# Electrical Engineering - GATE 2011 Paper Solution

Roots of the algebraic equation x3+ x2+ x + 1 = 0 are

With K as a constant, the possible solution for the first order differential equation $\frac{\mathit{d}y}{\mathit{d}x}={e}^{-3x}$ is

The r.m.s value of the current i(t) in the circuit shown below is

The fourier series expansion $\style{font-size:18px}{f\left(t\right)=a_0+\sum\limits_{n=1}^\infty a_n\cos n\omega t+b_n\sin n\omega t}$ of the periodic signal shown below will contain the following nonzero terms

A 4 point starter is used to start and control the speed of a

A three phase, salient pole synchronous motor is connected to an infinite bus. It is operated at no load a normal excitation. The field excitation of the motor is first reduced to zero and then increased in reverse direction gradually. Then the armature current

A nuclear power station of 500 MW capacity is located at 300 km away from a load center. Select the most suitable power evacuation transmission configuration among the following options

The frequency response of a linear system G(jω) is provided in the tubular form below

 $\left|G\left(j\omega \right)\right|$ 1.3 1.2 1.0 0.8 0.5 0.3 $\angle G\left(j\omega \right)$ −130oc −140oc −150oc −160oc −180oc −200oc

The gain margin and phase margin of the system are

The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is

Consider the following statement
(i) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the current coil.
(ii) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the voltage coil circuit.

A low – pass filter with a cut-off frequency of 30Hz is cascaded with a high-pass filter with a cut-off frequency of 20Hz. The resultant system of filters will function as

for the circuit shown below

The CORRECT transfer characteristic is

A three-phase current source inverter used for the speed control of an induction motor is to be realized using MOSFET switches as shown below. Switches S1 to S6 are identical switches.

The proper configuration for realizing switches S1 to S6 is

A point Z has been plotted in the complex plane, as shown in figure below.

The plot of the complex number $y=\frac{1}{Z}$ is

The voltage applied to a circuit is 100 $\sqrt{2}$ cos (100$\pi$t) volts and the circuit draws a current of 10 $\sqrt{2}$ sin (100$\pi$t + $\pi$ / 4) amperes. Taking the voltage as the reference phasor, the phasor representation of the current in amperes is

In the circuit given below, the value of R required for the transfer of maximum power to the load having a resistance of 3Ω is

Given two continuous time signals $x\left(i\right)={e}^{-t}$ and $y\left(i\right)={e}^{-2t}$ which exist for $t>0,$ the convolution $z\left(t\right)=x\left(t\right)*y\left(t\right)$ is