In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of  with phase sequence ABC. The star connected load has  and . The value of  in , for which the voltage difference across the nodes n and n’ is zero is

Two balanced three-phase loads, as shown in the figure, are connected to a 100√3 V, three-phase, 50 Hz main supply. Given  and .

The ammeter reading, in amperes, is _______. (round off to nearest integer)

The Fuel cost functions in rupess/hour for two 600 MW thermal power plants are given by

Plant 1 :

Plant 2 :

When  and  are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power  is 8 rupees per MWh. The two thermal power plan together meet a total power demand of 550 MW/ The optimal generation of plant 1 and plant 2 in MW respectively, are

For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is 

A balanced Wheatstone bridge ABCD has the following arm resistances: ; ;  is an unknown resistance; . The value of  and its accuracy is

The discrete time Fourier series representation of a signal x[n] with period N is written as . A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients:  and . The signal is

Let an input x(t) = 2 sin(10πt) + 5cos(15πt) + 7sin(42πt) + 4cos(45πt) is passed through an LTI system having an impulse response,                

The output of the system is

Let the probability density function of a random variable  be given as

The value of  is  __________.

For the circuit shown below with ideal diodes the output will be

The open loop transfer function of a unity gain negative feedback system is given by G(s)= . The range of k for which the system is stable, is

A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ /MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s² is ………………….. (round oft to nearest integer).

A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter. (in integer)

Let a causal LTI system be governed by the following differential equation , where x(t) and y(t) are the input and output respectively. Its impulse response is

The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flipflops, with each flip-flop having a propagation delay of 20 ns, is ___________. (round off to one decimal place)

Consider the system as shown below

where . The system is

Consider an ideal full-bridge single-phase DC-AC inverter with a DC bus voltage magnitude of 1000 V. The inverter output voltage 𝑣(𝑡) shown below, is obtained when diagonal switches of the inverter are switched with 50% duty cycle. The inverter feeds a load with a sinusoidal current given by, , where . The active power, in watts, delivered to the load is _________. (round off to nearest integer)

A 3-phase grid-connected voltage source converter with DC link voltage of 1000 V is switched using sinusoidal Pulse Width Modulation (PWM) technique. If the grid phase current is 10 A and the 3-phase complex power supplied by the converter is given by (−4000 − 𝑗3000) VA, then the modulation index used in sinusoidal PWM is ___________. (round off to two decimal places)

A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is  for the region r < b where r is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for r < b) is

The most commonly used relay, for the protection of an alternator against loss of excitation, is

If the magnetic field intensity (H) in a conducting region is given by the expression, . The magnitude of the current density, in , at 𝑥 = 1 m, 𝑦 = 2 m, and 𝑧 = 1 m, is

In the circuit shown below, the switch Sis closed at t = 0. The magnitude of the steady state voltage, in volts, across the 6Ω resistor is_________ (round off to two decimal places).

A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?

The steady state current flowing through the inductor of a DC-DC buck boost converter is given in the figure below. If the peak-to-peak ripple in the output voltage of the converter is 1 V, then the value of the output capacitor, in µF, is _______________. (round off to nearest integer)

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as  and ωn, respectively. The values of  and  are

In the circuit shown below, the magnitude of voltage V1 in volts, across the 8 kΩ resistor is ________ .  (round off to nearest integer)

Let . Then  decreases in the interval.

The transfer function of a real system, H(s), is given as:

where A, B, C and D are positive constants. This system cannot operate as

Let . The direction in which the function  increases most rapidly at point  is

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is −180°. This system has        

Let  be a region in the first quadrant of the  plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region  ?        

An LTI system is shown in the figure where G(s) . The steady state output of the system, to the input r(t), is given as  The values of a and b will be         

The open loop transfer function of a unity gain negative feedback system is given as

The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclemenets of the point (-1+j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

Let . The value of , where V is the volume enclosed by the unit cube defined by 0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 1, and 0 ≤ 𝑧 ≤ 1, is

Consider a  matrix  whose -th element, . Then the matrix  will be

As shown in the figure below, two concentric conducting spherical shells, centered at r = 0 and having radii r = c and r= d are maintained at potentials such that the potential V(r) at r = c is  and V(r) at r = d is . Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

 denotes the exponential of a square matrix . Suppose  is an eigen value and  is the corresponding eigen-vector of matrix .

Consider the following two statements:

Statement 1:  is an eigen value of .

Statement 2:  is an eigen-vector of .

Which one of the following options is correct?

Consider a matrix . The matrix  satisfies the equation , where  and  are scalars and  is the identity matrix. Then  is equal to

The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line. From the given choices are         

(i) 1.1, 0.15 and 0.08        

(ii) 0.15, 0.15 and 0.35

(iii) 0.2, 0.2 and 0.2

(iv) 0.1, 0.3 and 0.1

The steady State output  of the circuit shown below, will                 

The output impedance of a non-ideal operational amplifier is denoted by  The variation in the magnitude of  with increasing frequency, f, in the circuit shown below, is best represented by         

The current gain  in the circuit with an ideal current amplifier given below is

A single-phase full-bridge diode rectifier feeds a resistive load of 50 Ω from a 200 V, 50 Hz single phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is _____________. (round off to nearest integer).

The voltage at the input of an AC-DC rectifier is given by where ω = 2π × 50 rad/s. The input current drawn by the rectifier is given by .

The input power factor, (rounded off to two decimal places), is, _________________ lag.

An inductor having a 𝑄-factor of 60 is connected in series with a capacitor having a 𝑄-factor of 240. The overall 𝑄-factor of the circuit is ________. (round off to nearest integer)

A 280 V, separately excited DC motor with armature resistance of 1 Ω and constant field excitation drives a load. The load torque is proportional to the speed. The motor draws a current of 30A when running at a speed of 1000 rpm. Neglect frictional losses in the motor. The speed, in rpm, at which the motor will run, if an additional resistance of value 10 Ω is connected in series with the armature, is ___________. (round off the nearest integer).

The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The 𝑄-factor of the network is __________. (round off to nearest integer)

For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is  and is ripple free. The thyristors are fired with a delay angle of 45°. The amplitude of the fundamental component of the source current, in amperes, is __________. (round off to two decimal places)

Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in parallel to share a load of 500 MW. Assuming free governor action, the load shared in MW, by the 250 MW generating unit is _________. (round off to nearest integer)

A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has a synchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is 10 kW while the power factor is 0.8 leading. The loss in the motor is 2 kW. The magnitude of the per phase excitation emf of the motor, in volts, is ___________ (round off to nearest integer).

The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is

The frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is _________ (round off to nearest integer).

A 4-pole induction motor with inertia of  drives a constant load torque of 2 Nm. The speed of the motor is increased linearly from 1000 rpm to 1500 rpm in 4 seconds as shown in the figure below. Neglect losses in the motor. The energy, in joules, consumed by the motor during the speed change is ……… (round off to nearest integer).

A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ……………….. (round off to two decimal places).

The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘𝑟’, as shown in the figure below, is

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is _________. (round off to nearest integer)