Let  where. The value of d in the range , such that  is __________.        

The value of the integral , over the contour, taken in the anti – clockwise direction, would be

A function y(t), such that  and , is a solution of the differential equation . Then y(2) is

Suppose  and  have the Fourier transforms as shown below.                 

Which one of the following statements is TRUE?

The output of a continuous-time, linear time-invariant system is denoted by  where x(t) is the input signal. A signal z(t) is called Eigen-signal of the system T, when , where  is a complex number, in general and is called an Eigen value of T. Suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?

The value of , where  is the Dirac delta function, is

The Laplace Transform of  is

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colors that the candidates could bring. The probability that a candidates comes with all 3 pens having the same colour is _______.

A temperature in the range of  is to be measured with a resolution of . The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is

A 2-bit flash Analog to digital converter (ADC) is given below. The input is  Volts. The expression for the LSB of the output  as a Boolean function of  and  is

Consider a continuous-time system with input x(t) and output y(t) given by

This system is

Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The Boolean expression for output F in terms of A and B is

Given the following polynomial equation

,

the number of roots of the polynomial, which have real parts strictly less than -1, is ___________.

In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this iteration,

The switches T1 and T2 in figure

(a) are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage and the triangular carrier voltage  are as shown in figure

(b). The carrier frequency is 5kHz. The peak value of the 100Hz component of the load current , in ampere, is _______________.

The current state  of a two JK flip-flop system is 00. Assume that the clock rise-time is much smaller than the delay of the JK flip-flop. The next state of the system is

A single-phase full-bridge voltage source inverter (VSI) is fed from a 300V battery, A pulse of  duration is used to trigger the appropriate devices in each half-cycle. The rms value of the fundamental component of the output voltage, in volts, is

A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability  of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is _____________.

In the circuit shown, switch  has been closed for a long time. At time t = 0 switch  is closed. At , the rate of change of current through the inductor, in amperes per second, is _____________.

The maximum value attained by the function  in the interval [1, 2] is ______________.

Consider the following state-space representation of a linear time-invariant system.        

 and .

The value of y(t) for  is _______________.

A transistor circuit is given below. The Zener diode breakdown voltage is 5.3V as shown. Take base to emitter voltage drop to be 0.6V. The value of the current gain  is __________.

A buck converter, as shown in Figure (a) below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage  during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is ___________.

A steady dc current of 100A is flowing through a power module (S, D) as shown in Figure (a). The V-I characteristics of the IGBT (S) and the diode (D) are shown in the Figure (b) and (c), respectively. The conduction power loss in the power module (S, D), in watts, is ________________.

 and  are the input resistances of circuits as shown below. The circuit extends infinitely in the direction shown. Which one of the following statements is TRUE?

The voltage  across and the current  through a semiconductor switch during a turn-ON transition are shown in figure. The energy dissipated during the turn-ON transition, in mJ, is ____________.

In the portion of a circuit shown, if the heat generated in  resistance is 10 calories per second, then heat generated by the  resistance, in calories per second, is__________.

The transfer function of a system is . The steady state output y(t) is A  for the input . The value of A and , respectively are

In the given circuit, the current supplied by the battery, in ampere, is______________

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by , where f is a continuous function of r and z. Let  be the resulting electric field. Then the magnitude of

The phase cross-over frequency of the transfer function  in rad/s is

In the circuit shown below, the node voltage  is ________________V.

Consider a  matrix with every element being equal to 1. Its only non-zero Eigen value is ___________.

Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is

Let the Eigen values of a  matrix A be 1, -2 with eigenvectors  and  respectively. Then the Eigen values and eigenvectors of the matrix  would, respectively, be

Consider the following asymptotic Bode magnitude plot ( is in rad/s).

Which one of the following transfer functions is best represented by the above Bode magnitude plot?

Loop transfer function of a feedback system is . Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of G(s)H(s) encircles

Let A be a  real matrix with rank 2. Which one of the following statement is TRUE?

The magnitude of three-phase fault currents at buses A and B of a power system are 10pu and 8pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is 1.0pu. The voltage magnitude at bus B during a three-phase fault at bus A is 0.8pu. The voltage magnitude at bus A during a three-phase fault at bus B, in pu, is_______________.

A 30MVA, 3-phase, 50Hz, 13.8kV star-connected synchronous generator has positive, negative and zero sequence reactance. 15%, 15% and 5% respectively. A reactance  is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phase ‘b’ and ‘c’, with a fault impedance of j0.1 p.u. The value of  (in p.u.) that will limit the positive sequence generator current to 4270 A is______________.

A single-phase thyristor-bridge rectifier is fed from a 230V, 50Hz, single-phase AC mains. If it is delivering a constant DC current of 10A, at firing angle of , then value of the power factor at AC mains is

In the circuit shown below, the supply voltage is  volts. The peak value of the steady state current through the  resistor, in amperes, is _________________.  

The circuit below is excited by a sinusoidal source. The value of R, in , for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.

A three-phase, 50Hz salient-pole synchronous motor has a per-phase direct-axis reactance  of 0.8pu and a per-phase quadrature-axis reactance of 0.6pu. Resistance of the machine is negligible. It is drawing full-load current at 0.8pf (leading). When the terminal voltage is 1 pu, per-phase induced voltage, in pu, is_______________.

A 4-pole, lap-connected, separately excited dc motor is drawing a steady current of 40 A while running at 600rpm. A good approximation for the waveshape of the current in an armature conductor of the motor is given by

A DC shunt generator delivers at 45A at a terminal voltage of 220V.The armature and the shunt field resistance are  and  respectively. The stray losses are 375W. The percentage efficiency of the DC generator is________________.

A dc voltage with ripple is given by . Measurements of this voltage v(t), made by moving-coil and moving-iron voltmeters, show reading of  and  respectively. The value of in volts, is_____________.

In a constant V/f induction motor drive, the slip at the maximum torque

Consider a system consisting of a synchronous generator working at a lagging power factor, a synchronous motor working at an overexcited condition and a directly grid-connected induction generator. Consider capacitive VAr to be a source and inductive VAr to be a sink of reactive power. Which one of the following statements is TRUE?

If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the equivalent inductance at port 1 is

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage then,

A single-phase 400V, 50Hz transformer has an iron loss of 5000W at the rated condition. When operated at 200V, 25Hz, the iron loss is 2000W. When operated at 416V, 52Hz, the value of the hysteresis loss divided by the eddy current loss is _______.

A single-phase, 22KVA, 2200V/220V, 50Hz, distribution transformer is to be connected as an auto-transformer to get an output voltage of 2420V. Its maximum KVA rating as an auto-transformer is

A three-phase cable is supplying 800kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3kV, 50Hz, the capacitance per phase of the bank, expressed in microfarads, is _______________.  

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three phase line is fully transposed. This positive sequence inductance per phase of the three-phase system is to be 5% more than that of the inductance per conductor of the single-phase system. The distance D, in meters, is_________________.