If , then S has the value

The solution of the first order differential equation  is:

If u(t) is the unit step and  δ(t) is the unit impulse function, the inverse z-transform of for k ≥ 0 is:

If P and Q are two random events, then the following is TRUE:

For the function, the maximum occurs when x is equal to:

A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is:

For the equation, the solution x(t) approaches the following values at t →∞

For the scalar field , the magnitude of the gradient at the point (1,3) is:

For the three-phase circuit shown in Figure, the ratio of the current is given by

If X1 and X2 are the inputs to the circuit shown in figure, the output Q is:

The Laplace transform of a function f(t) is .  As t →∞, f(t) approaches

The Q-meter works on the principle of

The set-up in figure is used to measure resistance R. The ammeter and voltmeter resistances are 0.01Ω and 2000Ω, respectively. Their readings are 2A and 180V, respectively, giving a measured resistance of 90Ω. The percentage error in the measurement is:

A load centre is at an equidistant from the two thermal generating stations and as shown in Figure. The fuel cost characteristics of the generating stations are given by

Rs/hour

Rs/hour

Where and are the generation in MW of  and , respectively. For most economic generation to meet 300 MW of load, and , respectively, are

Assume that the N-channel MOSFET shown in Figure is ideal, and that its threshold voltage is +1.0V. The voltage  between nodes a and b is:

The Fourier series for the function  is:

The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in

An electric motor, developing a starting torque of 15 Nm, starts with a load torque of 7 Nm on its shaft. If the acceleration at start is , the moment of inertia of the systems must be (neglecting viscous and Coulomb/friction).

The charge distribution in a metal-dielectric-semiconductor specimen is shown in Figure.  The negative charge density decreases linearly in the semiconductor as shown. The electric field distribution is as shown in        

For the triangular waveform shown in Figure, the RMS value of the voltage is equal to

For the two-port network shown in Figure, the Z-matrix is given by         

The figure shows the root locus plot (location of poles not given) of a third-order system whose open-loop transfer function is                 

Assume that the threshold voltage of the N-channel MOSFET shown in Figure is +0.75V. The output characteristics of the MOSFET are also shown.

The transconductance of the MOSFET is:        

Assume that the threshold voltage of the N-channel MOSFET shown in Figure is +0.75V. The output characteristics of the MOSFET are also shown.

The voltage gain of the amplifier is:

Two networks are connected in cascade as shown in Figure. With the usual notations the equivalent A, B, C and D constants are obtained. Given that

C = 0.025∠45°, the value of  is:        

The simultaneous application of signals x(t) and y (t) to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of - 8 display. If P and Q are constants, and x(t)=P sin(4t+30) , then y (t) is equal to

In Figure, the Thevenin’s equivalent pair (voltage, impedance), as seen at the terminals P-Q, is given by

The output voltage waveform of a three-phase square-wave inverter contains

Assume that and in Figure are ideal diodes. The value of current I is

The digital circuit shown in figure works as a

The network shown in Figure has impedances in p.u. as indicated. The diagonal element of the bus admittance matrix YBUS of the network is:

A unity feedback system, having an open loop gain , becomes stable when

Select the circuit, which will produce the given output Q for the input signals X1 and X2 given in Figure.

A digital-to-analog converter with a full-scale output voltage of 3.5V has a resolution close to 14 mV. Its bit size is:

In figure, as long as  and , the output Q remains

In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x:

For the matrix , one of the Eigen values is equal to –2. Which of the following is an Eigen vector?

A state variable system

, with the initial condition and the unit step input  u(t) has

The state transition matrix

If , the top row of  is:

A state variable system

, with the initial condition and the unit step input u(t) has and the state transition equation

Figure shows a step-down chopper switched at 1 KHz with a duty ratio D = 0.5. The peak-peak ripple in the load current is close to

Consider a phase controlled converter shown in Figure. The thyristor is fired at an angle α in every positive half cycle of the input voltage. If the peak value of the instantaneous output voltage equals 230 V, the firing angle α is close to

The 8085 assembly language instruction that stores the contents of H and L registers into the memory locations 2050H and 2051H, respectively, is:

A generator with constant 1.0p.u. terminal voltage supplies power through a step-up transformer of 0.12p.u. reactance and a double-circuit line to an  infinite bus bas as shown in Figure. The infinite bus voltage is maintained at 1.0p.u.  Neglecting the resistances and susceptances of the system, the steady state stability power limit of the system is 6.25p.u. If one of the double-circuit is tripped, the resulting steady state stability power limit in p.u. will be

In Figure, the initial capacitor voltage is zero. The switch is closed at t = 0. The final steady-state voltage across the capacitor is:

The circuit shown in Figure is in steady state, when the switch is closed at t = 0.  Assuming that the inductance is ideal, the current through the inductor at equals

A system with zero initial conditions has the closed loop transfer function. The system output is zero at the frequency

A coil of inductance 10H resistance is connected as shown in figure. After the switch S has been in connected with point 1 for a very long time, it is moved to point 2 at t=0

If, at t = 0+, the voltage across the coil is 120V, the value of resistance R is:

The common emitter amplifier shown in Figure is biased using a 1mA ideal current source. The approximate base current value is:        

The gain margin of a unity feedback control system with the open loop transfer function  is:  

A coil of inductance 10H resistance is connected as shown in figure. After the switch S has been in connected with point 1 for a very long time, it is moved to point 2 at t=0

For the value of R =40 ohm, the time taken for 95% of the stored energy dissipated is close to

The conduction loss versus device current characteristic of a power MOSFET is best approximated by

In the GH(s) plane, the Nyquist plot of the loop transfer function passes through the negative real axis at the point  

Figure shows the voltage across a power semiconductor device and the current through the device during a switching transition. Is the transition a turn ON transition or a turn OFF transition? What is the energy lost during the transition?  

If the compensated system shown in Figure has a phase margin of 60° at the crossover frequency of 1rad/sec, the value of the gain K is:

Figure the value of R is

If  is the electric field intensity,  is equal to

An electronic switch S is required to block voltages of either polarity during its OFF state as shown in Figure a. This switch is required to conduct in only one direction during its ON state as shown in Figure b.

Which of the following are valid realizations of the switch S?

The p.u. parameters for a 500 MVA machine on its own base are:

Inertia M = 20 p.u.; reactance X = 2 p.u.

The p.u. values of inertia and reactance on 100 MVA common base, respectively, are

The parameters of a transposed overhead transmission line are given as:

Self reactance  / km and Mutual reactance

The positive sequence reactance and zero sequence reactance, respectively, in Ω/km are

At a 220 kV substation of a power system, it is given that the three-phase fault level is 4000 MVA and single-line to ground fault level is 5000 MVA. Neglecting the resistance and the shunt susceptances of the system,         

(A) The positive sequence driving point reactance at the bus is:

(a) 2.5 Ω          (b) 4.033 Ω

(c) 5.5 Ω          (d) 12.1 Ω

(B) And the zero sequence driving point reactance at the bus is:                

(a) 2.2 Ω          (b) 4.84 Ω

(c) 18.18 Ω          (d) 22.72 Ω

A three-phase diode bridge rectifier is fed from a 400V RMS, 50 Hz, three-phase AC source. If the load is purely resistive, the peak instantaneous output voltage is equal to

When subjected to a unit step input, the closed loop control system shown in Figure will have a steady state error of

The RMS value of the voltage is:

At a 220 kV substation of a power system, it is given that the three-phase fault level is 4000 MVA and single-line to ground fault level is 5000 MVA. Neglecting the resistance and the shunt susceptances of the system, the zero sequence driving point reactance at the bus is:  

The RL circuit of Figure is fed from a constant magnitude, variable frequency sinusoidal voltage source . At 100 Hz, the R and L elements each have a voltage drop . If the frequency of the source is changed to 50 Hz, the new voltage drop across R is:

Consider the inverting amplifier, using an ideal operational amplifier shown in Figure. The designer wishes to realize the input resistance seen by the small signal source to be as large as possible, while keeping the voltage gain between –10 and –25, the upper limit on  is 1 MΩ. The value of  should be

In relation to the synchronous machines, which one of the following statements is false?

In Figure if the input is a sinusoidal signal, the output will appear as shown in                

A 1000 kVA, 6.6 kV, 3-phase star connected cylindrical pole synchronous generator has a synchronous reactance of 20 Ω. Neglect the armature resistance and consider operation at full load and unity power factor.        

The induced emf (line-to-line) is close to

A 1000 kVA, 6.6 kV, 3-phase star connected cylindrical pole synchronous generator has a synchronous reactance of 20 Ω. Neglect the armature resistance and consider operation at full load and unity power factor.        

The power (or torque) angle is close to?

Two magnetic poles revolve around a stationary armature carrying two coils as shown in Figure. Consider the instant when the poles are in a position as shown. Identify the correct statement regarding the polarity of the induced EMF at this instant in coil sides and  

A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven (i) at half the rated speed by armature voltage control and (ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately

Two wattmeters, which are connected to measure the total power on a three phase system supplying a balanced load, read 10.5 kW and -2.5 kW, respectively. The total power and the power factor, respectively, are

In relation to DC machines, match the following and choose the correct combination.

On the torque/speed curve of induction motor shown in Figure, four points of operation are market as W, X, Y and Z. Which one of them represents the operation at a slip greater than 1?

A PMMC voltmeter is connected across a series combination of a DC voltage source  and an AC voltage source.  The meter reads

For an induction motor, operating at a slip s, the ratio of gross power output to air gap power is equal to:

A DC ammeter has a resistance of 0.1Ω and its current range is 0 – 100A. If the range is to be extended to 0 – 500A, the meter requires the following shunt resistance

Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,

A 1000 V DC supply has two 1-core cables as its positive and negative leads; their insulation resistances to earth are 4 MΩ and 6 MΩ, respectively, as shown in Figure. A voltmeter with resistance 50 KΩ is used to measure the insulation of the cable. When connected between the positive core and earth, the voltmeter reads

A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full load slip is 4%, the ratio of the starting developed torque to the full load torque is approximately equal to

Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages

In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve

Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

Assertion: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the sub-synchronous region.

Reason: The magnetic flux is maintained almost constant at the rated value by keeping the ratio V/f constant over the considered speed range.

The equivalent circuit of a transformer has leakage reactance and magnetizing reactance . Their magnitudes satisfy

An 800 kV transmission line has a maximum power transfer capacity P, on the operated at 400 kV with the series reactance unchanged, the new maximum power transfer capacity is approximately

The insulation strength of an EHV transmission line is mainly governed by

High Voltage DC (HVDC) transmission is mainly used for

At an industrial sub-station with a 4 MW load, a capacitor of 2 MVAR is installed to maintain the load power factor at 0.97 lagging. If the capacitor goes out of service, the load power factor becomes