# Electrical Engineering - GATE 2008 Paper Solution

The number of chords in the graph of the given circuit will be

The Thevenin’s equivalent of a circuit operation at ω = 5 rads/s, has At this frequency, the minimal realization of the Thevenin’s impedance will have a

A signal ${e}^{-\alpha t}\mathrm{sin}\left(\omega t\right)$ is the input to a real Linear Time Invariant system. Given K and $\phi$ are constants, the output of the system will be of the form $\style{font-size:18px}{Ke^{-\beta t}\sin\left(\nu t+\phi\right)}$ where

X  is a uniformly distributed random variable that takes values between 0 and 1.The value of E{X3} will be

The characteristic equation of a (3X3) matrix P is defined as

$\alpha \left(\lambda \right)=|\lambda \mathbf{I}-\mathbf{P}|={\lambda }^{3}+{\lambda }^{2}+1=0$

If I denotes identity matrix, then the inverse of  matrix P will be

If the rank of a (5X6) matrix Q is 4, then which one of the following statement is correct ?

A function y(t) satisfies the following differential equation :

$\frac{dy\left(t\right)}{dt}+y\left(t\right)=\delta \left(t\right)$

where δ(t) is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form

The equivalent circuits of a diode, during forward biased and reverse biased conditions, are shown in the figure.

If such a diode is used in clipper circuit of figure given above, the output voltage V0 of the circuit will be(A)(A)

 (A) (B) (C) (D)

Two 8-bit ADCs, one of single slope integrating type and other of successive approximation type, take TA  and TB times to convert 5 V analog input signal to equivalent digital output. If the input analog signal is reduced to 2.5 V, the approximate time taken by the two ADCs will respectively, be

An input device is interfaced with Intel 8085A microprocessor as memory mapped I/O. The address of the device is 2500H. In order to input data from the device to accumulator, the sequence of instructions will be

Distributed winding and short chording employed in AC machines will result in

Three single-phase transformer are connected to form a 3-phase transformer bank.The transformers are connected in the following manner :

The transformer connecting will be represented by

In a stepper motor, the detent torque means

A two machine power system is shown below. Transmission line XY has positive sequence impedance of Z1Ω and zero sequence impedance of Z0Ω

An ‘a’ phase to ground fault with zero fault impedance occurs at the centre of the transmission line. Bus voltage at X and line current from X to F for the phase ‘a’,
are given by Va  Volts and Ia amperes, respectively. Then, the impedance measured by the ground distance relay located at the terminal X of line XY will be given by

An extra high voltage transmission line of length 300 km can be approximateD by a lossless line having propagation constant β = 0.00127  radians per km. Then the
percentage ratio of line length to wavelength will be given by

A 3-phase transmission line is shown in figure :

Voltage drop across the transmission line is given by the following equation :

$\left[\begin{array}{c}\Delta {V}_{a}\\ \Delta {V}_{b}\\ \Delta {V}_{c}\end{array}\right]=\left[\begin{array}{ccc}{Z}_{s}& {Z}_{m}& {Z}_{m}\\ {Z}_{m}& {Z}_{s}& {Z}_{m}\\ {Z}_{m}& {Z}_{m}& {Z}_{s}\end{array}\right]\left[\begin{array}{c}{I}_{a}\\ {I}_{b}\\ {I}_{c}\end{array}\right]$

Shunt capacitance of the line can be neglected. If the has positive sequence impedance of 15 Ω  and zero sequence impedance of 48 Ω, then the  values of Zs and Zm  will be

In the single phase voltage controller circuit shown in the figure, for what range of triggering angle (α) , the input voltage (V0) is not controllable ?

A 3-phase Voltage Source Inverter is operated in 180° conduction mode. Which one of the following statements is true ?

The impulse response of a causal linear time-invariant system is given as h(t) . Now consider the following two statements :
Statement (I): Principle of superposition holds
Statement (II):h(t)=0 for t<0
Which one of the following statements is correct ?