GATE EC-2

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1. The I-V characteristics of three types of diodes at the room temperature, made of semiconductors X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If EgX, EgY and EgZ are the band gaps of X, Y and Z, respectively, then

(A) EgX > EgY > EgZ

(B) EgX = EgY = EgZ

(D) no relationship among these band gaps exists.

2. The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in

(A) Inversion

(B) Accumulation

(D) Flat band

3. In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be

(A) 4E and 0

(B) 4E and 1

(D) 4F and 1

4. The logic functionality realized by the circuit shown below is

(A) OR

(B) XOR

(D) AND

5. The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

(A) 4

(B) 5

(D) 7

6. The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

7. For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as

(A) 0

(B) 0.5

(D) ∞

9. If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

(A) right-handed circularly polarized

(B) left-handed circularly polarized

(D) horizontally polarized

10. The direct form structure of an FIR (finite impulse response) filter is shown in the figure.

The filter can be used to approximate a

(A) low-pass filter

(B) high-pass filter

(D) band-stop filter

11. The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown occurs in

(A) D1 only

(B) D2 only

(D) none of D1 and D2

12. Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is

(A) P Q S X + P Q S X + Q R S X + Q R S X

(B) Q S X + Q S X

(D) Q S + Q S

13. For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the counter is assumed to be zero.

If the clock (Clk) frequency is 1 GHz, then the counter behaves as a

(A) mod-5 counter

(B) mod-6 counter

(D) mod-8 counter

14. The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as

The range of K for which the system is stable is

(A) −2.0 < K < 0.5

(B) 0 < K < 0.5

(D) 0.5 < K < ∞

15.

(A) controllable but not observable

(B) observable but not controllable

(D) neither controllable nor observable

17. Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the cut-off frequencies for different modes is

(A) TE01 < TE10 < TE11 < TE20

(B) TE20 < TE11 < TE10 < TE01

(D) TE10 < TE11 < TE20 < TE01

18. Consider the charge profile shown in the figure. The resultant potential distribution is best described by

19. “By giving him the last of the cake, you will ensure lasting in our house today.” The words that best fill the blanks in the above sentence are

(A) peas, piece

(B) piece, peace

C) peace, piece

(D) peace, peas

20. “Even though there is a vast scope for its , tourism has remained a/an area.” The words that best fill the blanks in the above sentence are

(A) improvement, neglected

(B) rejection, approved

(D) interest, disinterested

21. If the number 715∎423 is divisible by 3 (∎ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ∎ is .

A) 0

(B) 2

(D) 6

22. A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

(A) 1.5

(B) 3

(D) 6

23. Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?

(A) 5,00,000

(B) 6,21,000

(D) 7,50,000

24. Two alloys A and B contain gold and copper in the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is .

(A) 5:10

(B) 7:13

(D) 9:13

25. Which of the following statements can be logically inferred from the above paragraph?

The Cricket Board has long recognized John’s potential as a leader of the However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression into big scores. Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain. After many years, it appears that the team has finally found a complete captain.

Even as a junior cricketer, John was considered a good
Finding a complete captain is a
Fans and the Cricket Board have differing views on what they want in a
Over the past three seasons John has accumulated big

(A) (i), (ii) and (iii) only

(B) (iii) and (iv) only

(D) (i), (ii), (iii) and (iv)

26. Which of the following options is closest to the probability that the accident was caused by a blue cab?

A cab was involved in a hit and run accident at You are given the following data about the cabs in the city and the accident.

(i) 85% of cabs in the city are green and the remaining cabs are
(ii) A witness identified the cab involved in the accident as
(iii) It is known that a witness can correctly identify the cab colour only 80% of the

Which of the following options is closest to the probability that the accident was caused by a blue cab?

(A) 12%

(B) 15%

(D) 80%

27. Which one of the following statements can be logically inferred from the information given in the above paragraph?

A coastal region with unparalleled beauty is home to many species of It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming crowded and polluted like any other major beach resorts.

(A) The culture and tradition of the local people will be influenced by the tourists.

(B) The region will become crowded and polluted due to tourism

(D) Helicopter connectivity would lead to an increase in tourists coming to the region.

28. A good transimpedance amplifier has

(A) low input impedance and high output impedance

(B) high input impedance and high output impedance.

(D) low input impedance and low output impedance.

29. The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

(A) Both the criteria provide information relative to the stable gain range of the system.

(B) The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.

(C) The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.

(D) The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

(A) 0

(B) 1

(D) 3

31. In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

(A) The hole and electron diffusion current components are in the same direction.

(B) The hole and electron drift current components are in the same direction.

(D) On an average, electrons drift and diffuse in the same direction.

32. The logic function f (X , Y) realized by the given circuit is

(A) NOR

B) AND

C) NAND

(D) XOR

33.

A function ?(?, ?, ?)defined by three Boolean variables A, B and C when expressed as sum of products is given by

? = ?̅ ⋅ ?̅ ⋅ ?̅ + ?̅ ⋅ ? ⋅ ?̅ + ? ⋅ ?̅ ⋅ ?̅

where, ?̅, ?̅ , and ?̅ are the complements of the respective variables. The product of sums

(POS) form of the function F is

34. The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:

(A) P: Open Circuit, Q: Short Circuit, R: Matched Load

(B) P: Open Circuit, Q: Matched Load, R: Short Circuit

(D) P: Short Circuit, Q: Open Circuit, R: Matched Load

35. Which one among the following is TRUE?

Let M be a real 4 ´ 4 Consider the following statements: S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible).

(A) S1 implies S2

(B) S1 implies S3

(D) S3 implies S2

36. A discrete-time all-pass system has two of its poles at 0.250 and 230 . Which one of the following statements about the system is TRUE?

(A) It has two more poles at 0.5<30 and 4< 0 .

(B) It is stable only when the impulse response is two-sided.

(D) It has constant phase response over the entire z-plane.

37. The circuit shown in the figure is used to provide regulated voltage (5 V) across the 1 kΩ resistor. Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a minimum required Zener current, IZ min =2 mA to its maximum allowable current. The input voltage VI may vary by 5% from its nominal value of 6 V. The resistance of the diode in the breakdown region is negligible.

The value of R and the minimum required power dissipation rating of the diode, respectively, are

(A) 186 Ω and 10 mW

(B) 100 Ω and 40 mW

(D) 186 Ωand 40 mW

38. A four-variable Boolean function is realized using 4* 1 multiplexers as shown in the figure.

The minimized expression for

F(U, V ,W, X ) is

(A) (U V +U V )W

(B) (U V +U V )(W X +W X )

U V +U V )(W X +W X )

39. The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is

(A) 0.12

(B) 0.23

(D) 2.3

40. For the circuit given in the figure, the voltage VC (in volts) across the capacitor is

(A) 1.25√ 2 sin(5t -0.25π)

(B) 1.25√ 2 sin(5t -0.125π)

(D) 2.5√ 2 sin(5t -0.125π)

41. She has a sharp tongue and it can occasionally turn _______.

A. Hurtful

B. left

C. Methodical

D. vital

42. Some table are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences?

(i) At least one bench is a table
(ii)At least one shelf is a bench
(iii)At least one chair is a table

All benches are chairs

A. only (i)

B. only (ii)

C. only (ii) and (iii)

D. only (iv)

43. 40% of deaths on city roads may be attributed to drunken driving. The number of degree needed to represent this as a slice of a pie chart is

A. 120

B. 144

C. 160

D. 212

44. Which of the following statement is correct?

In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

A. The ratio of household to other consumption is 8/17

B. The ratio of household to other consumption is 1/17

C. The ratio of household to other consumption is 17/8

D. There are errors in the official’s statement

45 I made arrangements had I_____informed earlier.

A. could have, been

B. would have, being

C. had, have

D. had been, been

46. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”. Here, the word „antagonistic‟ is closest in meaning to

A. Impartial

B. Argumentative

C. Separated

D. Hostile

47. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

A. 56

B. 52

C. 48

D. 44

48. A contour line joints locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot. The path from P to Q is best described by

A. Up-Down-Up-Down

B. Down-Up-Down-Up

C. Down-Up-Down

D. Up-Down-Up

49. Trucks (10m long) and cars (5 m long) go on a single lane bridge. There must be a gap of atleast 20 m after each truck and a gap of atleast 15m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternatively, what is the maximum number of vehicles that can use the bridge in one hour?

A. 1440

B. 1200

C. 720

D. 600

50. S, T, U, V, W, X, Y and Z are seated around a circular table. T’s neighbours are Y and V. Z is seated third to the left of T and second to the right of S.U’s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

A. X

B. W

C. U

D. T

51. The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 μs, then the number of T-states needed for executing the instruction is

A. 1

B. 6

C. 7

D. 8

52. Which one of the following statements is true about the system

Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as

A. It is causal and stable

B. It is causal but not stable

C. It is not causal but stable

D. It is neither causal nor stable

53. Which one among the following is correct?

Consider the following statement about the linear dependenceof the real valued functions y1 = 1, y2 = x and y 3 =x2, over the field of real
(i) y1,y2 and y3 are linearly independent on -1 ≤ x ≤

(ii) y1 , y2 andy3 are linearly dependent on 0 ≤ x ≤1
(iii) y1 , y2 andy3 are linearly independent on 0 ≤x

≤1

y1,y2 and y3 are linearly dependent on -1 ≤ x ≤

A. Which one among the following is correct?

B. Both I and III are true

C. Both II and IV are true

D. Both III and IV are true

54.

A. -2.5

B. 0

C. 15

D. 25

56. A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement is true?

A. Silicon atoms act as p-type dopants in Arsenic sites and n-type dopants in Gallium sites

B. Silicon atoms act as n-type dopants in Arsenic sites and p-type dopants in Gallium sites

C. Silicon atoms act as p-type dopants in Arsenic as well as Gallium sites

D. Silicon atoms act as n-type dopants in Arsenic as well as Gallium sites

57. In the latch circuit shown, the NAND gates have non- zero, but unequal propagation delays. The present input condition is: P = Q = ‘0’. If the input condition is changed simultaneously to P = Q = ‘1’, the outputs X and Y are

A. X = ‘1’, Y = ‘1’

B. either X = ‘1’, Y = ‘0’ or X = ‘0’, Y = ‘1’

C. either X = ‘1’, Y = ‘1’ or X = ‘0’, Y = ‘0’

D. X = ‘0’, Y = ‘0’

58. Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place)____.

A. 0.028

B. 1.02

C. 0.034

D. 1.80

59. An n+-n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of N D1 =1×1018 cm-3 and N D2 = 1×1015 cm-3 corresponding to the n and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic C. carrier concentration to be n i = 1×1010 cm -3. What is the magnitude of the built-in potential of this device?

A. 0.748 V

B. 0.460 V

C. 0.288 V

D. 0.173 V

60. A good transconductance amplifier should have

A. high input resistance and low output resistance

B. low input resistance and high output resistance

C. high input and output resistances

D. low input and output resistance

61. Let (X1, X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1 ; X2 ) between X1 and X2 in bits is_______.

A. 0

B. 1

C. 2

D. none of these

62. Which one among the following is correct?

Consider the following statements for continuous- time linear time invariant (LTI)
(i) There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex
(ii) There is non causal and BIBO stable system with a pole in the right half of the complex

A. Both I and II are true

B. Both I and II are not true

C. Only I is true

D. Only I is true

63. Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that X[0] = 1, x[1] =2, x[2]=1,h[0]=1. Let y[n] be the linear convolution od x[n] and h[n]. Given y[1]=3 and y[2]=4, the value of the expression (10y[3]+y[4]) is .

A. 31

B. 43

C. 23

D. 32

64. The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, A0 105V / V and an open-loop cut-off fc frequency The voltage gain of the amplifier at 15kHz, in V/V is .

A. 44.3

B. 45

C. 54

D. 34

65. A continuous time signal x(t)=4cos(200πt) + 8cos (400πt), where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

Let y(t) be the output of this filter. The maximum value of |y(t)| is .

A. 8

B. 16

C. 4

D. none of these

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