GATE 2010 Electrical Engineering

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 probabili...

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

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

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...

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

When a $$''CALL$$ $$addr'$$ instruction is executed, the $$CPU$$ carries out the following sequential operations internally. Note: $$(R)$$ means content of register $$R$$ $$\left(...

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 $$\...

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

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) =...

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

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

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

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

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

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

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\a...

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

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

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