GATE 2008 Electrical Engineering
48 questions across 1 session
$$X$$ is uniformly distributed random variable that take values between $$0$$ and $$1.$$ The value of $$E\left( {{X^3}} \right)$$ will be
A $$230V,$$ $$50Hz,$$ $$4$$ pole, single phase induction motor is rotating in the clockwise (forward) direction at a speed of $$1425$$ $$rpm.$$ If the rotor resistance at standstil...
$$A$$ is $$m$$ $$x$$ $$n$$ full rank matrix with $$m > n$$ and $${\rm I}$$ is an identity matrix. Let matrix $${A^ + } = {\left( {{A^T}A} \right)^{ - 1}}{A^T}.$$ Then which one of...
Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be
Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...
The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is state vector, $$U$$ is input, $$Y$$ is output and $$$A = \lef...
A single phase full bridge converter supplies a load drawing constant and ripple free load current. If the triggering angle is $${30^ \circ },$$ the input power factor will be
A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross-sectional area of 300 mm 2 . The inductance the coil corresponding to a magnet...
Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...
A function $$y(t)$$ satisfies the following differential equation : $${{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$ Where $$\delta \left( t \rig...
Voltage phasors at the two terminals of a transmission line of length $$70$$ km have a magnitude of $$1.0$$ per unit but are $$180$$ degrees out of phase. Assuming that the maximum...
An input device is interfaced with Intel $$8085$$ $$A$$ microprocessor as memory mapped $${\rm I}/O,$$ the address of the device is $$2500H.$$ In order to input data from the devic...
A synchronous motor is connected to an infinite bus at $$1.0$$ $$p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power factor. Its synchronous reactance is $$1.0$$ $$pu$$ and resis...
A $$400$$ $$V,$$ $$50$$ $$Hz,$$ $$30$$ $$hp,$$ three-phase induction motor is drawing $$50$$ A current at $$0.8$$ power factor lagging. The stator and rotor copper losses are $$1.5...
A three phase fully controlled bridge converter is feeding a load drawing a constant and ripple free load current of $$10$$ $$A$$ at a firing angle of $${30^ \circ }.$$ The approxi...
A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space between the metal plates is filled with a glass plate of $$4$$ $...
An extra high voltage transmission line of length $$300$$ km can be approximate by a lossless line having propagation constant $$\beta = 0.00127$$ radians per km. then the percenta...
A $$240V$$ $$dc$$ shunt motor draws $$15A$$ while supplying the rated load at a speed of $$80$$ $$rad/s$$. The armature resistance is $$0.5$$ $$ohm$$ and the field winding resistan...
A $$3$$ - phase voltage source Inverter is operated in $${180^ \circ }$$ conduction mode. Which one of the following statements is true?
A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the system with cost curves $${C_1}$$ and $${C_2}$$ respectively defi...
Equation $${e^x} - 1 = 0\,\,$$ is required to be solved using Newton's method with an initial guess $$\,\,{x_0} = - 1.\,\,$$ Then after one step of Newton's method estimate $${x_1}...
The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is
Two point charges $${Q_1} = 10\,\,\mu C$$ and $${Q_2} = 20\,\,\mu C$$ are placed at coordinates $$(1,1,0)$$ and $$\left( { - 1, - 1,0} \right)$$ respectively. The total electric fl...
A $$240V$$ $$dc$$ shunt motor draws $$15A$$ while supplying the rated load at a speed of $$80$$ $$rad/s$$. The armature resistance is $$0.5$$ $$ohm$$ and the field winding resistan...
Let $$P$$ be $$2x2$$ real orthogonal matrix and $$\overline x $$ is a real vector $${\left[ {\matrix{ {{x_1}} & {{x_2}} \cr } } \right]^T}$$ with length $$\left| {\left| {\overline...
The transfer function of two compensators are given below: $${C_1} = {{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}},\,{C_2} = {{s + 10} \over {10\left( {s + 1} \right...
The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as $$\alpha \left( \lambda \right) = \left| {\lambda {\rm I} - P} \right| = {\lambda ^3} + 2\lambda...
In a stepper motor, the detent torque means
Distributed winding and short chording employed in AC machines will result in
A differential equation $${{dx} \over {dt}} = {e^{ - 2t}}\,\,u\left( t \right)\,\,$$ has to be solved using trapezoidal rule of integration with a step size $$h=0.01$$ sec. Functio...
The Thevenin's equivalent of a circuit operating at $$\omega = 5\,\,rad/s\,\,{V_{oc}} = 3.71\angle - {15.9^ \circ }$$ and $${Z_0} = 2.38 - j0.667\Omega .$$ At this frequency, the m...
A synchronous motor is connected to an infinite bus at $$1.0p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power factor. Its synchronous reactance is $$1.0$$ $$pu$$ and resistance...
If the rank of a $$5x6$$ matrix $$Q$$ is $$4$$ then which one of the following statements is correct?
The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}$$ The steady state value of the output of the system for a unit...
It is desired to measure parameters of $$230$$ $$V/115$$ $$V,$$ $$2$$ $$kVA$$, single-phase transformers. The following watt-meters are available in a laboratory: $${W_1}:250\,\,V,...
A $$400$$ $$V,$$ $$50$$ $$Hz$$, $$4$$ pole, $$1400$$ $$rpm$$, star connected squirrel cage induction motor has the following parameters referred to the stator: $$R = 1.0\,\Omega ,{...
A lossless transmission line having Surge Impedance Loading $$(SIL)$$ of $$2280$$ $$MW.$$ A Series capacitive compensation of $$30$$% is emplaced. Then $$SIL$$ of the compensated t...
Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...
A system with input $$x(t)$$ and output $$y(t)$$ is defined by the input $$-$$ output relation: $$y\left( t \right) = \int\limits_{ - \infty }^{ - 2t} {x\left( \tau \right)} d\tau...
The impulse response of a causal linear time-invariant system is given as $$h(t)$$. Now consider the following two statements: Statement-$$\left( {\rm I} \right)$$: Principle of su...
Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t 0 ) + x(t + t 0 ) for some t 0 . The Fourier Series coefficient of y(t) are denoted by b k . If b k =0 for all...
A function y(t) satisfies the following differential equation:$$$\frac{\operatorname dy\left(t\right)}{\operatorname dt}+\;y\left(t\right)\;=\;\delta\left(t\right)$$$ where $$\delt...
Given X(z)=$$\frac z{\left(z-a\right)^2}$$ with $$\left|z\right|$$ > a, the residue of X(z)z n-1 at z = a for n $$\geq$$ 0 will be
A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha $$ is a real constant $$\left( {\sin \,c\left( x \right) = {{\sin \left( {\pi x} \right)} \over {\pi...
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Given $$K$$ and $$\phi $$ are constants, the output of the syste...
The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}.$$ The steady state value of the output of this system for a un...
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Given $$K$$ and $$\phi $$ are constants, the output of the syste...
Two $$8$$ $$A$$ $$D$$ $$C$$ $$s$$ one of single slope integrating type and other of successive approximation type. Take $${T_A}$$ and $${T_B}$$ times to connect $$5V$$ analog input...