Assuming that the diodes an ideal in the given circuit, the voltage $${V_0}$$ is

The transistor circuit shown uses a silicon transistor with $${V_{BE}} = 0.7V,{{\rm I}_C} \approx {{\rm I}_E}$$ and a $$DC$$ current gain of $$100.$$ The value of $${V_0}$$ is

Given that the op-amp is ideal, the $$O/P$$ voltage $${V_0}$$ is

As shown in the figure, a negative feedback system has an amplifier of gain $$100$$ with $$ \pm 10\% $$ tolerance in the forward path, and an attenuator of value $$9/100$$ in the feedback path. The overall system gain is approximately.

The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plotted in the complex $$\,G\left( {j\omega } \right)$$ plane $$\left( {for\,\,0 < \omega < \infty } \right)$$ is

For the system $${2 \over {\left( {s + 1} \right)}},$$ the approximate time taken for a step response to reach $$98$$% of its final value is

The characteristic equation of a closed-loop system is $$s\left( {s + 1} \right)\left( {s + 3} \right) + \,\,k\left( {s + 2} \right) = 0,\,\,k > 0.$$

Which of the following statements is true?

The system $$\mathop X\limits^ \bullet = AX + BU$$ with $$A = \left[ {\matrix{ { - 1} & 2 \cr 0 & 2 \cr } } \right],$$ $$B = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$ is

A minimized form of the function $$F$$ is

Which of the following circuits is a realization of the previous function $$F$$ $$?$$

The $$TTL$$ circuit shown in the figure is fed with the waveform $$X$$ (also shown). All gates have equal propagation delay of $$10$$ $$ns.$$ The output $$Y$$ of the circuit is

When a $$''CALL$$ $$addr'$$ instruction is executed, the $$CPU$$ carries out the following sequential operations internally.

Note:
$$(R)$$ means content of register $$R$$
$$\left( {\left( R \right)} \right)$$ means content of memory locating pointed by $$R$$
$$PC$$ means Program Counter
$$SP$$ means Stack Pointer

As shown in the figure, a 1 Ω resistance is connected across a source that has a load line v + i = 100. The current through the resistance is

If the 12 Ω resistor draws a current of 1A as shown in the figure, the value of resistance R is

The switch in the circuit has been closed for a long time. It is opened at t = 0. At t = 0⁺, the current through the 1μF capacitor is

The two-port network P shown in the figure has ports 1 and 2, denoted by terminals (a, b) and (c, d), respectively. It has an impedance matrix Z with parameters denoted by z_ij. A 1 Ω resistor is connected in series with the network at port 1 as shown in the figure. The impedance matrix of the modified two-port network (shown as a dashed box) is

If the electrical circuit of figure (b) is an equivalent of the coupled tank system of figure (a), then

An ammeter has a current range of $$0$$-$$5A,$$ and its internal resistance is $$0.2\Omega $$. In order to change the range to $$0$$-$$25$$ $$A$$ we need to add a resistance of

The Maxwell's bridge shown in the fig. is at balance, the parameters of the inductive coil are

A wattmeter is connected as shown in the fig. the wattmeter reads

A separately excited $$dc$$ machine is coupled to a $$50Hz,$$ three-phase, 4-pole induction machine as shown in the figure. The dc machine is energized first and the machines rotate at $$1600$$ $$rpm.$$ Subsequently the induction machine is also connected to a $$50Hz,$$ three-phase source, the phase sequence being consistent with the direction of rotation. In steady state

A $$50$$ $$Hz$$ synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator?

A separately excited DC motor runs at 1500 rpm under no-load with 200 V applied to the armature. The field voltage is maintained at its rated value. The speed of the motor, when it delivers a torque of 5 Nm, is 1400 rpm as shown in the figure. The rotational losses and armature reaction are neglected. The armature resistance of the motor is,

A separately excited DC motor runs at 1500 rpm under no-load with 200 V applied to the armature. The field voltage is maintained at its rated value. The speed of the motor, when it delivers a torque of 5 Nm, is 1400 rpm as shown in the figure. The rotational losses and armature reaction are neglected. For the motor to deliver a torque of 2.5 Nm at 1400 rpm the armature voltage to be applied is

A single-phase transformer has a turns ratio of 1:2, and is connected to a purely resistive load as shown in the figure. The magnetizing current drawn is 1 A, and the secondary current is 1 A. If core losses and leakage reactances are neglected, the primary current is

A balanced star-connected and purely resistive load is connected at the secondary of a star-delta transformer as shown in the figure. The line-to-line voltage rating of the transformer is 110 V/220 V. Neglecting the non-idealities of the transformer, the impedance 'Z' of the equivalent star-connected load, referred to the primary side of the transformer, is

A balanced three-phase voltage is applied to a star-connected induction motor, the phase to neutral voltage being V. The stator resistance, rotor resistance referred to the stator, stator leakage reactance, rotor leakage reactance referred to the stator, and the magnetizing reactance are denoted by $$r_s,\;r_r,\;r_s,\;r_r\;and\;X_m$$, respectively. The magnitude of the starting current of the motor is given by

Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is

Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$
$$\mathop {Lt}\limits_{t \to \propto } \,\,f\left( t \right) = 1$$ then value of $$k$$ is

For the set of equations $$${x_1} + 2{x_2} + {x_3} + 4{x_4} = 2,$$$ $$$3{x_1} + 6{x_2} + 3{x_3} + 12{x_4} = 6.$$$
The following statement is true

An eigen vector of $$p = \left[ {\matrix{ 1 & 1 & 0 \cr 0 & 2 & 2 \cr 0 & 0 & 3 \cr } } \right]$$ is

The value of the quantity, where $$P = \int\limits_0^1 {x{e^x}\,dx\,\,\,} $$ is

At $$t=0,$$ the function $$f\left( t \right) = {{\sin t} \over t}\,\,$$ has

Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r $$ is

A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probability that the $$2$$^nd removed ball is red is

For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(0)=1$$ and $${\left( {{{dx} \over {dt}}} \right)_{t = 0}}$$ $$=0$$ the solution

Figure shows a composite switch consisting of a power transistor $$(BJT)$$ in series with a diode. Assuming that the transistor switch and the diode are ideal, the $$I$$-$$V$$ characteristic of the composite switch is

The fully controlled thyristor converter in the figure is fed from a single-phase source. When the firing angle is $${0^ \circ }$$, the $$dc$$ output voltage of the converter is $$300V.$$ What will be the output voltage for a firing angle of $${60^ \circ }$$, assuming continuous conduction?

The power electronic converter shown in the figure has a single-pole double-throw switch. The pole $$P$$ of the switch is connected alternately to throws $$A$$ and $$B.$$ The converter shown is a

The L-C circuit shown in the figure has an inductance $$L=1mH$$ and a capacitance $$C = 10\mu F.$$

The initial current through the inductor is zero, while the initial capacitor voltage is $$100$$ $$V.$$ The switch is closed at $$t = 0.$$ The current $$i$$ through the circuit is:

The L-C circuit shown in the figure has an inductance $$L=1mH$$ and a capacitance $$C = 10\mu F.$$

The $$L$$-$$C$$ circuit $$Q.13$$ is used to commutate a thyristor, which is initially carrying a current of $$5A$$ as shown in the figure below. The values and initial conditions of $$L$$ and $$C$$ are the same as in $$Q.13.$$ The switch is closed at $$t = 0.$$ If the forward drop is negligible, the time taken for the device to turn off is

Consider a three-phase, $$50Hz,$$ $$11$$ $$kV$$ distribution system. Each of the conductors is suspended by an insulator string having two identical porcelain insulators. The self capacitance of the insulator is $$5$$ times the shunt capacitance between the link an the ground, as shown in the figure. The voltage across the two insulators are

The zero-sequence circuit of the three phase transformer shown in the figure is

A three-phase, $$33$$ kV oil circuit breaker is rated $$1200$$ A, $$2000$$ MVA, $$3$$s. The symmetrical breaking current is

Consider a stator winding of an alternator with an internal high resistance ground fault. The currents under the fault condition are as shown in the figure. The winding is protected using a differential current scheme with current transformers of ratio $$400/5$$ $$A$$ as shown. The current through the operating coil is

Power is transferred from system $$A$$ to system $$B$$ by an $$HVDC$$ link as shown in the figure. If the voltage $${V_{AB}}$$ and $${V_{CD}}$$ are as indicated in the figure, and 1 > 0, then

For the power system shown in the figure below, the specifications of the components are the following:
$$G1: 25$$ $$kV,$$ $$100$$ $$MVA,$$ $$X=9$$%
$$G2: 25$$ $$kV,$$ $$100$$ $$MVA,$$ $$X=9$$%
$$T1: 25$$ $$kV/220$$ $$kV,$$ $$90$$ $$MVA,$$ $$X=12$$%
$$T2: 220$$ $$kV/ 25$$ $$kV,$$ $$90$$ $$MVA,$$ $$X=12$$%
$$Line$$ $$1: 220$$ $$kV,$$ $$X= 150$$ $$ohms$$

Choose $$25$$ $$kV$$ as the base voltage at the generator $$G1,$$ and $$200$$ $$MVA$$ as the $$MVA$$ base. The impedance diagram is

A $$50$$ $$Hz$$ synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator?

Consider two buses connected by an impedance of $$\left( {0 + j5} \right)\Omega .$$ The bus $$1$$ voltage is $$100$$$$\angle {30^ \circ }\,\,\,V,$$ and bus $$2$$ voltage is $$100\angle {0^ \circ }\,\,\,V,$$ The real and reactive power supplied by bus $$1,$$ respectively, are

Consider a three-core, three phase, $$50$$ $$Hz$$, $$11$$ $$kV$$ cable whose conductors are denoted as $$R, Y$$ and $$B$$ in the figure. The inter-phase capacitance $$\left( {{C_1}} \right)$$ between each pair of conductors is $$0.2$$ $$\mu F$$ and the capacitance between each line conductor and the sheath is $$0.4$$ $$\mu F$$ . The per-phase charging current is

For the system $$\frac2{\left(s+1\right)}$$, the approximate time taken for a step response to reach 98% of its final value is

Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is

The system represented by the input-output relationship $$y\left(t\right)=\int_{-\infty}^{5t}x\left(\tau\right)d\tau$$, t > 0 is

The period of the signal $$x\left(t\right)=8\sin\left(0.8\mathrm{πt}+\frac{\mathrm\pi}4\right)$$ is

The second harmonic component of the periodic waveform given in the figure has an amplitude of

x(t) is a positive rectangular pulse from t = -1 to t = +1 with unit height as shown in the figure. The value of $$\int_{-\infty}^\infty\left|X\left(\omega\right)\right|^2d\omega$$ {where X($$\mathrm\omega$$) is the Fourier transform of x(t)} is

Given f(t) and g(t)as shown below: The Laplace transform of g(t) is

Given f(t) and g(t)as shown below: g(t) can be expressed as