GATE 2012 Electrical Engineering Sample Paper with Solutions

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Question

The value of the quantity P, where $P = \int_{0}^1 \ xe^x \ dx$ , is equal to

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	0
	1
	e
	1/e

Question

Divergence of the three-dimensional radial vector field $\vec r$ is :

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Selected	Possible Answer
	3
	1/r
	$\hat i + \hat j + \hat k$
	$(\hat i + \hat j + \hat k)$

Question

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

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Selected	Possible Answer
	$0.4 \pi s$
	$0.8 \pi s$
	$1.25 \ s$
	$2.5\ s$

Question

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

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Selected	Possible Answer
	Linear and causal
	Linear but not causal
	Causal but not linear
	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 :

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	0 A
	1 A
	1.25 A
	5 A

Question

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

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	0
	1
	$2 / \pi$
	$\sqrt{5}$

Question

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

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	25 A
	50 A
	100 A
	200 A

Question

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

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	Zero always
	Total power consumed by $Z_1\ and\ Z_2$
	Power consumed by
	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

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Selected	Possible Answer
	$0.8 \Omega$ in series with the meter
	$1.0 \Omega$ in series with the meter
	$0.04 \Omega$ in parallel with the meter
	$0.05 \Omega$ 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 :

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Selected	Possible Answer
	10 $\pm$ 1 %
	10 $\pm$ 2 %
	10 $\pm$ 5 %
	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 :

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	1s
	2s
	4s
	8s

Question

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

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	A, B are resistances and C, D capacitances
	A, C are resistances and B, D capacitances
	A, B are capacitances and C, D resistances
	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 1 A, and the secondary current is 1 A. If core losses and leakage reactances are neglected, the primary current is :

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Selected	Possible Answer
	1.41 A
	2 A
	2.24 A
	3 A

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

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Selected	Possible Answer
	$V_{AB} < 0,\ V_{CD} < 0,V_{AB} > V_{CD}$
	$V_{AB} > 0,\ V_{CD} > 0,V_{AB} < V_{CD}$
	$V_{AB} > 0,\ V_{CD} > 0,V_{AB} > V_{CD}$
	$V_{AB} > 0,\ V_{CD} < 0,$

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

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

Question

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

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Selected	Possible Answer
	- 1 pu
	1 pu
	2 pu
	3 pu

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

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Selected	Possible Answer
	1000 W, 268 VAr
	- 1000 W, -134 VAr
	276.9 W, – 56.7 VAr
	276.9 W, 56.7 VAr

Question

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

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Selected	Possible Answer
	1200 A
	3600 A
	35 kA
	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 :

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	0.17875 A
	0.2A
	0.375A
	60 kA

Question

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

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Question

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

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	4 V
	6 V
	7.5 V
	12.12 V

Question

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

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Selected	Possible Answer
	4 V
	5 V
	7.5 V
	12.12 V

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

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Selected	Possible Answer
	step-down chopper (buck converter)
	half-wave rectifier
	step-up chopper (boost converter)
	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 :

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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 ?

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Selected	Possible Answer
	150 V
	210 V
	300 V
	100 $\pi$ V

Question

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

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	a minimum
	a discontinuity
	a point of inflection
	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 :

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Selected	Possible Answer
	1/3
	3/7
	1/2
	4/7

Question

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

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	$[-1\ 1\ 1]^T$
	$[1\ 2\ 1]^T$
	$[1\ - 1\ 2]^T$
	$[2\ 1\ - 1]^T$

Question

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

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Selected	Possible Answer
	$x (t) = 2e^{-6t} - e^{-2t}$
	$x (t) = 2e^{-2t} - e^{-4t}$
	$x (t) = - e^{-6t} + 2e^{-4t}$
	$x (t) = e^{-2t} + 2e^{-4t}$

Question

For the set of equations,

x_1 + 2x_2 + x_3 + 4x_4 = 2

3x_1 + 6x_2 + 3x_3 + 12x_4 = 6

The following statement is true

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	Only the trivial solution exists
	There are no solutions
	A unique non-trivial solution exists
	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 $\int_{- \infty}^\infty$ $|X (\omega)|^2 \ d\ \omega$ { where X $(\omega)$ is the Fourier transform of x(t) } is :

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Selected	Possible Answer
	2
	2 $\pi$
	4
	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 :

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Selected	Possible Answer
	$h[n] = \lbrace \overset{1}{\uparrow} ,$ $0 , 0, 1 \rbrace$
	$h[n] = \lbrace \overset{1}{\uparrow} ,$ $0 , 1 \rbrace$
	$h[n] = \lbrace \overset{1}{\uparrow} ,$ $1 , 1, 1 \rbrace$
	$h[n] = \lbrace \overset{1}{\uparrow} ,$ $1, 1 \rbrace$

Question

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

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Selected	Possible Answer
	$4 \Omega$
	$6 \Omega$
	$8 \Omega$
	$18 \Omega$

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 1W 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 :

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Selected	Possible Answer
	$\bigg[ \overset{z_{11}+1}{z_{21}}$ $\overset{z_{12}+1}{z_{22}+1} \bigg]$
	$\bigg[ \overset{z_{11}+1}{z_{21}}$ $\overset{z_{12}}{z_{22}+1} \bigg]$
	$\bigg[ \overset{z_{11}+1}{z_{21}}$ $\overset{z_{12}}{z_{22}} \bigg]$
	$\bigg[ \overset{z_{11}+1}{z_{21+1}}$ $\overset{z_{12}}{z_{22}} \bigg]$

Question

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

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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 :

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Question

The system x = Ax + Bu with $A = \bigg[ \overset{-1}{0}$ $\overset{2}{2} \bigg]$ , $B = \bigg[ \overset{0}{1} \bigg]$ is :

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	stable and controllable
	stable but uncontrollable
	unstable but controllable
	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 ?

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

Question

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, 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 ?

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	The magnitude of terminal voltage decreases, and the field current does not change
	The magnitude of terminal voltage increases, and the field current does not change
	The magnitude of terminal voltage increases, and the field current increases
	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-hase, 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,

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Selected	Possible Answer
	Both machines act as generators
	The dc machine acts as a generator, and the induction machine acts as a motor
	The dc machine acts as a motor, and the induction machine acts as a generator
	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 :

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

Question

Consider a three-phase, 50 Hz, 11 kV 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 are

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Selected	Possible Answer
	e1 = 3.74 kV, e2 = 2.61 kV
	e1 = 3.46 kV, e2 = 2.89 kV
	e1 = 6.0 kV, e2 = 4.23 kV
	e1 = 5.5 kV, e2 = 5.5 kV

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 line conductor and the sheath is $0.4 \mu F$ . The per-phase charging current is :

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Selected	Possible Answer
	2.0 A
	2.4 A
	2.7 A
	3.5 A

Question

For the power system shown in the figure below, the pecifications of the components are the following :

G1: 25 kV, 100 MVA, X = 9%

G2: 25 kV, 100 MVA, 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 :

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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_0 is :

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	4.65 V
	5 V
	6.3 V
	7.23 V

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 :

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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

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	(SP)incremented (PC) $\leftarrow$ Addr ((SP)) $\leftarrow$ (PC)
	(PC) $\leftarrow$ Addr ((SP)) $\leftarrow$ (PC) (SP)incremented
	(PC) $\leftarrow$ Addr (SP)incremented ((SP)) $\leftarrow$ (PC)
	((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
	$2 \Omega$
	$3.4 \Omega$
	$4.4 \Omega$
	$7.7 \Omega$

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
	125.5 V
	193.3 V
	200 V
	241.7 V

Question

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

g(t) can be expressed as

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Selected	Possible Answer

	$g(t) = f \bigg($ $\cfrac{t}{2} - 3 \bigg)$
	$g(t) = f \bigg($ $2t - \cfrac{3}{2} \bigg)$
	$g(t) = f \bigg($ $\cfrac{t}{2} - \cfrac{3}{2} \bigg)$

Question

The Laplace transform of g(t) is :

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{s}\ (e^{3s} - e^{5s})$
	$\cfrac{1}{s}\ (e^{-5s} - e^{-3s})$
	$\cfrac{e^{-3s}}{s}\ (1 - e^{-2s})$
	$\cfrac{1}{s}\ (e^{5s} - e^{3s})$

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
	$F = \overline{X}Y +YZ$
	$F = \overline{X}\ \overline{Y} +YZ$
	$F = \overline{X}\ \overline{Y}$ $+ \overline{Y}\ \overline{Z}$
	$F = \overline{X}\ \overline{Y}$ $+ \overline{Y} Z$

Question

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

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Question

Directions for next two questions: The L-C circuit shown in the figure has an inductance L = 1 mH 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
	$5\ cos(5\ x\ 10^3\ t)\ A$
	$5\ sin(10^4\ t)\ A$
	$10\ cos(5 \ x\ 10^3\ t)\ A$
	$10\ sin(10^4\ t)\ A$

Question

The L-C circuit of Q.54 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 Q54. 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
	$52 \mu s$
	$156 \mu s$
	$312 \mu s$
	$26 \mu s$

Question

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
	2
	17
	13
	3

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
	uphold
	restrain
	cherish
	conserve

Question

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

Unemployed : Worker

Possible Answers

Selected	Possible Answer
	fallow : land
	unaware : sleeper
	wit : jester
	renovated : house

Question

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

Circuitous

Possible Answers

Selected	Possible Answer
	cyclic
	indirect
	confusing
	crooked

Question

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

His rather causal remarks on politics ________ his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	masked
	belied
	betrayed
	suppressed

Question

Hari (H), Gita (G), Irfan (I) and Saira (S) are sibiligs (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 than3 years. Given the following facts :

i. Hair’s age + Gita’s age > Irfan’s age + Saira’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 not twins.

In what order were they born (oldest first) ?

Possible Answers

Selected	Possible Answer
	HSIG
	SGHI
	IGSH
	IHSG

Question

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

Possible Answers

Selected	Possible Answer
	20 days
	18 days
	16 days
	15 days

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
	Modern warfare has resulted in civil strife.
	Chemical agents are useful in modern warfare.
	Use of chemical agents in warfare would be undesirable.
	Use of chemical agents in warfare would be undesirable.

Question

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

Possible Answers

Selected	Possible Answer
	50
	51
	52
	54

Question

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

Possible Answers

Selected	Possible Answer
	534
	1403
	1623
	1513

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GATE 2012 Electrical Engineering Sample Paper with Solutions

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