Let  be a function defined by , where [x] represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of g(x) is __________.        

Let  be the set of points in the complex plane corresponding to the unit circle: . Consider the function  where  denotes the complex conjugate of . The f(z) maps S to which one of the following in the complex plane.

Let f(t) be a continuous time signal and let  be its Fourier transform defined by

Define g(t) by

What is the relationship between f(t) and g(t)?

The solution for the differential equation

with initial conditions  and , is

The fuel cost functions of two power plants are

Where  are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 1000MW load at incremental foul cost of 100 Rs/MWh, the ratio of load shared by plants  is

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n – 3) is

Let  be the Z – transform of a causal signal x[n], Then, the values of x[2] and x[3] are

The root locus of a unity feedback system is shown in the figure

The closed loop transfer function of the system is

Let  be the Laplace transform of a signal x(t). Then,  is

For a periodic square wave, which one of the following statements is TRUE?

The function shown in the figure can be represented as

The reading of the voltmeter (rms) in volts, for the circuit shown in the figure is __________.

In the Wien bridge oscillator circuit shown in figure, the bridge is balanced when

In an oscilloscope screen, linear sweep is applied at the

x(t) is nonzero only for , and similarly, y(t) is nonzero only for . Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?

Which of the following logic circuits is a realization of the function F whose Karnaugh map is shown in figure

A cascade of three identical modulo – 5 counters has an overall module of

In the formation of Routh – Hurtwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

For the given system, it is desired that the system be stable. The minimum value of  for this condition is ______________.                  

Let . The maximum value of the function in the interval  is

The figure shows one period of the output voltage of an inverter.  should be chosen such that . If rms value of the fundamental component is 50V, then  in degree is ____________

The line integral of function F=yzi, in the counter clockwise direction, along the circle  at z = 1 is

The following four vector fields are given in Cartesian co – ordinate system. The vector field which does not satisfy the property of magnetic flux density is

Figure (i) shows the circuit diagram of a chopper. The switch S in the circuit in the figure (i) is switched such that the voltage  across the diode has the wave shape as shown in figure (ii). The capacitance C is large so that the voltage across it is constant. If switch S and the diode are ideal, the peak to peak ripple (in A) in the inductor current is ______________

A combination of  capacitor with an initial voltage  in series with a  resistor is connected to a 20mA ideal dc current source by operating both switches at t = 0 s as shown. Which of the following graphs shown in the options approximates the voltage  across the current source over the next few seconds?

An output device is interfaced with 8–bit microprocessor 8085A. The interfacing circuit is shown in figure

The interfacing circuit makes use of 3 Line to 8 Line decoder having 3 enable lines . The address of the device is

The magnitude of the mid – band voltage gain of the circuit shown in figure is (assuming  of the transistor to be 100)

The Bode magnitude plot of the transfer function  is shown below :

Note that -6dB/octave = -20dB/decade. The value of  is _______________.

The over current relays for the line protection and loads connected at the buses are shown in the figure.

The relays are IDMT in nature having the characteristic

The maximum and minimum fault current at bus B are 2000A and 500A respectively. Assuming the time multiplier setting and plug setting for relay  to be 0.1 and 5A respectively, the operating time of  (in seconds) is _______________.

is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity, the expression for the modified capacitance is

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watt is _______________.

An incandescent lamp is marked 40W, 240V. If resistance at room temperature  is  and temperature coefficient of resistance is , then its ‘ON’ state filament temperature is  is approximately______________.

In the figure shown, assume the op – amp to be ideal. Which of the alternatives gives the correct Bode plots for the transfer function ?

In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ________________.

Given a system of equations:

Which of the following is true regarding its solutions

A system matrix is given as follows.

The absolute value of the ratio of the maximum Eigen value to the minimum Eigen value is ______________.

Figure shows four electronic switches (i), (ii), (iii) and (iv). Which of the switches can block voltages of either polarity (applied between terminals ‘a’ and ‘b’) when the active device is in the OFF state?

     (i)                    (ii)               (iii)              (iv)

Three – phase to ground fault takes place at locations  in the system shown in the figure         

If the fault takes place at location , then the voltage and the current at bus A are  and  respectively. If the fault takes place at location , then the voltage and the current at bus A are  respectively. The correct statement about voltages and currents during faults at  is

A 2 – bus system and corresponding zero sequence network are shown in the figure.        

The two transformers  and  are connected as,

In an unbalanced three phase system, phase current pu, negative sequence current , zero sequence current . The magnitude of phase current  in pu is

The figure shows the circuit of a rectifier fed from a 230 – V (rms), 50 – Hz sinusoidal voltage source. If we want to replace the current source with a resistor so that the rms value of the current supplied by the voltage source remains unchanged, the value of the resistance (in ohms) is _________ (Assume diodes to be ideal)         

The figure shows the circuit diagram of the rectifier. The load consists of a reactance  and an inductance 0.05H connected in series. Assuming ideal thyristor and ideal diode, the thyristor firing angle (in degree) needed to obtain an average load voltage of 70V is_____________

A 15kW, 230V dc shunt motor has armature circuit resistance of  and field circuit resistance of . At no load and rated voltage, the motor runs at 1400rpm and the line current drawn by the motor is 5A. At full load, the motor draws a line current of 70A. Neglect armature reaction. The full load speed of the motor in rpm is_____________.

Given that the op – amps in the figure are ideal, the output voltage  is                 

A star connected 400V, 50Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results:

Open circuit Test: at field current

Short circuit Test:  at field current

The value of per phase synchronous impedance in at rated voltage is______________.

A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The phase sequence of bus voltage is R-Y-B and that of incoming generator voltage is R-Y-B.

It was found that the lamps are becoming dark in the sequence . It means that the phase sequence of incoming generator is

Power consumed by a balanced 3 – phase, 3 – wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle in radians is

The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is , and the area of the coil is . The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5 mH/deg. The spring constants of both the meters are equal. The value of current, at which the deflections of the two meters are same, is_____________

For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is

The core loss of a single phase, 230/115 V, 50Hz power transformer is measured from 230V side by feeding the primary (230V side) from a variable voltage frequency source while keeping the secondary open circuited. The core loss is measured to be 1050 W for 230V, 50Hz input. The core loss is again measured to be 500W for 138V, 30Hz input. The hysteresis and eddy current losses of the transformer for 230V, 50Hz input are respectively,

An 8–pole, 3–phase, 50Hz induction motor is operating at a speed of 700rpm. The frequency of the rotor current of the motor in Hz is _______________.

A 3 phase, 50Hz, six pole induction motor has a rotor resistance of  and reactance of . Neglect the voltage drop in stator and assume that the rotor resistance is constant.

Given that the full load slip of 3%, the ratio of maximum torque to full load torque is

The undesirable property of an electrical insulating material is

A distribution feeder of 1km length having resistance, but negligible reactance, is fed from both the ends by 400V, 50Hz balanced sources. Both voltage source  are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.

The contributions of  and  in 100A current supplied at location P respectively, are

A two bus power system shown in the figure supplies load of 1.0 + j0.5 p.u

The values of  in p.u. and  respectively are