EC Forenoon 31st January Updated

All MADE EASY students (Current Session or Previous sessions) enrolled

in Classroom Course, Postal Course, Online Test Series, Offline Test Series,

Interview Guidance are requested to inform their GATE result to MADE EASY

office, after result announcement.

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Distribution soon after the result announcement.

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AttentionMADe eASY GAte 2015 ASpirAntS

GATE-2015

Answer Key ofElectronics Engineering

Forenoon Session 31st Jan, 2015

Corporate Office: 44-A/1, Kalu Sarai, New Delhi-16 | Email : [email protected] | Visit: www.madeeasy.in

GATE-2015 | Electronics Engg.31st January 2015 Forenoon Session

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Page1

Section - I (General Aptitude)

Q.1 Choose the appropriate word/phrase, out of the four options given below, tocomplete the following sentence :Frogs ______________(a) croak (b) roar(c) hiss (d) patter

Ans. (a)

Q.2 If logx (5/7) = 1/3, then the value of x is(a) 343/125 (b) 125/343(c) 25/49 (d) 49/25

Ans. (a)

Q.3 Operates , and are defined by: =+

;a ba ba b

+= =

; .a ba b a b aba b

Find the value of ( ) 66 6 (66 6)(a) 2 (b) 1(c) 1 (d) 2

Ans. (c)

Q.4 Choose the word most similar meaning to the given word:Educe(a) Exert (b) Educate(c) Extract (d) Extend

Ans. (c)

Q.5 Choose the most appropriate word from the options given below to complete thefollowing sentence.

The principal presented the chief guest with a ___________, as token of appreciation.(a) momento (b) memento(c) momentum (d) moment

Ans. (b)



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Q.6 The following question presents a sentence, part of which is underlined. Beneaththe sentence you find four ways of phrasing the underlined part. Following therequirements of the standard written English, select the answer that producesthe most effective sentence.Tuberculosis, together with its effects, ranks one of the leading causes of death in India.(a) ranks as one of the leading causes of death(b) rank as one of the leading causes of death(c) has the rank of one of the leading causes of death(d) are one of the leading causes of death

Ans. (a)

Q.7 Humpty Dumpty sits on a wall every day while having lunch. The wall sometimesbreaks. A person sitting on the wall falls if the wall breaks.Which one of the statements below is logically valid and can be inferred fromthe above sentences?(a) Humpty Dumpty always falls white having lunch(b) Humpty Dumpty does not fall sometimes while having lunch(c) Humpty Dumpty never falls during dinner(d) When Humpty Dumpty does not sit on the wall, the wall does not break

Ans. (b)

Q.8 A cube side 3 units is formed using a set of smaller cubes of side 1 unit. Findthe proportion of the number of faces of the smaller cubes visible to those whichare NOT visible.(a) 1 : 4 (b) 1 : 3(c) 1 : 2 (d) 2 : 3

Ans. (c)

Q.9 Fill in the missing value

1 9 2 8 1 2 1

7 4 7 2 1

4 1 5 2 3

3 3

6 45

Ans. (3)



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Q.10 Read the following paragraph and choose the correct statement.Climate change has reduced human security and threatened human well being.An ignored reality of human progress is that human security largely depends uponenvironmental security. But on the contrary, human progress seems contradictoryto environmental security. To keep up both at the required level is a challengeto be addressed by one and all. One of the ways to curb the climate change maybe suitable scientific innovations, while the other may be the Gandhian perspectiveon small scale progress with focus on sustainability.(a) Human progress and security are positively associated with environmental security.(b) Human progress is contradictory to environmental security.(c) Human security is contradictory to environmental security.(d) Human progress depends upon environmental security.

Ans. (b)

Section - II (Electronics and Communication Engineering)

Q.1 A silicon sample is uniformly doped with donor type impurities with a concentrationof 1016/cm3. The electron and hole mobilities in the sample are 1200 cm2/V-s and400 cm2/V-s respectively. Assume complete ionization of impurities. The chargeof an electron is 1.6 1019 C. The resistivity of the sample (in -cm) is________.

Ans. (0.520)

Q.2 Negative feedback in a closed-loop control system DOES NOT(a) reduce the overall gain(b) reduce bandwidth(c) improve disturbance rejection(d) reduce sensitivity to parameter variation

Ans. (b)

Q.3 In the network shown in the figure, all resistors are identical with R = 300 .The resistance Rab (in ) of the network is ______________.

a

b

Rab

R

R R

R

R RR R R

R

RR

R R R

R = 300

Ans. (100)

AIR Car or Equivalent Amount11

22AIR Rs. 2.5 Lacs AIR 33 Rs. 1 Lac

Announces

AIR 4-5 Rs. 25,000

Note: Those candidates whose name/photo appears in other institute will not be eligible for these award.

These awards will be given only to MADE EASY Current/Previous year students enrolled in Classroom/ Postal/ Online test/ Interview Guidance).

AIR 6-10 Rs. 10,000

www.madeeasy.in

Meritorious Awards

For its & GATE-2015 ESE-2014

Selected Candidates



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Q.4 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (inVolts) across the capacitor is ____________.

1 F100 cos (V)t

4 0.1 mH

+

Ans. (25)

Q.5 Suppose A and B are two independent events with probabilities P(A) 0 andP(B) 0. Let A and B be their complements. Which one of the followingstatements is FALSE?(a) P(A B) = P(A) P(B) (b) P(A/B) = P(A)(c) P(A B) = P(A) + P(B) (d) =( ) ( ) ( )P A B P A P B

Ans. (c)

Q.6 In the circuit shown, the switch SW is thrown from position A to position B attime t = 0. The energy (in J) taken from the 3 V source to charge the 0.1 Fcapacitor form 0 V to 3 V is(a) 0.3 3 V 120 B ASW

0.1 F

t = 0(b) 0.45(c) 0.9(d) 3

Ans. (c)

Q.7 Let z = x + iy be a complex variable. Consider that contour integration is performedalong the unit circle in anticlockwise direction. Which one of the followingstatements is NOT TRUE?

(a) The residue of

2 1z

z at z = 1 is 1/2

(b) = 2 0C z dz(c) =

1 1 12 C dzi z(d) z (complex conjugate of z) is analytical function

Ans. (d)



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Q.8 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents thedependence of H on r, where H is the magnitude of the azimuthal componentof magnetic field outside the conductor and r is the radial distance from theconductor?

(a)

H

r(a)

(b)

H

r(b)

(c)

H

r(c)

(d)

H

r(d)

Ans. (c)

Q.9 The waveform of aperiodic signal x(t) is shown in the figure.

4 1 2 32 1 4

3

x( )t

3

t

A signal g(t) is defined by g(t) = x 1 .

2t The average power of g(t) is ___________.

Ans. (6)

Q.10 Consider a system of linear equations : x 2y + 3z = 1,

x 3y + 4z = 1, and2x + 4y 6z = k

The value of k for which the system has infinitely many solution is _________.

Ans. (2)



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Q.11 A function f(x) = 1 x2 + x3 is defined in the closed interval [1, 1]. The valueof x, in the open interval (1, 1) for which the mean value theorem is satisfied,is(a) 1/2 (b) 1/3(c) 1/3 (d) 1/2

Ans. (b)

Q.12 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. Thesampling rate and step-size of the delta modulator are 20,000 samples per secondand 0.1 V, respectively. To prevent slope overload, the maximum amplitude ofthe sinusoidal signal (in Volts) is

(a)

12 (b)

1

(c)

2 (d)

Ans. (a)

Q.13 The electric field component of a plane wave travelling in a lossless dielectric

medium is given by = 8( , ) 2cos 10 2yzE z t a t

V/m. The wavelength (in m) for

the wave is___________.

Ans. (8.89)

Q.14 In the given circuit, the values of V1 and V2 respectively are

V2+

5 A 4 4

4

I

+

V12I

(a) 5 V, 25 V (b) 10 V, 30 V(c) 15 V, 35 V (d) 0 V, 20 V

Ans. (a)



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Q.15 Consider a four bit D to A converter. The analog value corresponding to a digitalsignals of values 0000 and 0001 are 0 V and 0.0625 V respectively. The analogvalue (in Volts) corresponding to the digital signal 1111 is ____________.

Ans. (0.9375)

Q.16 In an 8085 microprocessor, the shift registers which store the result of an additionand the overflow bit are, respectively(a) B and F (b) A and F(c) H and F (d) A and C

Ans. (b)

Q.17 A region of negative differential resistance is observed in the current voltagecharacteristics of a silicon PN junction if(a) both the P-region and the N-region are heavily doped(b) the N-region is heavily doped compared to the P-region(c) the P-region is heavily doped compared to the N-region(d) an intrinsic silicon region is inserted between the P-region and the N-region

Ans. (a)

Q.18 Consider the signal s(t) = m(t) cos (2 fct) + m (t) sin(2 fct) where m (t) denotesthe Hilber transform of m(t) and the bandwidth of m(t) is very small comparedto fc. The signal s(t) is a(a) high-pass signal(b) low-pass signal(c) band-pass signal(d) double sideband suppressed carrier signal

Ans. (c)

Q.19 The polar plot of the transfer function +=+

10( 1)( )10

sG ss

for < will be in the

(a) first quadrant (b) second quadrant(c) third quadrant (d) fourth quadrant

Ans. (a)



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Q.20 The result of the convolution x(t) * (t t0) is(a) x(t + t0) (b) x(t t0)(c) x(t + t0) (d) x(t t0)

Ans. (d)

Q.21 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratioof one (number of rows is equal to the number of columns). The minimum numberof address lines needed for the row decoder is ____________.

Ans. (7)

Q.22 For the circuit with ideal diodes shown in the figure, the shape of the output (vout)for the given sine wave input (vin) will be

+

vout

+

vin0 0.5 T

T

(a) 0 0.5 TT (b) 0 0.5 T T

(c)0

0.5 TT

(d)0 0.5 T

T

Ans. (c)

Q.23 The value of p such that the vector

123

is an eigenvector of the matrix

4 1 22 1

14 4 10p

is

Ans. (17)



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Q.24 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6V. The output voltage V0 (in volts) is____________.

10 V

1 k

1 k+

V0

Ans. (5)

Q.25 A unity negative feedback system has the open-loop transfer function

=

+ +( ) .

( 1) ( 3)KG s

s s s The value of the gain K (>0) at which the root locus crosses

the imaginary axis is ___________.

Ans. (12)

Q.26 For the NMOSFET in the circuit shown, the threshold voltage is Vth, where Vth> 0. The source voltage VSS is varied from 0 to VDD. Neglecting the channel lengthmodulation, the drain current ID as a function of VSS is represented by

Vss

VDD

(a)

ID

VssV VDD Th

(b)

ID

VssVTh

(c)

ID

VssV VDD Th

(d)

ID

VssV VDD Th

Ans. (a)



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Q.27 The longitudinal component of the magnetic field inside an air-filled rectangularwaveguide made of a perfect electric conductor is given by the following expression

Hz (x, y, z, t) = 0.1 cos(25x) cos(30.3 y) cos(12 109 t z) (A/m)(a) TM12 (b) TM21(c) TE21 (d) TE12

Ans. (c)

Q.28 The input X to Binary Symmetric Channel (BSC) shown in the figure is 1 withprobability of 0.8. The cross-over probability is 1/7. If the received bit Y = 0, theconditional probability that 1 was transmitted is ____________.

6/7

6/7

1/71/7

1 1

X0

Y0

P X[ = 0] = 0.2

P X[ = 1] = 0.8

Ans. (0.4)

Q.29 The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 usersshare a common bandwidth using TDMA. If at a given time 12 users are talkingin a cell, the total bandwidth of the signal received by the base station of thecell will be at least (in kHz)___________.

Ans. (*)

Q.30 A lead compensator network includes a parallel combination of R and C in the

feed-forward path. If the transfer function of the compensator is +=+

2( ) ,4c

sG ss

the value of RC is____________.

Ans. (0.5)



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Q.31 Consider a uniform plane wave with amplitude (E0) of 10 V/m and 1.1 GHzfrequency travelling an air, and incident normally on a dielectric medium withcomplex relative permittivity (r) and permeability (r) as shown in the figure.

E0 = 10 V/mFreq. = 1.1 GHz

Dielectric

r = 1 2j

r = 1 2j

E = ?10 cm

Air = 120

The magnitude of the transmitted electric field component (in V/m) after it hastravelled a distance of 10 cm inside the dielectric region is____________.

Ans. (0.1)

Q.32 For a silicon diode with long P and N regions, the accepter and done impurityconcentrations are 1 1017 cm3 and 1 1015 cm3, respectively. The lifetimesof electrons in P region and holes in N region are both 100 s. The electron andhole diffusion coefficients are 49 cm2/s and 36 cm2/s, respectively. AssumekT/q = 26 mV, the intrinsic carrier concentration is 1 1010 cm3, andq = 1.6 1019 C. When a forward voltage of 208 mV is applied across the diode,the hole current density (in nA/cm2) injected from P region to N region is _______.

Ans. (286.17)

Q.33 A plant transfer function is given as = + +1( ) .

( 2)I

PKG s Ks s s

When the plant

operates in a unity feedback configuration, the condition for the stability of theclosed loop system is

(a) > > 02

IP

KK (b) 2KI > KP > 0

(c) 2KI < KP (d) 2KI > KPAns. (a)



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Q.34 Which one of the following graphs describes the function f(x) = ex(x2 + x + 1)?

(a)

f ( )x

x

(b)

f ( )x

x

(c)

f ( )x

x

(d)

f ( )x

x

Ans. (b)

Q.35 A 3-input majority gate is defined by the logic function M(a, b, c) = ab + bc +ca. Which one of the following gate is represented by the function

( ( , , ), ( , , ) )?M M a b c M a b c c(a) 3-input NAND gate (b) 3-input XOR gate(c) 3-input NOR gate (d) 3-input XNOR gate

Ans. (b)

Q.36 In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth WHz. The frequency response of the band-pass filter H(f) is shown in Figure (b).If it is desired that the output signal z(t) = 10 x(t), the maximum value of W (in Hz)should be strictly less than ____________.

1700 700 0 700 1700 f (Hz)

H f( )

Amplifiery t t t( ) = 10 ( ) + ( )x x

2 H f( )Band-pass

filter

z t( )x( ) = m( ) cos(2400 )t t t

Fig. (a)

Fig. (b)

Ans. (350)



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Q.37 A MOSFET in saturation has a drain current of 1 mA for VDS = 0.5 V. If thechannel length modulation coefficient is 0.05 V1, the output resistance (in k)of the MOSFET is ____________

Ans. (20)

Q.38 For the discrete-time system shown in the figure, the poles of the system transferfunction are located at(a) 2, 3

+ +x[ ]n y[ ]n

16

56

Z1

Z1

(b) 1 ,32

(c) 1 1,2 3

(d) 12,3

Ans. (c)

Q.39 A vector P is given by = 3 2 2 2x y zP x ya x y a x yz a

Which of the followingstatements is TRUE?(a)

P is solenoidal, but not irrotational

(b)P is irrotational, but not solensoidal

(c)P is neither solenoidal nor irrotational

(d)P is both solenoidal and irrotational

Ans. (a)

Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltageV0 (in mV) for = 0.05 is ____________.

250 (1 )

250 (1 + )

250 (1 + )

250 (1 )

V0 +

100

100

+

50

Ans. (250)



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Q.41 The circuit shown in the figure has an ideal opamp. The oscillation frequencyand the condition to sustain the oscillations, respectively, are

+

R2CC 2R

Vo

R2

R1

(a) 1CR and R1 = R2 (b)1

CR and R1 = 4R2

(c) 12CR and R1 = R2 (d)1

2CR and R1 = 4R2

Ans. (d)

Q.42 In the circuit shown, I1 = 80 mA and I2 = 4 mA. Transistors T1 and T2 areidentical. Assume that the thermal voltage VT is 26 mV at 27 C. At 50 C, thevalue of voltage V12 = V1 V2 (in mV) is

I2 I1

Vs

V2 V1V12

T2 T1

Ans. (83.15)

Q.43 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance(CJ) at a reverse bias (VR) of 1.25 V is 5 pF, the value of CJ (in pF) when VR = 7.25 Vis_______.

Ans. (2.5)



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Q.44 The electric field intensity of a plane wave traveling in free space is given by thefollowing expression

E(x, t) = ay 24 cos(t k0x) (V/m)In this field, consider a square area 10 cm 10 cm on a plane x + y = 1. Thetotal time-averaged power (in mW) passing through the square area is___________.

Ans. (53.29)

Q.45 The open-loop transfer function of a unity feedback configuration is given as

+=

+ 2( 4)( ) .

( 8)( 9)K sG s

s s The value of a gain K(>0) for which 1+ j2 lies on the root

locus is __________.

Ans. (25.54)

Q.46 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions,the value of vc(t) (in Volts) at t = 1 sec is ______________.

t = 0 3

+

v tC( )10 V

SW

2 56 F

Ans. (2.528)

Q.47 The solution of the differential equation + + =2

2 2 0d y dy y

dtdt with y(0) = y(0) = 1 is

(a) (2 t)et (b) (1 + 2t)et(c) (2 + t)et (d) (1 2t)et

Ans. (b)

Q.48 The maximum area (in square unit) of a rectangle whose vertices lies on the ellipsex2 + 4y2 = 1 is_______

Ans. (4)



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Q.49 The Boolean expression F(X, T, Z) = XYZ+XYZ+XYZ+XYZ converted into canonicalproduct of sum (POS) form is(a) (X+Y+Z)(X+Y+Z)(X+Y+Z)(X+Y+Z)

(b) (X+Y+Z)(X+Y+Z)(X+Y+Z)(X+Y+Z)

(c) (X+Y+Z)(X+Y+Z)(X+Y+Z)(X+Y+Z)

(d) (X+Y+Z)(X+Y+Z)(X+Y+Z)(X+Y+Z)

Ans. (a)

Q.50 The damping ratio of a series RLC circuit can be expressed as

(a)2R

2CL

(b) 22L

R C

(c) 2R C

L (d)2 LR C

Ans. (c)

Q.51 The pole-zero diagram of a causal and stable discrete-time system is shown inthe figure. The zero at the origin has multiplicity 4. The impulse response of thesystem is h[n]. If h[0] = 1, we can conclude

(a) h[n] is real for all n

0.5

0.5

0.50.5

Img (z)

Re (z)(b) h[n] is purely imaginary for all n

(c) h[n] is real for only even n

(d) h[n] is purely imaginary for only odd n

Ans. (c)



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Q.52 Two sequences [a, b, c] and [A, B, C] are related as,

= =

21 2 3

3 3 32 4

3 3

1 1 11 where1

jA aB W W b W eC cW W

If another sequence [p, q, r] is derived as,

=

1 2 23 3 32 4 4

3 3 3

1 1 1 1 0 0 /31 0 0 /3

/31 0 0

p Aq W W W Bc CW W W

then the relationship between the sequences [p, q, r] and [a, b, c] is(a) [p, q, r] = [b, a, c] (b) [p, q, r] = [b, c, a](c) [p, q, r] = [c, a, b] (d) [p, q, r] = [c, b, a]

Ans. (c)

Q.53 All the logic gates shown in the figure have a propagation delay of 20 ns. LetA = C = 0 and B = 1 until time t = 0. At t = 0, all the inputs flip (i.e. A = C = 1 andB = 0) and remain in that state. For t > 0, output Z = 1 for a duration (in ns) of

AB

C

Z

Ans. (40)

Q.54 In the given circuit, the maximum power (in Watts) that can be transferred tothe load RL is

2

j2 RL4 0 Vrms

Ans. (1.649)



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Q.55 A source emits bit 0 with probability 13 and bit with probability 2 .3 The emitted

bits are communicated to the receiver. The receiver decides for either 0 or 1 basedon the received value R. It is given that the conditional density functions of Ras

= =

0 0

11 , 1 5, 3 1( ) and ( ) 640, otherwise 0, otherwise

R Rxxf r f r

The minimum decision error probability is

(a) 0 (b) 112

(c) 19 (d)16

Ans. (b)

EC Forenoon 31st January Updated

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