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GATE Paper 2011 Electrical Engineering

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Question

The value of the quantity P, where $P = \overset{1}{\underset{0}{\int}} xe^xdx,$ is equal to

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. e
	D. 1/e

Question

Divergence of the three-dimensional radial vector field $\overset{-}{r}$ is

Possible Answers

Selected	Possible Answer
	A. 3
	B. 1/r
	C. $\hat{i} + \hat{j} + \hat{k}$
	D. $3 \Big(\hat{i} + \hat{j} + \hat{k}\Big)$

Question

The period of the signal $x(t) = 8\sin \Bigg(0.8\pi t + \cfrac{\pi}{4}\Bigg)$ is

Possible Answers

Selected	Possible Answer
	A. $0.4\pi s$
	B. $0.8\pi s$
	C. 1.25s
	D. 2.5s

Question

The system represented by the input-output relationship $y(t) = \overset{5t}{\underset{-\infty}{\int}} x (\tau) d\tau, t > 0$ is

Possible Answers

Selected	Possible Answer
	A. Linear and causal
	B. Linear but not causal
	C. Causal but not linear
	D. Neither linear nor causal

Question

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 $1\mu F$ capacitor is

Possible Answers

Selected	Possible Answer
	A. 0A
	B. 1A
	C. 1.25A
	D. 5A

Question

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

Possible Answers

Selected	Possible Answer
	A. 0
	B. 1
	C. $2 / \pi$
	D. $\sqrt{5}$

Question

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

Possible Answers

Selected	Possible Answer
	A. 25A
	B. 50A
	C. 100A
	D. 200A

Question

A wattmeter is connected as shown in the figure. The wattmeter reads

Possible Answers

Selected	Possible Answer
	A. Zero always
	B. Total power consumed by $Z_1\ and\ Z_2$
	C. Power consumed by
	D. Power consumed by

Question

An ammeter has a current range of 0 – 5 A, 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

Possible Answers

Selected	Possible Answer
	A. $0.8 \Omega$ in series with the meter
	B. $1.0 \Omega$ in series with the meter
	C. $0.04 \Omega$ in parallel with the meter
	D. $0.05 \Omega$ in parallel with the meter

Question

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:

Possible Answers

Selected	Possible Answer
	A. 10 $\pm$ 1%
	B. 10 $\pm$ 2%
	C. 10 $\pm$ 5%
	D. 10 $\pm$ 10%

Question

For the system $2/_{(S+1)},$ the approximate time taken for a step response to reach 98% of its final value is

Possible Answers

Selected	Possible Answer
	A. 1s
	B. 2s
	C. 4s
	D. 8s

Question

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

Possible Answers

Selected	Possible Answer
	A. A, B are resistances and C, D capacitances
	B. A, C are resistances and B, D capacitances
	C. A, B are capacitances and C, D resistances
	D. A, C are capacitances and B, D resistances

Question

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 1A, and the secondary current is 1A. If core losses and leakage reactanceâ€™s are neglected, the primary current is

Possible Answers

Selected	Possible Answer
	A. 1.41A
	B. 2A
	C. 2.24A
	D. 3A

Question

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

Possible Answers

Selected	Possible Answer
	A. $V_{AB}<0, V_{CD}<0, V_{AB}>V_{CD}$
	B. $V_{AB}>0, V_{CD}>0, V_{AB}>V_{CD}$
	C. $V_{AB}>0, V_{CD}>0, V_{AB}<V_{CD}$
	D. $V_{AB}>0, V_{CD}<0$

Question

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 $r_s,r_r,x_s,x_r\ and\ X_m$ respectively. The magnitude of the starting current of the motor is given by

Possible Answers

Selected	Possible Answer
	A. $\cfrac{V}{\sqrt{(r_s + r_r)^{^2} + (x_s + x_r)^{^2}}}$
	B. $\cfrac{V}{\sqrt{r_s{}^{^2} + (x_s + X_m)^{^2}}}$
	C. $\cfrac{V}{\sqrt{(r_s + r_r)^{^2} + (X_m + x_r)^{^2}}}$
	D. $\cfrac{V}{\sqrt{r_s{}^{^2} + (X_m + x_r)^{^2}}}$

Question

Consider a step voltage wave of magnitude 1pu travelling along a loss less transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is

Possible Answers

Selected	Possible Answer
	A. -1pu
	B. 1pu
	C. 2pu
	D. 3pu

Question

Consider two buses connected by an impedance of $(0+j5)\Omega.$ 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

Possible Answers

Selected	Possible Answer
	A. 1000W, 268VAr
	B. -1000W, -134Var
	C. 276.9W, -56.7Var
	D. -276.9W, 56.7Var

Question

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

Possible Answers

Selected	Possible Answer
	A. 1200 A
	B. 3600 A
	C. 35 kA
	D. 104.8 kA

Question

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

Possible Answers

Selected	Possible Answer
	A. 0.17875 A
	B. 0.2A
	C. 0.375A
	D. 60 kA

Question

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

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

Given that the op-amp is ideal, the output voltage V_0 is

Possible Answers

Selected	Possible Answer
	A. 4V
	B. 6V
	C. 7.5V
	D. 12.12V

Question

Assuming that the diodes in the given circuit are ideal, the voltage V_0 is

Possible Answers

Selected	Possible Answer
	A. 4V
	B. 5V
	C. 7.5V
	D. 12.12V

Question

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

Possible Answers

Selected	Possible Answer
	A. step-down chopper (buck converter)
	B. half-wave rectifier
	C. step-up chopper (boost converter)
	D. full-wave rectifier

Question

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

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

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 300 V. What will be the output voltage for a firing angle of $60^{^{\circ}},$ assuming continuous conduction?

Possible Answers

Selected	Possible Answer
	A. 150V
	B. 210V
	C. 300V
	D. 100 $\pi$ V

Question

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

Possible Answers

Selected	Possible Answer
	A. a minimum
	B. a discontinuity
	C. a point of inflection
	D. a maximum

Question

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

Possible Answers

Selected	Possible Answer
	A. 1/3
	B. 3/7
	C. 1/2
	D. 4/7

Question

An eigenvector of $P = \Bigg(\overset{1}{\underset{0}{0}}\ \overset{1}{\underset{0}{2}}\ \overset{0}{\underset{3}{2}}\Bigg)$ is

Possible Answers

Selected	Possible Answer
	A. $\big[-111\big]^T$
	B. $\big[121\big]^T$
	C. $\big[1-12\big]^T$
	D. $\big[21-1\big]^T$

Question

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

Possible Answers

Selected	Possible Answer
	A. $x(t) = 2e^{-6t} - e^{-2t}$
	B. $x(t) = 2e^{-2t} - e^{-4t}$
	C. $x(t) = -e^{-6t} + 2e^{-4t}$
	D. $x(t) = e^{-2t} + 2e^{-4t}$

Question

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

Possible Answers

Selected	Possible Answer
	A. Only the trivial solution exists
	B. There are no solutions
	C. A unique non-trivial solution exists
	D. Multiple non-trivial solutions exist

Question

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

Possible Answers

Selected	Possible Answer
	A. 2
	B. 2 $\pi$
	C. 4
	D. 4 $\pi$

Question

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

Possible Answers

Selected	Possible Answer
	A. $\underset{\uparrow}{h[n] = \{1,0,0,1\}}$
	B. $\underset{\uparrow}{h[n] = \{1,0,1\}}$
	C. $\underset{\uparrow}{h[n] = \{1,1,1,1\}}$
	D. $\underset{\uparrow}{h[n] = \{1,1,1\}}$

Question

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

Possible Answers

Selected	Possible Answer
	A. $4\Omega$
	B. $6\Omega$
	C. $8\Omega$
	D. $18\Omega$

Question

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 $z_{ij}. A\ 1\Omega$ 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

Possible Answers

Selected	Possible Answer
	A. $\bigg({}^{Z_{11} + 1}_{Z_{21}$ ${}^{Z_{12} + 1}_{Z_{22} + 1}\bigg)$
	B. $\bigg({}^{Z_{11} + 1}_{Z_{21}$ ${}^{Z_{12}}_{Z_{22} + 1}\bigg)$
	C. $\bigg({}^{Z_{11} + 1}_{Z_{21}$ ${}^{Z_{12}}_{Z_{22}}\bigg)$
	D. $\bigg({}^{Z_{11} + 1}_{Z_{21 + 1}$ ${}^{Z_{12}}_{Z_{22}}\bigg)$

Question

The Maxwell’s bridge shown in the figure is at balance. The parameters of the inductive coil are

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

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

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

The system x = Ax + Bu with $A = \Big[{}^{-1}_0\ {}^2_2\Big], B = \Big[{}^0_1\Big]\ is$

Possible Answers

Selected	Possible Answer
	A. stable and controllable
	B. stable but uncontrollable
	C. unstable but controllable
	D. unstable and uncontrollable

Question

The characteristic equation of a closed-loop system is s(s+1)(s+3)+k(s+2)=0, k>0. Which of the following statements is true?

Possible Answers

Selected	Possible Answer
	A. Its roots are always real
	B. It cannot have a breakaway point in the range -1 < Re [s] < 0
	C. Two of its roots tend to infinity along the asymptotes Re [s] = -1
	D. It may have complex roots in the right half plane

Question

A 50 Hz synchronous generator is initially connected to a long loss less transmission line which is open circuited at the receiving end. With the f i e l d 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?

Possible Answers

Selected	Possible Answer
	A. The magnitude of terminal voltage decreases, and the field current does not change
	B. The magnitude of terminal voltage increases, and the field current does not change
	C. The magnitude of terminal voltage increases, and the field current increases
	D. The magnitude of terminal voltage does not change, and the field current decreases

Question

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,

Possible Answers

Selected	Possible Answer
	A. Both machines act as generators
	B. The dc machine acts as a generator, and the induction machine acts as a motor
	C. The dc machine acts as a motor, and the induction machine acts as a generator
	D. Both machines act as motors

Question

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 110V/220V. 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

Possible Answers

Selected	Possible Answer
	A. $(3 + j0) \Omega$
	B. $(0.866 - j0.5) \Omega$
	C. $(0.866 + j0.5) \Omega$
	D. $(1 + j0) \Omega$

Question

Consider a three-phase, 50Hz, 11kV 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 and the ground, as shown in the figure. The voltage across the two insulators is

Possible Answers

Selected	Possible Answer
	A. e1=3.74kV, e2=2.61kV
	B. e1=3.46kV, e2=2.89kV
	C. e1=6.0kV, e2=4.23kV
	D. e1=5.5kV, e2=5.5kV

Question

Consider a three-core, three-phase, 50Hz, 11kV cable whose conductors are denoted as R, Y and B in the figure. The inter-phase capacitance (C1) between each pair of conductors is $0.2\mu F$ and the capacitance between each l ine conductor and the sheath is $0.4\mu F.$ The per-phase charging current is

Possible Answers

Selected	Possible Answer
	A. 2.0A
	B. 2.4A
	C. 2.7A
	D. 3.5A

Question

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, 100MVA, X=9%
T1: 25 kV/220 kV, 90 MVA, X=12%
T2: 220kV/ 25 kV, 90 MVA, X=12%
Line1: 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

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

The transistor circuit shown uses a silicon transistor with $V_{BE} = 0.7V, I_C \approx I_E$ and a dc current gain of 100. The value of V_O is

Possible Answers

Selected	Possible Answer
	A. 4.65A
	B. 5V
	C. 6.3V
	D. 7.23V

Question

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

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

When a “CALL Addr” instruction is executed, the CPU carries out the following sequential operations internally:
Note: (R) means content of register R
((R)) means content of memory location pointed to by R
PC means Program Counter
SP means Stack Pointer

Possible Answers

Selected	Possible Answer
	A. (SP) incremented (PC) $\leftarrow$ Addr ((SP)) $\leftarrow$ (PC)
	B. (PC) $\leftarrow$ Addr ((SP)) $\leftarrow$ (PC) (SP) incremented
	C. (PC) $\leftarrow$ Addr (SP) incremented ((SP)) $\leftarrow$ (PC)
	D. ((SP)) $\leftarrow$ (PC) (SP) incremented (PC) $\leftarrow$ Addr

Question

Directions for next two questions:
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,

Possible Answers

Selected	Possible Answer
	A. $2\Omega$
	B. $3.4\Omega$
	C. $4.4\Omega$
	D. $7.7\Omega$

Question

For the motor to deliver a torque of 2.5 Nm at 1400 rpm the armature voltage to be applied is

Possible Answers

Selected	Possible Answer
	A. 125.5V
	B. 193.3V
	C. 200V
	D. 241.7V

Question

Directions for next two questions:
Given f(t) and g(t)as shown below:

g(t)can be expressed as

Possible Answers

Selected	Possible Answer
	A.
	B. $g(t) = f \bigg(\cfrac{t}{2} - 3\bigg)$
	C. $g(t) = f \bigg(2t - \cfrac{3}{2}\bigg)$
	D. $g(t) = f \bigg(\cfrac{t}{2} - \cfrac{3}{2}\bigg)$

Question

The Laplace transform of g(t) is

Possible Answers

Selected	Possible Answer
	A. $\cfrac{1}{s}\ (e^{3s} - e^{5s})$
	B. $\cfrac{1}{s}\ (e^{-5s} - e^{-3s})$
	C. $\cfrac{e^{-3s}}{s}\ (1 - e^{-2s})$
	D. $\cfrac{1}{s}\ (e^{5s} - e^{3s})$

Question

Directions for next two questions: The following Karnaugh map represents a function F.

A minimized form of the function F is

Possible Answers

Selected	Possible Answer
	A. $F = \overset{-}{X}Y + YZ$
	B. $F = \overset{-}{X}\overset{-}{Y} + YZ$
	C. $F = \overset{-}{X}\overset{-}{Y} + Y\overset{-}{Z}$
	D. $F = \overset{-}{X}\overset{-}{Y} + \overset{-}{Y}Z$

Question

Which of the following circuits is a realization of the above function F?

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.

Question

Directions for next two questions: 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:

Possible Answers

Selected	Possible Answer
	A. $5 \cos (5 \times 10^3t) A$
	B. $5 \sin (10^4t) A$
	C. $10 \cos (5 \times 10^3t) A$
	D. $10 \sin (10^4t) A$

Question

The L-C circuit of last question 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 last question. The switch is closed at t = 0. If the forward drop is negligible, the time taken for the device to turn off is

Possible Answers

Selected	Possible Answer
	A. $52\mu s$
	B. $156\mu s$
	C. $312\mu s$
	D. $26\mu s$

Question

Directions for next five questions: General Aptitude (GA) Questions Carry One Mark Each

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is

Possible Answers

Selected	Possible Answer
	A. 2
	B. 17
	C. 13
	D. 3

Question

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker

Possible Answers

Selected	Possible Answer
	A. fallow: land
	B. unaware: sleeper
	C. wit: jester
	D. renovated: house

Question

Choose the most appropriate word from the options given below to complete the following sentence

If we manage to …................ our natural resources, we would leave a better planet for our children.

Possible Answers

Selected	Possible Answer
	A. uphold
	B. restrain
	C. cherish
	D. conserve

Question

Which of the following options is closest in meaning to the word: Circuitous?

Possible Answers

Selected	Possible Answer
	A. cyclic
	B. indirect
	C. confusing
	D. crooked

Question

Choose the most appropriate word from the options given below to the complete the following sentence:
His rather casual remarks on politics …................. his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	A. masked
	B. belied
	C. betrayed
	D. suppressed

Question

Directions for next five questions: Carry Two Mark Each

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:

i. Hariâ€™s age + Gitaâ€™s age > Irfanâ€™s age + Sairaâ€™s age
ii. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.

In what order were they born (oldest first)?

Possible Answers

Selected	Possible Answer
	A. HSIG
	B. SGHI
	C. IGSH
	D. IHSG

Question

5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Possible Answers

Selected	Possible Answer
	A. 20
	B. 18
	C. 16
	D. 15

Question

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.
Which of the following statements best sums up the meaning of the above passage:

Possible Answers

Selected	Possible Answer
	A. Modern warfare has resulted in civil strife.
	B. Chemical agents are useful in modern warfare.
	C. Use of chemical agents in warfare would be undesirable
	D. People in military establishments like to use chemical agents in war.

Question

Given digits 2, 2, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

Possible Answers

Selected	Possible Answer
	A. 50
	B. 51
	C. 52
	D. 54

Question

If 137+276=435 how much is 731+672?

Possible Answers

Selected	Possible Answer
	A. 534
	B. 1403
	C. 1623
	D. 1513

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GATE Paper 2011 Electrical Engineering

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