A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratio  is ________.

The input impedance , for the network shown in

Two generators have cost functions  and . Their incremental-cost characteristics are,

They need to deliver a combined load of 260 MW. Ignoring the network losses for economic operation, the generation  and  (in MW) are         

Consider a closed-loop system as shown. is the plant transfer function and Gc(s) = 1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ……….. rad/s. (Round off to 2 decimal places)

In the given figure, plant

 and compansatorinput is D(s). It is desired that when the disturbance is a unit step, the steady-steady error should not exceed 0.1 unit. The minimum value of K is …………..(Round off to 2 decimal places) 

The causal signal with z-transform   is (u[n] is the unit step signal)

Let , where  is a complex number. Which one of the following is true?        

Inductance is measured by

Let  and  be the vertices of rectangle  in the complex plane. Assuming that  is traversed in counter-clockwise direction, the value of the contour integral  is

Let f(t) be an even function i.e., f(–t) = f(t) for all t. Let the Fourier transform of f(t) be defined as . Suppose  for all ω and F(0) = 1. Then

Consider a continuous-time signal x(t) defined by x(t) = 0 for |t| > 1, and x(t) = 1 – |t| for |t| ≤ 1. Let the Fourier transform of x(t) be defined as . The maximum magnitude of X(ω) is __________.

For the closed-loop system shown, the transfer function  is

Suppose the probability that a coin toss shows "head" is , where . The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is

For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals 'ab' is

In the circuit shown, the input  is a sinusoidal AC voltage having an RMS value of 230V±20%. The worst-case peak-inverse voltage seen across any diode is _________ V. (Round off to 2 decimal places.) 

In the circuit shown, a 5V Zener diode is used to regulate the voltage across load . The input is an unregulated DC voltage with a minimum value of 6V and a maximum value of 8V. The value of  is 6Ω. The Zener diode has a maximum rated power dissipation of 2.5 W, Assuming the Zener diode to be ideal, the minimum value of  is ___________ Ω. 

The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the RMS value of the full wave rectified waveform to the RMS value of the clipped waveform is _______.

(Round off to 2 decimal places.)        

A 16-bit synchronous binary up-counter is clocked with a frequency fCLK. The two most significant bits are OR-ed together to form an output Y. Measurements show' that Y is periodic, and the duration for which Y remains high in each period is 24 ms. The clock frequency fCLK is _________ MHz. (Round off to 2 decimal places.)

A counter is constructed with three D flip-flops. The input-output pairs are named (D0, Q0), (D1, Q1), and (D2, Q2), where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the Q2 Q1 Q0 format. The combinational logic expression for D1 is

If the input x(t) and output y(t) of a system are related as y(t) = max (0, x(t)), then the system is

Two discrete-time linear time-invariant systems with impulse responses  and  are connected in cascade, where  is the Kronecker delta. The impulse response of the cascaded system is

A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across ‘ab’ as shown. To achieve a modulation index of 0.8, the angle 0 expressed in degrees should be ________. (Round off to 2 decimal places.)        

(Modulation index is defined as the ratio of the peak of the fundamental component of  to the applied DC value.)

Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is . The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:

The dimensions of the sub-matrix M is

A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the  matrix correspond to Bus 1, 2 and 3 respectively, then  of the network is

Which one of the following vector functions represents a magnetic field ? (, and  are unit vectors along x-axis, y-axis, and z-axis, respectively)

One coulomb of point charge moving with a uniform velocity enters the region x ≥ 0 having a magnetic flux density

. The magnitude of force on the charge at  is ________ N.

( and  are unit vectors along x-axis, y-axis, and z-axis, respectively.)

In the BJT circuit shown, beta of the PNP transistor is 100. Assume . .

The voltage across  will be 5 V when  is ……… kΩ. (Round off 2 decimal places)

The state space representation of a first-order system is given as

y = x

where, x is the state variable, u is the control input and y is the controlled output. Let u =-Kx be the control law, where K is the controller gain. To place a closed-loop pole at -2, the value of K is _________.        

In the circuit, switch 'S’ is in the closed position for a very long time if the switch is opened at time t = 0, then iL(t) in amperes, for t > 0 is

A 100 Hz square wave, switching between 0V and 5V, is applied to a CR high-pass filter circuit as shown, The output voltage waveform across the resistor is 6.2V peak-to-peak, If the resistance R is 820Ω. then the value C is_________ μF. (Round off to 2 decimal places.)

Consider the boost converter shown. Switch Q is operating at 25 kHz with a duty cycle of 0.6. Assume the diode and switch to be ideal. Under steady-state condition, the average resistance  as seen by the source is _______Ω. (Round off to 2 decimal places.)

Consider the buck-boost converter shown. Switch Q is operating at 25 kHz and 0.75 duty-cycle. Assume diode and switch to be ideal. Under steady-state condition, the average current flowing through the inductor is _______A.

Let  be a real-valued function such that  for some  and  for all . Then  has

In the given circuit, for voltage Vy to be zero, value of β should be_________ (round off to 2 decimal places).

Suppose the circles  and  intersect each other orthogonally at the point (u,v). Then   __________.

The Bode magnitude plot for the transfer function  of the circuit is as shown. The value of R is _______ Ω. (Round off to 2 decimal places.)

In the open interval , the polynomial   has

A signal generator having a source resistance of . is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is ________ . (Round off to 2 decimal places.)

A  point charge is held at the origin of a cartesian coordinate system. If a second point charge of  is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is _______ mJ. (Round off to 2 decimal places).

Take  in SI units. All coordinates are in meters.        

Let  and  be real numbers such that .

The eigenvalues of the matrix  are

Let  be a  matrix such that  is null matrix, and let  be the  identity matrix. The determinant of  is _______.

Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field  in the gap to the original electric field  is __.

Suppose  and  are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current  If phase-A current  and phase-C current , then  in p.u is

A CMOS Schmitt-trigger inverter has a low output level of 0 V and a high output level of 5 V. It has input thresholds of 1.6 V and 2.4 V. The input capacitance and output resistance of the Schmitt-trigger are negligible. The

frequency of the oscillator shown is ______________ Hz.

(Round off to 2 decimal places.)        

In the given circuit, the value of capacitor C that makes current I = 0 is _________ μF.

In the given circuit, for maximum power to be delivered to , its value should be …………… Ω. (Round off to 2 decimal places).        

A belt-driven DC shunt generator running at 300 RPM delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is 0.025 Ω, field resistance is 50 Ω, and brush drop is 2 V. Ignoring armature reaction, the speed of the motor is _________ RPM. (Round off 2 decimal places)

Consider the table given:

The correct combination that relates the constructional feature, machine type and mitigation is

The power input to a 500 V, 50 Hz, 6-pole. 3-phase induction motor running at 975 RPM is 40 kW. The total stator losses are 1 kW. If the total friction and windage losses are 2.025 kW. then the efficiency is __________ %.

An 8-pole, 50 Hz. three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is …………… Ω. (Round off to 2 decimal places.)

Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.

In a single-phase transformer, the total iron loss is 2500 W at nominal voltage of 440V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss respectively are

An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is __________ μH. (Round off to 2 decimal places.)

Two single-core power cables have total conductor resistances of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ______

An alternator with internal voltage of . and synchronous reactance of 0.4 p.u is connected by a transmission line of reactance 0.1 p.u. to a synchronous motor having synchronous reactance 0.35 pu. and internal voltage of  If the real power supplied by the altemator is 0.866 p.u, then  is …………… degrees. (Round off to 2 decimal places) (Machines are of non-salient type. Neglect resistances)

In the figure shown, self-impedances of the two transmission Iines are 1.5j p.u each, and  is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that , the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is