consider the complex function . The coefficient of  in the Taylor series expansion of  about the origin is ________ (rounded off to 1 decimal place).

The sum of the eigenvalues of the matrix  is ________ (rounded off to the nearest integer).

Let  be the Fourier transform of the signal

The value of the derivative of  at  is ________ (rounded off to 1 decimal place).

The incremental cost curves of two generators (Gen A and Gen B) in a plant supplying a common load are shown in the figure. If the incremental cost of supplying the common load is Rs. 7400 per MWh, then the common load in MW is ________ (rounded off to the nearest integer).

A forced commutated thyristorized step-down chopper is shown in the figure. Neglect the ON-state drop across the power devices. Assume that the capacitor is initially charged to 50 V with the polarity shown in the figure. The load current  can be assumed to be constant at 10 A. Initially,  is  and  is OFF. The turn-off time available to  in microseconds, when  is triggered, is _______ (rounded off to the nearest integer).

Consider a vector , where  represent unit vectors along the coordinate axes  respectively. The directional derivative of the function  at the point  in the direction of  is

The input  and the output  of a system are related as

Consider the discrete-time systems  and  defined as follows:                                       

Which one of the following statements is true?

If the -transform of a finite-duration discrete-time signal  is , then the  transform of the signal  is

A 3-phase, 11kV, 10 MVA synchronous generator is connected to an inductive load of power factor  via a lossless line with a per-phase inductive reactance of . The per-phase synchronous reactance of the generator is  with negligible armature resistance. If the generator is producing the rated current at the rated voltage, then the power factor at the terminal of the generator is

For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit , and the differences of the voltage phase angles are very small. The line reactances are marked in the figure, where , and  are strictly positive. The bus injections  and  are in pu. If , where , and the real power flow from bus 1 to bus 2 is , then which one of the following options is correct?

A BJT biasing circuit is shown in the figure, where  and . The Quiescent Point values of  and  are respectively

Let  be a real-valued function whose second derivative is positive for . Which of the following statements is/are always true?

Consider the function  for , where  denotes the maximum of  and . Which of the following statements is/are true?

Two passive two-port networks  and  are connected as shown in the figure. The impedance matrix of network  is . The admittance matrix of network  is . Let the ABCD matrix of the two-port network  in the figure be . The value of  in  is _______(rounded off to 2 decimal places).

For the circuit shown in the figure, the source frequency is . The mutual inductance between the magnetically coupled inductors is  with their self inductances being  and . The Thevenin's impedance, , between the terminals  and Q in  is _______ (rounded off to 2 decimal places).

In the circuit shown,  and . It is supplied by a three phase  source with the phase sequence being R-Y-B. Assume the watt meters  and  to be ideal. The magnitude of the difference between the readings of  and  in watts is _______ (rounded off to 2 decimal places).

In the  coordinate system, three point-charges , and  are located in free space at , and , respectively. The value of  for the electric field to be zero at  is ________(rounded off to 1 decimal place).

The given equation represents a magnetic field strength  in the spherical coordinate system, in free space. Here,  and  represent the unit vectors along  and , respectively. The value of  in the equation should be ________ (rounded off to the nearest integer).        

If the energy of a continuous-time signal  is  and the energy of the signal  is , then  is ________ (rounded off to 1 decimal place).

A 3-phase star connected slip ring induction motor has the following parameters referred to the stator:

The per phase stator to rotor effective turns ratio is . The rotor winding is also star connected. The magnetizing reactance and core loss of the motor can be neglected. To have maximum torque at starting, the value of the extra resistance in ohms (referred to the rotor side) to be connected in series with each phase of the rotor winding is ________ (rounded off to 2 decimal places).

A  DC shunt motor has  armature resistance including brushes. The motor draws a no-load current of . The field current is constant at . Assuming that the core and rotational losses are constant and independent of the load, the current (in amperes) drawn by the motor while delivering the rated load, for the best possible efficiency, is ________ (rounded off to 2 decimal places).

The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being , where  is the load angle and the mechanical power input is . A fault occurs on line 2 such that the power output of the generator is less than  during the fault. After the fault is cleared by opening line 2 , the power output of the generator is . If the critical fault clearing angle is  radians, the accelerating area on the power angle curve is ________times  (rounded off to 2 decimal places).

Consider the closed-loop system shown in the figure with

The root locus for the closed-loop system is to be drawn for . The angle of departure (between and ) of the root locus branch drawn from the pole , in degrees, is __________ (rounded off to the nearest integer)

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of has a constant slope of  decade at least till with the gain crossover frequency being . The asymptotic Bode phase plot remains constant at  at least till . The steady-state error of the closed-loop system for a unit ramp input is ________ (rounded off to 2 decimal places).

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of  are given in the table. The value of the gain  for a  phase margin is ________ (rounded off to 2 decimal places).

In the given circuit, the diodes are ideal. The current  through the diode  in milliamperes is ________ (rounded off to two decimal places).

A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in ) of the difference amplifier is ________ (rounded off to 2 decimal places).

A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering angle of the converter is . The ratio of the rms value of the fundamental component of the input current to the rms value of the total input current of the bridge is ________ (rounded off to 3 decimal places).

A single-phase full bridge voltage source inverter (VSI) feeds a purely inductive load. The inverter output voltage is a square wave in  conduction mode. The fundamental frequency of the output voltage is 50 Hz. If the DC input voltage of the inverter is 100 V and the value of the load inductance is 20mH, the peak-to peak load current in amperes is ________ (rounded off to the nearest integer).

In the DC-DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is 500 Hz. The voltage  across the load is assumed to be constant and ripple free. The peak inductor current in amperes is ________(rounded off to the nearest integer).

A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications:

Assume that the motor is running at 600rpm and the armature terminals of the motor are suitably reversed for regenerative braking. If the armature current of the motor is to be maintained at the rated value, the triggering angle of the converter bridge in degrees should be ________ (rounded off to 2 decimal places).

To obtain the Boolean function , the inputs  in the figure should be

Let  be a discrete random variable that is uniformly distributed over the set . Which of the following random variables is/are uniformly distributed?

Which of the following differential equations is/are nonlinear?

For a two-phase network, the phase voltages  and  are to be expressed in terms of sequence voltages  and  as . The possible option(s) for matrix S is/are

Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?