gateforum ece question paper-25

7/25/2019 GATEFORUM ECE QUESTION PAPER-25

1/16

ECTest ID: 161275 TarGATE16 www.gateforum.com

ICPIntensive Classroom ProgrameGATE-Live Internet Based ClassesDLPTarGATE-All India Test SeriesLeaders in GATE Preparation 65+ Centers across India

All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

1

Q. No. 1 5 Carry One Mark Each

General Ability

1. Wisdom is the mark of the sage; similarly, _______ is the mark of the _______.(A) torpor..zealot (B) disloyalty..renegade

(C) credulity..skeptic (D) temerity..coward

2. Analogy

GERONTOLOGY: AGING

(A) Morphology: flexibilities (B) Menology: calendar

(C) Otology: ear (D) Sitology: appendix

3. Gary Johnson, a major star in track and field, advertises a certain brand of vitamin

supplements for aspiring athletes. Alan runs cross country for his university and has decided

to start a fitness regimen including the vitamins to improve his event rankings.

The statements above, if true, best support which of the following assertions below?

(A) The vitamins have been shown to improve stamina in scientific studies.

(B) Alans regimen also includes changes in his workout and diet.

(C) Alan is not satisfied with some aspects of his current athletic performance.

(D) Alan has fallen victim to the marketing strategies of the company that manufactures the

Vitamins.

4. If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer,

then y must be __________.

(A) 2 (B) 5 (C) 6 (D) 14

5. Find the number of pairs of positive integers (a, b) such that 6 2a b 127 (A) 0 (B) 1 (C) 2 (D) 4

Q. No: 6-10 Carry Two Marks Each

6. Which of the following CANNOT yield an integer when divided by 7?

(A) The sum of three consecutive integers

(B) An integer with only even prime factors

(C) The product of two odd integers

(D) An even integer


2/16




2

7. If1

a b4

and c = 7a, then which of the following represents the average (arithmetic

mean) of a, b, and c, in terms of a?

(A) a 4 (B)1

1 a3

(C) 4a (D)1

4 a7

8. Ricardo deposits $1,000 in a bank account that pays 10% interest, compounded semiannually.

Poonam deposits $1,000 in a bank account that pays 10% interest, compounded annually. If

no more deposits are made, the difference between the two account balances after 1 year is

__________$.

(A) $2.50 (B) $10 (C) $5 (D) $100

9. In Raisin in the Sun, Lorraine Hansberry does not reject integration or the economic and

moral promise of the American dream; rather, she remains loyal to this dream while looking,realistically, at its incomplete realization. Once we recognize this dual vision, we can accept

the plays ironic nuances as deliberate social commentaries by Hansberry rather than as the

unintentional irony that Bigsby attributes to the work.Indeed, a curiously persistent refusal

to credit Hansberry with a capacity for intentional irony has led some critics to interpret the

plays thematic conflicts as mere confusion, contradiction, or eclecticism. Isaacs, for example,

cannot easily reconcile Hansberrys intense concern for her race with her ideal of human

reconciliation. But the plays complex view of Black self-esteem and human solidarity as

compatible is no more contradictory than Du Boiss famous, well-considered ideal of ethnic

self-awareness coexisting with human unity, or Fanons emphasis on an ideal internationalism

that also accommodates national identities and roles

Indicate the best answer: The authors primary purpose in the passage is to

(A) Explain some critics refusal to consider Raisin in the Sun a deliberately ironic play

(B) Suggest that ironic nuances ally Raisin in the Sun with Du Boiss and Fanons writings

(C) Analyze the fundamental dramatic conflicts in Raisin in the Sun

(D) Emphasize the inclusion of contradictory elements in Raisin in the Sun

10. Choose the best order for the sentences given. The best order is one which will result in a

coherent paragraph:

p. The sunlight shining through the gaps in the leaves has almost exactly the same colouring

as the deer's spotted coat.

q. The spotted deer, for example, is almost invisible inside the jungle.

r. So the animal seems to become a part of the forest.

s. Many living creatures use colour to protect themselves from their enemies.

The best order is

(A) s - q - pr (B) p - r - qs (C) s - p - qr (D) p - s - q - r


3/16




3

Electronics and Communication Engineering

Q. No: 1-25 Carry One Mark Each

1.

j5 t j3 tx t e u t e u t . Period of conjugate symmetric part of x(t) is ________.

2. A unity feedback system has the forward loop transfer function

2

2

k s 2G s H s .

s s 1

The range of k for stable operation is

(A) k 2 (B) k 2 (C) 0 k 1 (D) 0 k 2

3. Let us consider a 2s complementer, which will find 2s complement of their input and will

produce 2s complemented output. If such type of 100 units is cascaded then the output is

(A) 100 N (B) 99N (C) N (D) -N

4. In the figure given below the phase margin is ________ degrees.

5. A 25 Transmission line is feeding a quarter wave dipole antennas. If power reflected at

antenna end is 100W, then power transmitted by antenna is ________W.

6. If the free carrier density in pure silicon is 6 31.5 10 m , electrical resistivity is 3500 m and

the electron mobility is three times the hole mobility, then the mobility of electrons is

_____________ 8 210 m V sec

070 eR

1, j0

mI

2' s

complementer

2' s

complementer

2' s

complementer

100

output

1 2

N


4/16




4

7. The minimum number of 2-input NOR gates required to implement Boolean function

Z ABC is ________.

8. Find IB (in mA) when cI 4A for the circuit given,

9. Energy of a signal 2sin4 t

x tt

is _________.

10. Fundamental Fourier term of a half-wave rectified sinusoid shown below is,

(A)1 1

cos t2 2

(B)

1cos t

2 2

(C)

1sin t

2 2

(D)

1 1cos t

2 2

11. Match the following

In a source free series RLC circuit.

List-1 List-II

(1) Critically damped(a)

R C1

2 L

(2) Under damped(b)

1 1

2RC LC

1

1123 2 3 4 t

x t

1 30

BI

cI

2 80

EI


5/16




5

(3) Over damped(c)

R C1

2 L

(d)R C

1

2 L

(e)1 R

2LC

(A) 1 e, 2 c, 3 d (B) 1 d, 2 a, 3 c

(C) 1 c, 2 a, 3 d (D) 1 a, 2 e, 3 b

12. The diagonal matrix of

8 6 2

6 7 4

2 4 3

is

(A)

0 0 0

0 5 0

0 0 15

(B)

0 0 0

0 3 0

0 0 15

(C)

1 0 0

0 3 0

0 0 15

(D

1 0 0

0 15 0

0 0 3

13. Input output relation of two LTI systems is given as follows:

System 1: dx ty tdt

System 2: t

y t x d

Which of the following statement is correct?

(A) System 1, System 2 are invertible

(B) System 1, System 2 are non-invertible

(C) System 1 is invertible; System 2 is non- invertible

(D) System 1 is non-invertible, System 2 is invertible

14. Diagonal clipping in envelop detection is avoided if

(A)c m

1 1RC

f f (B)

m

1RCf

(C)C

1RCf

(D)C

m C

1 1R

f f

15. The input x[n] and impulse response h[n] of a LTI system is given by,

x n 1,1,2, 2 ;h n 0.5,1, 1,2,0.75


6/16




6

If the result of circular convolution is same as linear convolution number of zeros padded to

x[n], h[n] respectively are ________.

(A) 4, 3 (B) 3, 4 (C) 0, 1 (D) 1, 0

16.cotx

(x+1) for x 0If f(x) =

K for x = 0

is continuous at x = 0 then K=______ ?

(A) 1 (B) 0 (C) e (D) -1

17. Calculate the thermal equilibrium hole concentration in silicon at T = 400K. Assume that the

Fermi energy is 0.25eV above the valence band energy. The value of NVfor silicon at T =

300K is 19 31.04 10 cm .

(A) 15 38.6 10 cm (B) 15 36.43 10 cm (C) 15 310 10 cm (D) 16 31.148 10 cm

18. Consider the following statements in relation to a large value of capacitor filter used in a full

wave rectifier.

It gives the

(1) Low conduction period for the diode rectifier

(2) Increased peak current rating of the diode

(3) Large peak inverse rating of the diode.

Which of these statements are correct?

(A) 1 and 2 (B) 2 and 3 (C) 1 and 3 (D) 1,2 and 3

19. If 2 A sin u u and L is contour of the figure then circulationL

A.dl is _________.

20. A light is connected to 4 switches in such a way that the bulb glows only when at least 3

switches are ON. The circuit is designed using 3 input and 4 input gates. Cost of a 3 input

gate is Rs 10 and cost of 4 input gate is Rs 15. The minimum cost of implementation is

_________Rs.

21. Assertion (A): Superposition can be applied to nonlinear circuits

Reason (R): Superposition is derived from principle of linearity

2 3

2

3


7/16




7

(A) Both A & R are true and R is the correct explanation of A

(B) Both A & R are true and R is not the correct explanation of A

(C) A is true, R is false

(D) A is false but R is true

22. The solution of the differential equationdy

2y 12, y(0) 10is _________ .dt

(A) 2t6 4e (B) 2t6 4e (C) 2t6 4e (D) 2t6 4e

23. Consider the circuit shown below. The value of Ix is ____________ A

24. Consider a closed loop system with open loop transfer function3s

keG .

s

The maximum

value of k for which system is stable is ________.

25. The incremental voltage V2 interms of the incremental current i of the circuit shown in the

figure below is, (assume that the MOSFET is in saturation).

(A)3 3 3

2 2

m

Rv R i

g

(B) 2 m

1v g i

R

R

2 2v V

5V

I i

3

2

12A5V

xI


8/16




8

(C) 2m

1v R i

g

(D) 2

m

1v R i

g

Q. No: 26-55 Carry Two Marks Each

26.3

2

1

1dx = _____

(x 1)

(A) Converges to "1" (B) Converges to "2"

(C) Converges to "0" (D) Diverges

27. Consider the Network given below.

Find the value of 0Z given that current gain2

1

I2

I

28. AnSSB Transmitter withC

A 100V is being tested by modulating it with a Triangular

waveform, wherePV 0.5V. This SSB transmitter connected to a 50 resistive load. The

actual power dissipated into the load is _______ W.

29. For an ideal silicon pn junction diode 7no po 2 10 s, Dn= 25 cm

2/s, Dp= 16 cm2/s. At a

voltage aV the ratio of Na/Ndso that 90% of the current in the depletion region is carried by

electrons is __________.

1V

2V

1I 2I

1 2Z

122

0Z SV

SR

PV

m t

mT

t

PV


9/16




9

30. The probability of being less than 1.33 SDs above the mean is 0.90824 and the probability of

being less than 1.67 SDs below the mean is 0.04746 then the value of

2z

2

1.67

1e .dz is

2

31.

The current through the 2H inductor is __________ A.

32. Consider the below sequential circuit

The initial state of the sequential circuit is3 2 1 0Q Q Q Q 1010. After 8 clock pulses the state is

__________.

(A) 1010 (B) 0011 (C) 0000 (D) 1100

33. For the circuit shown in figure, each diode hasV 0.7V . The 0V For S10 V 10Vis

10V

20k

2D1D

SV

3D 4D20k

0V

20k

10V

S3Q

R

MSB

3Q

J2Q

K2Q

D1

Q

1Q

T0Q

0Q

LSB

CLK

V1_

2V

+

2H2

3V1

2A

3

6V

2

3


10/16




10

34. For the system shown in figure, with a damping ratio of 0.7 and an undamped natural

frequencynof 4rad /sec, the values of k and a are

(A) k = 64 , a = 0.225 (B) k = 16 , a = 0.225

(C) k = 4 , a = 0.35 (D) k = 16 , a = 1.225

35. The equation of the curve passing through the point

1,4

and having slope at any point

(x, y) as 2y y

- cosx x

is

8.43

OV

10S

V

10

A B 7.48OV

10S

V

D

4.65

OV

4.65S

V

4.6510

10

4.65

OV

6.8S

V

10

C

6.8

10

5.68

5.68

R S C S

k

s(s+2)

1 as


11/16




11

(A)

y1-tan

xx = e

(B)

y1+tan

xx = e

(C)

yx 1- tan

x

(D) None

36. Determine the range of values of iV that will maintain the zener diode in ON state. Z(min)I 0

(A)i23.67 V 36.87 (B) i20 V 40V

(C)i25.5 V 45.3V (D) None of these

37. x(t) is a real and odd signal with a Fourier transform X( ). Another signal y(t) is defined as

j ty t X e d

If y(t) is expressed in terms of x(t) the proportionality factor is

(A)1

2 (B)

1

2

(C) 2 (D) 2

38. The oscillator frequency for the circuit shown below is _________kHz.

RI330

ZV 20V

ZmaxI 60mA

LR 1.2k

ZI

LI

iV

12V

3R

1R

3C

2R

4R4C

5C

outV

50mH

1C

2C

0.1 F 0.01 F


12/16




12

39. Consider a discrete memoryless channel as shown below:

1

P x 0 P x 12

The probability of error is ________ if the decision rule is as shown below.

y p q r

x 0 0 1

40. In the op-AMP voltage regulator circuit shown in Figure, if unregulated input voltage is

increased by 30%, the power dissipation across1Q is

(A) Less than 50% (B) Between 50% and 60%

(C) Greater than 60% (D) None of the above

41. The Boolean expression f(x, y, z) for the combinational logic circuit shown is _________.

x 0

x 1

y r

y q

y p

0.5

0.4

0.10.2

0.5

0.3

ODD

PARITY

GENERATOR0

1

2 1

MUX

z

f x,y,z

1

0

x

10

1y 1

CI

1k 12K

36K

15V

6V

10

0V

1Q


13/16




13

(A) x y z (B) x y z (C) x y z (D) x y z

42. For on LTI system if the impulse response h (t) is periodic signal, then the system is

(A) Stable, non-causal (B) unstable, non-causal(C) Unstable, causal (D) Stable, causal

43. A special logic function q is generated to run a turbine as shown in the following figure.

The function is developed making use of a BCD to seven segment decoder followed by 2 bit

Magnitude comparator the minimal function of q(A, B, C, D) is _________.

(A) ABC (B) BCD (C) ACD (D) BDA

44. Given 1

cos 2t sin 2tstate transition matrix t ,2

2sin2t cos2t

y 0 1 x t , 1

x 01

Find the output for the above system matrix.

(A) 2sin2t cos2t (B) 2sin2t cos2t

(C)1

cos2t sin2t2

(D) None

45. Consider a potential function V as2

10V sin cos

r . The work done in moving a 10 C

charge from 0 0P(1,30 ,120 ) to point 0 0Q(4,90 ,60 ) is _________ J.

MSB

A

B

C

D

BCD to

seven

segment

decoder

a

b

c

d

e

fg

1x

0x

1y

0y

2 bitmag.

comparator

p x y

q x y

r x y

a

b

c

d

e

bg


14/16




14

46. with the distance interface halfway between the inner conductor is at1r 2cm and the outer

at 2r 2.5cm, where 1r 2 and 1r 5. Voltage drop across first dielectric in below figure is

_______V

47. A casual LTI system is described by a difference equation y n ay n 1 bx n x n 1 .

If j1a and H e 12 for all , for an input

n

n

1x n u n , y n _________ 2

48. The transfer function of a system is 2

2 2jH

4 4j

If the input x(t) = e-tu(t) and output

y(t) = kt e-tu(t), the value of k is _________.

49. Consider a binary signaling scheme in which two symbols were transmitted with probability

01

P s 4 and 13

P s 4 symbols where 0s is mapped to voltage level of +3V and 1s ismapped to voltage level of -3V. The channel noise has probability density function (channel

noise is additive)

N

14 n n 4

16f n

0 n 4

The threshold for a optimum receiver using Maximum

aposteriori criteria (MAP) is __________.

50. Consider electric field intensity x y zE 2 xa ya za V / m is associated with a 5 Coulomb

charge which moves between points P(2,0,0) and Q(1,2,3) then the potential between point

P and Q is ________V.

51. A semiconductor is known to have a band gap of 1.25eV and intrinsic carrier concentration of10 31.6 10 cm at room temperature. NC and NV are respectively ___________(Assume

* *

n pm :m 4 :1 & kT = 0.025 eV)

(A) 20 34.07 10 cm , 21 34.07 10 cm (B) 20 34.07 10 cm , 21 33.26 10 cm

(C) 20 33.26 10 cm , 21 33.26 10 cm (D) 21 33.07 10 cm , 21 33.26 10 cm

100V

1r

2r

2r1r


15/16




15

52. A semiconductor is having the hole concentration profile given by

15 3x

p x 10 exp cm x 0L

Where L = 12 m . The hole diffusion coefficient is

2

P

cmD 12

s and the electron mobility is

2

n

cm1000 .

v s

The hole diffusion current density

at x = 8 m is _________ 2mA cm .

53. Consider the circuit shown below

For maximum power transfer, RL= ___________ .

54. For the certain negative unit feedback system

kG s

s s 1 2s 1 3s 1

the nyquist plot

is

j6

-j5

5 5 RL010

B

0

0

A


16/16




16

55. The Newton-Raphson iteration formula to find the inverse of cube root of a positive real

number M is

(A) 3nn 1 nx

x 4 Mx3

(B)3n

n 1 n

xx 4 Mx

3

(C) n 1 n 2n

1 Mx 2x

3 x

(D) n 1 n 2

n

1 Mx 2x

3 x

0 c

D

0

(C)

gateforum ece question paper-25

Documents