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

The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}}}\,\,$$ in $$rad/s$$ is

Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which have real parts strictly less than $$-1$$ is _____________.

The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady state $$y(t)$$ is $$Acos$$$$\left( {2t + \phi } \right)$$ for the input $$\cos \left( {2t} \right).$$ The values of $$A$$ and $$\phi ,$$ respectively are

Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ 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 $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3} \right)}}.$$ Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of $$G(s)$$ $$H(s)$$ encircles $$-1+j0$$

Consider the following state - space representation of a linear time-invariant system.
$$\mathop x\limits^ \bullet \left( t \right) = \left[ {\matrix{ 1 & 0 \cr 0 & 2 \cr } } \right]\,\,x\left( t \right),\,\,y\left( t \right) = {c^T}x\left( t \right),\,c = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$ and
$$x\left( 0 \right) = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$

The value of $$y(t)$$ for $$t\,\,\, = \,\,{\log _e}2$$ ___________.

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

The current state $${Q_A}{Q_B}$$ 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 $$2$$-bit flash Analog to Digital Converter $$(ADC)$$ is given below. The input is $$0 \le {V_N} \le 3$$ Volts. The expression for the $$LSB$$ of the output $${B_0}$$ as Boolean function of $${X_2},\,{X_1}$$ and $${X_0}$$ is

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

In the circuit shown below, the node voltage V_A is _________ V.

In the given circuit, the current supplied by the battery, in ampere, is ________.

In the circuit shown, switch S₂ has been closed for a long time. A time t = 0 switch S₁ is closed. At t=0⁺ , the rate of change of current through the inductor, in amperes per second, is _______.

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

In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady state current through the 1Ω resistor, in amperes, is _________.

In the portion of a circuit shown, if the heat generated in 5 Ω resistance is 10 calories per second then heat generated by the 4 Ω resistance, the calories per second, is ______.

A dc voltage with ripple is given by $$v\left( t \right)\,\,\,\, = \,\,\,\,\left[ {100 + 10\sin \left( {\omega t} \right) - 5\sin \left( {3\omega t} \right)} \right]$$ volts. Measurements of this voltage $$v\left( t \right),$$ made by moving-coil and moving iron voltmeters, show readings of $${V_1}$$ and $${V_2}$$ respectively. The value of $${V_2} - {V_1},$$ in volts, is _______.

A three-phase, $$50$$ $$Hz$$ salient-pole synchronous motor has a per-phase direct-axis reactance $$\left( {{X_d}} \right)$$ of $$0.8$$ $$pu$$ and a per-phase quadrature-axis reactance $$\left( {{X_q}} \right)$$ of $$0.6$$ $$pu.$$ Resistance of the machine is negligible. It is drawing full-load current at $$0.8$$ $$pf$$ (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 600 rpm. A good approximation for the waveshape of the current in armature conductor of the motor is given by

A DC shunt generator delivers 45 A at a terminal voltage of 220 V. The armature and the shunt field resistance are 0.01 Ω and 44 Ω respectively. The stray losses are 375 W. The percentage efficiency of the DC generator is ______.

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

A single-phase, 22 kVA, 2200 V/220 V, 50 Hz, distribution transformer is to be connected as an autotransformer to get an output voltage of 2420 V. Its maximum kVA rating as an auto-transformer 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 400 V, 50 Hz transformer has an iron loss of 5000 W at the condition. When operated at 200 V, 25 Hz, the iron loss is 2000 W. When operated at 416 V, 52 Hz, the value of the hysteresis loss divided by the eddy current loss is ________.

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

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

In cylindrical coordinate system, the potential produced by a uniform ring charge is given $$\phi=f\left(r,\;z\right)$$, where f is a continuous function of r and z. Let $$\overrightarrow E$$ be the resulting electric field. Then the magnitude of $$\nabla\times\overrightarrow E$$

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

A function $$y(t),$$ such that $$y(0)=1$$ and $$\,y\left( 1 \right) = 3{e^{ - 1}},\,\,$$ is a solution of the differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ Then $$y(2)$$ is

Let $$\,\,S = \sum\limits_{n = 0}^\infty {n{\alpha ^n}} \,\,$$ where $$\,\,\left| \alpha \right| < 1.\,\,$$ The value of $$\alpha $$ in the range $$\,\,0 < \alpha < 1,\,\,$$ such that $$\,\,S = 2\alpha \,\,$$ is ___________.

The value of the integral $$\oint\limits_c {{{2z + 5} \over {\left( {z - {1 \over 2}} \right)\left( {{z^2} - 4z + 5} \right)}}} dz$$ over the contour $$\left| z \right| = 1,$$ taken in the anti-clockwise direction, would be

Consider $$3 \times 3$$ matrix with every element being equal to $$1.$$ Its only non-zero eigenvalue is __________.

Let $$A$$ be a $$4 \times 3$$ real matrix which rank$$2.$$ Which one of the following statement is TRUE?

Let the eigenvalues of a $$2 \times 2$$ matrix $$A$$ be $$1,-2$$ with eigenvectors $${x_1}$$ and $${x_2}$$ respectively. Then the eigenvalues and eigenvectors of the matrix $${A^2} - 3A + 4{\rm I}$$ would respectively, be

The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.

A steady dc current of 100 A 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 Figures (b) and (c), respectively. The conduction power loss in the power module (S, D), in watts, 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 $${V_L}$$ during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is ________.

The switches $$T1$$ and $$T2$$ in Figure are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage $${v_m}\left( t \right) = 0.8\sin \left( {200\pi t} \right)\,\,V$$ and the triangular carrier $$\left( {{V_c}} \right),$$ voltage $$\left( {{V_c}} \right)$$ are as shown in figure $$(b).$$ The carrier frequency is $$5$$ $$kHz.$$ The peak value of the $$100$$ $$Hz$$ component of the load current $$\left( {{i_L}} \right)$$ in Ampere, is ______.

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m 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. The 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 ________.

A three-phase cable is supplying $$800$$ kW and $$600$$ kVAr to an inductive load. It is intended to supply an additional resistive load of $$100$$ kW 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 $$3.3$$ kV, $$50$$ Hz, the capacitance per phase of the bank expressed in microfarads, is ________.

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

The magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu, 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 1.0 pu. The voltage magnitude at bus B during a three-phase fault at bus A is 0.8 pu. The voltage magnitude at bus A during a three-phase fault at bus B in pu, 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 output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is the input signal. A signal z(t) is called eigen-signal of the system T, when T{z(t)}= yz(t), where $$\gamma$$ 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 $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is

Consider a continuous-time system with input x(t) and output y(t) given by $$y\left(t\right)=x\left(t\right)\cos\left(t\right)$$. This system is

Suppose x₁(t) and x₂(t) have the Fourier transforms as shown below. Which one of the following statements is TRUE?