The eigen values of the matrix given below are

.

A 10 1/2 digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is ___________.

For the balanced Y-Y connected 3-phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is         

Two resistors with nominal resistance values  and  have additive uncertainties, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

The transfer function C(s) of a compensator is given below.

The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is

Let x and y be integers satisfying the following equations

The value of (x + y) is ________ .

The value of the contour integral in the complex-plane . Along the contour , taken counter-clockwise is

The pole-zero plots of three discrete-times systems P, Q and R on the z-plane are shown below.

Which one of the following is TRUE about the frequency selectivity of these systems?

For a 3-input logic circuit shown below, the output Z can be expressed as

The figure shows the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where  is a complex number with non-zero real and imaginary parts.

For the given circuit,  and  are bus admittance matrix and bus impedance matrix, respectively, each of size 2 × 2. Which one of the following statements is true?

The root locus of the feedback control system having the characteristic equation where K>0, enters into the real axis at        

For the given 2-port network, the value of transfer impedance  in ohms is _________         

The mean square value of the given periodic waveform f(t) is ______

A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHz. The frequency of the vertical input is 

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its color. The probability to get a red ball in the second draw is

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is __________.

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y}, where var denotes the variance, equals

A cascade system having the impulse responses and is shown in the figure below, where symbol denotes the time origin.

The input sequence x(n) for which the cascade system produces an output sequence  is

The range of K for which all the roots of the equation are in the left half of the complex s-plane is

For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions

The minimum number of clock cycles after which the output Z would again become zero is ___________.

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA. 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ___________ electrical degrees.

A three-phase voltage source inverter with ideal devices operating in 180° conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is . The peak of the fundamental component of the phase voltage is

The figure below shows a half-bridge voltage source inverter supplying an RL-load with  and . The desired fundamental frequency of the load voltage is 50 Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index, . At 50 Hz, the RL-load draws an active power of 1.44 kW. The value of DC source voltage  in volts is

The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ________ . (Give the answer up to one decimal place).

Consider the system described by the following state space representation

 and

If u(t) is a unit step input and , the value of output y(t) at t = 1 sec (rounded off to three decimal places ) is ___________ .

For the circuit shown in the figure below, it is given that . The transistor has and when the B-E junction is forward biased.

For this circuit, the value of  is

Consider a function f(x,y,z) given by . The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is __________ .         

In the circuit shown all elements are ideal and the switch S is operated at 10kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is ___________. (Give the answer up to one decimal place).

Let

Consider the composition of f and g. i.e., . The number of discontinuities in  present in the interval is:         

When a unit ramp input is applied to the unity feedback system having closed loop transfer function , the steady rate error will be

Which of the following systems has maximum peak overshoot due to a unit step input?

The figures show diagrammatic representations of vector fields  . Respectively. Which one of the following choices is true?        

In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed

A thin soap bubble of radius R = 1 cm, and thickness a = 3.3  ), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r . The volume of the soap in the thin bubble is  and that of the drop is . The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is ___________. (Give the answer up to two decimal places.)

For the network given in figure below, the Thevenin’s voltage Vab is

Let  and . The value of  equals _________. (Give the answer up to three decimal places)

In the circuit shown, the diodes are ideal, the inductance is small, and . Which one of the following statements is true?

The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors  and  are 90° and 270°, respectively.

The RMS value of the current though diode  in amperes is ___________.

A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is

In the circuit shown in the figure, the diode used is ideal. The input power factor is ___________ . (Give the answer up to two decimal places)

If a synchronous motor is running at a leading power factor, its excitation induced voltage () is

Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger unit is ___________ MW.

For the circuit shown below, assume that the OPAMP is ideal         

A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is  and the shunt field resistance is . The no load speed, in rpm, is ___________.

A 25 kVA, 400 V, –connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is ___________.

A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature . When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is

A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

A star-connected, 12.5kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: , , , . Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3-phase AC source is ___________.

If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA,  transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is ____________ .

The nominal- circuit of a transmission line is shown in the figure.                 

Impedance  and reactance. The magnitude of the characteristic impedance of the transmission line, in , is ______________ . (Give the answer up to one decimal place)

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length  as shown in figure below. The resistances of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01 m. Neglecting the effect of ground, the magnitude of positive sequence reactance in  (rounded off to three decimal places ) is ___________

A 3-phase, 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are  and  respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ___________ .