## Gate 2017 Mathematics Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mathematics 5th Feb 2017

Subject Name: Mathematics

Duration : 180

Total Marks: 100

1. Consider the vector space V = {a0 + a1x + a2x2 : ai ∈ ℝ for i = 0, 1, 2} of polynomials of degree at most 2. Let f : V → ℝ be a linear functional such that f(1 + x) = 0, f(1 – x2) = 0 and f(x2 – x) = 2. Then f(1 + x + x2) equals _____.

Ans: (1)

2. Let A be a 7 × 7 matrix such that 2A2 A4 = I, where I is the identity matrix. If A has two distinct eigenvalues and each eigenvalue has geometric multiplicity 3, then the total number of nonzero entries in the Jordan canonical form of A equals ____.

Ans: (8)

3. Let f(z) = (x2 + y2) + i2xy and g(z) = 2xy + i(y2 – x2) for z = x + iy ∈ ℂ. Then, in the complex plane ℂ,

(A)  f is analytic and g is not analytic

(B)  f is not analytic and g is analytic

(C)  neither f nor g is analytic

(D)  both f and g are analytic

Ans: (B)

4. If  is the Laurent series of the function  for z ∈ ℂ\{2}, then a−2 equals _____.

Ans: (48)

5. Let fn : [0, 1] → ℝ be given by Then the sequence (fn)

(A)  converges uniformly on [0,1]

(B)  does NOT converge uniformly on [0, 1] but has a subsequence that converges uniformly on [0, 1]

(C)  does NOT converge pointwise on [0, 1]

(D)  converges pointwise on [0, 1] but does NOT have a subsequence that converges uniformly on [0, 1]

Ans: (D)

6. Let C : x2 + y2 = 9 be the circle in ℝ2 oriented positively. Then  equals ____.

Ans: (36)

7. Consider the following statements :

(P) : There exists an unbounded subset of ℝ whose Lebesgue measure is equal to 5.

(Q) If f : ℝ → ℝ is continuous and g : ℝ → ℝ is such that f = g almost everywhere on ℝ, then g must be continuous almost everywhere on ℝ.

Which of the above statements hold TRUE?

(A)  Both P and Q

(B)  Only P

(C)  Only Q

(D)  Neither P nor Q

Ans: (B)

8. If x3y2 is an integrating factor of (6y2 + a xy) dx + (6xy + bx2) dy = 0, where a, b ∈ ℝ, then

(A)  3a – 5b = 0

(B)  2a – b = 0

(C)  3a + 5b = 0

(D)  2a + b = 0

Ans: (A)

9. If x(t) and y(t) are the solutions of the system  with the initial conditions x(0) = 1 and y(0) = 1, then x(π/2) + y(π/2) equals _____.

Ans: (0)

10. If y = 3e2x + e−2x – αx is the solution of the initial value problem  where α, β ∈ ℝ, ,then

(A)  α = 3 and β = 4

(B)  α = 1 and β = 2

(C)  α = 3 and β = −4

(D)  α = 1 and β = −2

Ans: (C)

11. Let G be a non-abelian group of order 125. Then the total number of elements in Z(G) = {x ∈ G : g x = x g for all g ∈ G} equals ______.

Ans: (5)

12. Let F1 and F2 be subfields of a finite field F consisting of 29 and 26 elements, respectively. Then the total number of elements in F1 ⋂ F2 equals ____.

Ans: (8)

13. Consider the normed linear space ℝ2 equipped with the norm given by ||(x, y)|| = |x| + |y| and the subspace X = {(x, y) ∈ ℝ2 : x = y}. Let f be the linear functional on X given by f(x, y) = 3x. If g(x, y) = αx + βy, α, β ∈ ℝ, is a Hahn-Banach extension of f on ℝ2 then α – β equals _____.

Ans: (0)

14. In n ∈ ℤ, define  where i2 = −1. Then equals

(A)  cosh(π)

(B)  sinh(π)

(C)  cosh(2π)

(D)  sinh(2π)

Ans: (D)

15. If the fourth order divided difference of f(x) = αx4 + 5x3 + 3x + 2, α ∈ ℝ, at the points 0.1, 0.2, 0.3, 0.4, 0.5 is 5, then α equals ___.

Ans: (5)

16. If the quadrature rule  where c1­, c2 ∈ ℝ, is exact for all polynomials of degree ≤ 1, then c1 + 3c2­ equals _____.

Ans: (1)

17. If u(x, y) = 1 + x + y + f(xy), where f : ℝ2 → ℝ is a differentiable function, then u satisfies

(A)

(B)

(C)

(D)

Ans: (C)

18. The partial differential equation  is

(A)  hyperbolic along the line x + y = 0

(B)  elliptic along the line x – y = 0

(C)  elliptic along the line x + y = 0

(D)  parabolic along the line x + y = 0

Ans: (D)

19. Let X and Y be topological spaces and let f : X → Y be a continuous surjective function. Which one of the following statements is TRUE?

(A)  If X is separable, then Y is separable

(B)  If X is first countable, then Y is first countable

(C)  If X is Hausdorff, then Y is Hausdorff

(D)  If X is regular then Y is regular

Ans: (A)

20. Consider the topology T = {U ⊆ ℤ: ℤ\U is finite or 0 ∉ U} on ℤ. Then, the topological space (ℤ, T) is

(A)  compact but NOT connected

(B)  connected but NOT compact

(C)  both compact and connected

(D)  neither compact nor connected

Ans: (A)

21. Let F(x) be the distribution function of a random variable X. Consider functions :

G1(x) = (f(x))3, x ∈ ℝ,

G2(x) = 1 – (1 – F(x))5, x ∈ ℝ.

Which of the above functions are distribution functions?

(A)  Neither G1 nor G2

(B)  Only G1

(C)  Only G2

(D)  Both G1 and G2

Ans: (D)

22. Let X1, X2, …., Xn (n ≥ 2) be independent and identically distributed random variables with finite variance σ2 and let   Then the covariance between   is

(A)  0

(B)     −σ2

(C)

(D)

Ans: (A)

23. Let X1, X2, …., Xn(n ≥ 2) be a random sample from a N(μ, σ2) population, where σ2 = 144. The smallest n such that the length of the shortest 95% confidence interval for μ will not exceed 10 is _____.

Ans: (23)

24. Consider the linear programming problem (LPP) :

Maximize 4x1 + 6x2

Subject to x1 + x2 ≤ 8,

2x1 + 3x2­ ≥ 18,

x1 ≥ 6, x2 is unrestricted in sign.

Then the LPP has

(A)  no optimal solution

(B)  only one basic feasible solution and that is optimal

(C)  more than one basic feasible solution and a unique optimal solution

(D)  infinitely many optimal solutions

Ans: (B)

25. For a linear programming problem (LPP) and its dual, which one of the following is NOT TRUE?

(A)  The dual of the dual is primal

(B)  If the primal LPP has an unbounded objective function, then the dual LPP is infeasible

(C)  If the  primal LPP is infeasible, then the dual LPP must have unbounded objective function

(D)  If the primal LPP has a finite optimal solution, then the dual LPP also has a finite optimal solution

Ans: (C)

26. If U and V are null spaces of  , respectively, then the dimension of the subspace U + V equals ______.

Ans: (3)

27. Given two n × n matrices A and B with entries in ℂ, consider the following statements:

(P): If A and B have the same minimal polynomial, then A is similar to B.

(Q) : If A has n distinct eigenvalues, then there exists u ∈ ℂn such that u, Au, ,…, An1u are linearly independent.

Which of the above statements hold TRUE?

(A)  Both P and Q

(B)  Only P

(C)  Only Q

(D)  Neither P nor Q

Ans: (C)

28. Let A = (aij) be a 10 × 10 matrix such that aij = 1 for i ≠ j and aij = α + 1, where α > 0. Let λ and μ be the largest and the smallest eigenvalues of A, respectively. If λ + μ = 24, then α equals ______.

Ans: (7)

29. Let C be the simple, positively oriented circle of radius 2 centered at the origin in the complex plane. Then  equals ______.

Ans: (3)

30. Let Re(z) and Im(z), respectively, denote the real part and the imaginary part of a complex number z. Let T : ℂ ⋃ {∞} → ℂ ⋃ {∞} be the bilinear transformation such that T(6) = 0, T(3 – 3i) = i and T(0) = ∞. Then, the image of D = {z ∈ ℂ : |z – 3| < 3} under the mapping w = T(z) is

(A)  {w ∈ ℂ : Im(w) < 0}

(B)  {w ∈ ℂ : Re(w) < 0}

(C)  {w ∈ ℂ : Im(w) > 0}

(D)  {w ∈ ℂ : Re(w) > 0}

Ans: (D)

31. Let (xn) and (yn) be two sequences in a complete metric space (X, d) such that and  and  for all n ∈ ℕ. Then

(A)  both (xn) and (yn) converge

(B)  (xn) converges but (yn) need NOT converge

(C)  (yn) converges but (xn) need NOT converge

(D)  neither (xn) nor (yn) converges

Ans: (B)

32. Let f : [0, 1] → ℝ be given by f(x) = 0 if x is rational, and if x is irrational then f(x) = 9n, where n is the number of zeroes immediately after the decimal point in the decimal representation of x. Then the Lebesgue integral  equals _____.

Ans: (9)

33. Let f : ℝ2 → ℝ be defined by  Then, at (0, 0),

(A)  f is continuous and the directional derivative of f does NOT exist in some direction

(B)  f is NOT continuous and the directional derivatives of f exist in all directions

(C)  f is NOT differentiable and the directional derivatives of f exist in all directions

(D)  f is differentiable

Ans: (C)

34. Let D be the region in ℝ2 bounded by the parabola y2 = 2x and the line y = x. Then  equals _______.

Ans: (2)

35. Let y1(x) = x3 and y2(x) = x2|x| for x ∈ ℝ.

Consider the following statements.

(P) : y1(x) and y2(x) are linearly independent solutions of

on ℝ.

(Q) : The Wronskian  for all x ∈ ℝ.

Which of the above statement hold TRUE?

(A)  Both P and Q

(B)  Only P

(C)  Only Q

(D)  Neither P nor Q

Ans: (A)

36. Let α and β with α > β be the roots of the indicial equation of  at x = −1.  Then α − 4β equals _____.

Ans: (2)

37. Let S9 be the group of all permutations of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Then the total number of elements of S9 that commute with  in S9 equals _______.

Ans: (24)

38. Let ℚ[x] be the ring of polynomials over ℚ. Then the total number of maximal ideals in the quotient ring ℚ[x]/(x4 – 1) equals ____.

Ans: (3)

39. Let {en : n ∈ ℕ} be an orthonormal basis of a Hilbert space H. Let T : H → H be given by  For each n ∈ ℕ, define Tn : H → H by  Then

(A)  ||Tn – T|| → 0 as n → ∞

(B)  ||Tn – T|| ↛ 0 as n → ∞ but for each x ∈ H, ||Tnx – Tx|| → 0 as n → ∞

(C)  for each x ∈ H, ||Tnx – Tx|| → 0 as n → ∞ but the sequences (||Tn||) is unbounded

(D)    there exist x, y ∈ H such that  as n → ∞

Ans: (A)

40. Consider the subspace  of the Hilbert space ℓ2 of all square summable real sequences. For n ∈ ℕ, define Tn : V → ℝ by

Consider the following statements:

(P): {Tn : n ∈ ℕ} is pointwise bounded on V.

(Q): {Tn : n ∈ ℕ}is uniformly bounded on {x ∈ V : ||x||2 = 1}.

Which of the above statements hold TRUE?

(A)  Both P and Q

(B)  Only P

(C)  Only Q

(D)  Neither P nor Q

Ans: (B)

41. Let p(x) be the polynomial of degree at most 2 that interpolates the data (−1, 2), (0, 1) and (1, 2). If q(x) is a polynomial of degree at most 3 such that p(x) + q(x) interpolates the data (−1, 2), (0, 1), (1, 2) and (2, 11), then q(3) equals ______.

Ans: (24)

42. Let J be the Jacobi iteration matrix of the linear system

Consider the following statements :

(P): One of the eigenvalues of J lies in the interval [2, 3]

(Q): The Jacobi iteration converges for the above system.

Which of the above statements hold TRUE?

(A)  Both P and Q

(B)  Only P

(C)  Only Q

(D)  Neither P nor Q

Ans: (B)

43. Let u(x, y) be the solution of  satisfying the condition u(x, y) = 1 on the circle x2 + y2 = 1. Then u(2, 2) equals _____.

Ans: (64)

44. Let u(r, θ) be the bounded solution of the following boundary value problem in polar coordinates:

u(2, θ) = cos2 θ,   0 ≤ θ ≤ 2π.

Then u(1, π/2) + u(1, π/4) equals

(A)  1

(B)  9/8

(C)  7/8

(D)  3/8

Ans: (C)

45. Let Tu and Td denote the usual topology and the discrete topology on ℝ, respectively.

Consider the following three topologies:

T1 = Usual topology on ℝ2 = ℝ × ℝ,

T2 = Topology generated by the basis {U × V : U ∈ Td, V ∈ Tu} on ℝ × ℝ,

T3 = Dictionary order topology on ℝ × ℝ.

Then

(A)

(B)

(C)

(D)

Ans: (D)

46. Let X be a random variable with probability mass function  for n = 1, 2, ….. . Then E(X – 3 |X > 3) equals _____.

Ans: (4)

47. Let X and Y be independent and identically distributed random variables withi probability mass function p(n) = 2n, n = 1, 2….. .

Then P(X ≥ 2Y) equals (rounded to 2 decimal places) ____.

Ans: (0.27 to 0.30)

48. Let X1, X2, …. be a sequence of independent and identically distributed Poisson random variables with mean 4. Then  equals ____.

Ans: (0.67 to 0.70)

49. Let X and Y be independent and identically distributed exponential random variables with probability density function

The P(max(X, Y) < 2) equals (rounded to 2 decimal places)______.

Ans: (0.73 to 0.77)

50. Let E and F be any two events with P(E) = 0.4, P(F) = 0.3 and P(F\E) = 3 P(F\EC). Then P(E\F) equals (rounded to 2 decimal places)______.

Ans: (0.65 to 0.68)

51. Let X1, X2…, Xm (m ≥ 2) be a random sample from a binomial distribution with parameters n = 1 and p, p ∈ (0, 1), and let

Then a uniformly minimum variance unbiased estimator for p(1 – p) is

(A)

(B)

(C)

(D)

Ans: (A)

52. Let X1, X2, …., X9 be a random sample from a N(0, σ2) population. For teting H0 : σ2 = 2 against H1 : σ2 = 1, the most powerful test rejects H0 if  where c is to be chosen such that the level of significance is 0.1. Then the power of this test equals ______.

Ans: (0.49 to 0.51)

53. Let X1, X2,…, Xn (n ≥ 2) be a random sample from a N(θ, θ) population, where θ > 0, and let  Then the maximum likelihood estimator of θ is

(A)

(B)

(C)

(D)

Ans: (D)

54. Consider the following transportation problem. The entries inside the cells denote per unit cost of transportation from the origins to the destinations.

The optimal cost of transportation equals ______.

Ans: (590)

55. Consider the linear programming problem (LPP) :

Maximize kx1 + 5x2

subject to x1 + x2 ≤ 1,

2x1 + 3x2 ≤ 1,

x1, x2 ≥ 0.

If x* = (x1*, x2*) is an optimal solution of the above LPP with k = 2, then the largest value of k (rounded to 2 decimal places) for which x* remains optimal equals ______.

Ans: (3.32 to 3.34)

56. The ninth and the tenth of this month are Monday and Tuesday _______.

(A)  figuratively

(B)  retrospectively

(C)  respectively

(D)  rightfully

Ans: (C)

57. It is _______ to read this year’s textbook ______ the last year’s

(A)  easier, than

(B)  most easy, than

(C)  easier, from

(D)  easiest, from

Ans: (A)

58. A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

(A)  Only P’s drink

(B)  Only P’s drink and S’s age

(C)  Only S’s age

(D)  Only P’s drink, Q’s drink and S’s age

Ans: (B)

59. Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?

(A)  8 km, East

(B)  12 km, North

(C)  6 km, East

(D)  10 km, North

Ans: (A)

60. 500 students are taking one or more courses out of Chemistry, Physics and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A)  37

(B)  43

(C)  147

(D)  53

Ans: (D)

61. “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 sections, 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.”

Which of the following statements best reflects the author’s opinion?

(A)  An intimate association does not allow for the necessary perspective.

(B)  Matters are recorded with an impartial perspective.

(C)  An intimate association offers an impartial perspective.

(D)  Actors are typically associated with the impartial recording of matters.

Ans: (A)

62. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A)  X is the mother-in-law of R

(B)  P and R are not married to each other

(C)  P is a son of X and Y

(D)  Q cannot be married to R

Ans: (D)

63. 1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A)  3000

(B)  3300

(C)  3600

(D)  3900

Ans: (C)

64. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A)  781

(B)  791

(C)  881

(D)  891

Ans: (C)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of geographical region. Contour lines are shown at 25 m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A)  P to Q

(B)  P to R

(C)  P to S

(D)  P to T

Ans: (B)

## Gate 2017 Instrumentation Engineering Question Paper 12th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Instrumentation Engineering 12th Feb 2017

Subject Name: Instrumentation Engineering

Duration : 180

Total Marks: 100

1. A system is described by the following differential equation:

Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is

(A)

(B)

(C)

(D)

Ans: (B)

2. If v is a non-zero vector of dimension 3×1, then the matrix A=vvT has a rank = _______

Ans: (1)

3. A periodic signal x(t) is shown in the figure. The fundamental frequency of the signal x (t) in Hz is________

Ans: (1)

4. The silicon diode, shown in the figure, has a barrier potential of 0.7 V. There will be no forward current flow through the diode, if Vdc, in volt, is greater than

(A) 0.7

(B) 1.3

(C) 1.8

(D) 2.6

Ans: (D)

5. For a first order low pass filter with unity d.c. gain and -3 dB corner frequency of 2000π rad/s, the transfer function H( jω ) is

(A)

(B)

(C)

(D)

Ans: (C)

6. A and B are the logical inputs and X is the logical output shown in the figure. The output X is related to A and B by

(A)

(B)

(C)

(D)

Ans: (C)

7. The most suitable pressure gauge to measure pressure in the range of 104 to 103 torr is

(A)  Bellows

(B)  Barometer

(C)  Strain gauge

(D)  Pirani gauge

Ans: (D)

8. The standard for long distance analog signal transmission in process control industry is

(A)  4-20 mV

(B)  0-20 mA

(C)  4-20 mA

(D)  0-5V

Ans: (C)

9. If a continuous-time signal x(t) = cos(2πt) is sampled at 4 Hz, the value of the discrete-time sequence x(n) at n = 5 is

(A)  −0.707

(B)  −1

(C)  0

(D)  1

Ans: (C)

10. The term hysteresis is associated with

(A) ON-OFF control

(B) P-I control

(C) Feed-forward control

(D) Ratio control

Ans: (A)

11. A current waveform, i(t), shown in the figure, is passed through a Permanent Magnet Moving coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is

(A)  −0.25 A

(B)  −0.12A

(C)  0.37 A

(D)  0.5 A

Ans: (A)

12. The connection of two 2-port networks is shown in the figure. The ABCD parameters of N1 and N2 networks are given as

The ABCD parameters of the combined 2-port network are

(A)

(B)

(C)

(D)

Ans: (A)

13. The figure shows a shape ABC and its mirror image A1B1C1 across the horizontal axis (X – axis). The coordinate transformation matrix that maps ABC to A1B1C1 is

(A)

(B)

(C)

(D)

Ans: (D)

14. The differential amplifier, shown in the figure, has a differential gain of Ad = 100 and common mode gain of Ac = 0.1. If V1 = 5.01 V and V2 = 5.00 V, then V0, in volt (up to one decimal place) is ______.

Ans: (1.4 to 1.6)

15. A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at Node-1 is – 1 V, then the voltage at Node-2 is _________V.

Ans: (2)

16. The eigen values of the matrix  are

(A)  −1, 5, 6

(B)  1, −5 ± j6

(C)  1, 5 ± j6

(D)  1, 5, 5

Ans: (C)

17. The figure shows a phase locked loop. The output frequency is locked at f0 = 5kHz. The value of fi in kHz is __________.

Ans: (1)

18. Identify the instrument that does not exist:

(A) Dynamometer-type ammeter

(B) Dynamometer-type wattmeter

(C) Moving-iron voltmeter

(D) Moving-iron wattmeter

Ans: (D)

19. The output Vo shown in the figure, in volt, is close to

(A)  −20

(B)  −15

(C)  −5

(D)  0

Ans: (B)

20. An 8-bit microcontroller with 16 address lines has 3 fixed interrupts i.e., Int1, Int2 and Int3 with corresponding interrupt vector addresses as 0008H. 0010H and 0018H. To execute a 32-byte long Interrupt Service Subroutine for Int1 starting at the address ISSI, The location 0008H onwards should ideally contain

(A) a CALL to ISSI

(D) only ISSI

Ans: (A or B)

21. A series R-L-C circuit is excited with a 50V, 50 Hz sinusoidal source. The voltage across the resistance and the capacitance are shown in the figure. The voltage across the inductor (VL) is __________V

Ans: (50)

22. The condition for oscillation in a feedback oscillator circuit is that at the frequency of oscillation, initially the loop gain is greater than unity while the total phase shift around the loop in degree is

(A)  0

(B)  90

(C)  180

(D)  270

Ans: (A)

23. Let z = x + jy where

(A)    cos z

(B)

(C)  sin z

(D)

Ans: (B)

24. The region of Convergence (ROC) of the Z-transform of a causal unit step discrete-time sequence is

(A)  |z| < 1

(B)  |z| ≤ 1

(C)  |z| > 1

(D)  |z| ≥ 1

Ans: (C)

25. The pressure drop across an orifice plate for a particular flow rate is 5 kg/m2. If the flow rate is doubled (within the operating range of the orifice), the corresponding pressure drop in kg/m3 is

(A)  2.5

(B)  5.0

(C)  20.0

(D)  25.0

Ans: (C)

26. The two-input voltage multiplier, shown in the figure, has a scaling factor of 1 and produces voltage output. If V1 = +15V and V2 = +3V, the value of V0 in volt is _______.

Ans: (−5 to 5)

27. For the circuit, shown in the figure, the total real power delivered by the source to the loads is _________kW

Ans: (1.75 to 1.96)

28. The magnetic flux density of an electromagnetic flow meter is 100 mWb/m2. The electrodes are wall-mounted inside the pipe having a diameter of 0.25m. A voltage of 1V is generated when a conducting fluid is passed through the flow meter. The volumetric flow rate of the fluid in m3/s is ____________.

Ans: (1.9 to 2)

29. In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by  where VGS is in V. If Vs = +5V, then the value of RS in kΩ is ______.

Ans: (9.9 to 10.1)

30. The hot junction of a bare thermocouple, initially at room temperature (30℃), is suddenly dipped in molten metal at t = 0s. The cold junction is kept at room temperature. The thermocouple can be modeled as a first-order instrument with a time constant of 1.0s and a static sensitivity of 10μV/℃. If the voltage, measured across the thermocouple indicates 10.0 mV at t = 1.0s, then the temperature of the molten metal in ℃ is __________.

Ans: (1605 to 1618)

31. A series R-L-C circuit is excited with an a.c. voltage source. The quality factor (Q) of the circuit is given as Q = 30. The amplitude of current in ampere at upper half-power frequency will be __________.

Ans: (6 to 7)

32. An angle modulated signal with carrier frequency ωc = 2π × 106 rad/s is given by φm(t) = cos(ωct + 5sin(1000πt)) + 10sin(2000πt). The maximum deviation of the frequency in the angle modulated signal from that of the carrier is _________ kHz.

Ans: (12 to 13)

33. Three DFT coefficients, out of five DFT coefficients of a five-point real sequence are given as : X(0) = 4, X(1) = 1 – j1 and X(3) = 2 + j2. Then zero-th value of the sequence x(n), x(0), is

(A)  1

(B)  2

(C)  3

(D)  4

Ans: (B)

34. A closed-loop system is shown in the figure. The system parameter α is not known. The condition for asymptotic stability of the closed loop system is

(A)  α < −0.5

(B)  −0.5 < α < 0.5

(C)  0 < α < 0.5

(D)  α > 0.5

Ans: (D)

35. The power delivered to a single phase inductive load is measured with a dynamometer type wattmeter using a potential transformer (PT) of turns ratio 200:1 and the current transformer (CT) of turns ratio 1:5. Assume both the transformers to be ideal. The power factor of the load is 0.8. If the wattmeter reading is 200W, then the apparent power of the load in kVA is _________.

Ans: (250)

36. The overall closed loop transfer function  represented in the figure, will be

(A)

(B)

(C)

(D)

Ans: (A)

37. When the voltage across a battery is measured using a d.c. potentiometer, the reading shows 1.08V. But when the same voltage is measured using a Permanent Magnet Moving Coil (PMMC) voltmeter, the voltmeter reading shows 0.99V. If the resistance of the voltmeter is 1100Ω, the internal resistance of the battery, in Ω, is _________.

Ans: (100)

38. The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is

(A)  0.181

(B)  0.191

(C)  0.222

(D)  0.826

Ans: (C)

39. The current response of a series R-L circuit to a unit step voltage is given in the table. The value of L is ___________H.

Ans: (1)

40. A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo =+ 2.0V, then the value of x is __________.

Ans: (0.19 to 0.21)

41. The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between ±7V. The width of the hysteresis band is _________V.

Ans: (0.6 to 0.7)

42. The loop transfer function of a closed-loop system is given by  The breakaway point of the root-loci will be ____________.

Ans: (−1.2 to 1.0)

43. The unbalanced voltage of the Wheatstone bridge, shown in the figure, is measured using digital voltmeter having infinite input impedance and a resolution of 0.1mV. If R = 1000Ω, then the minimum value of ∆R in Ω to create detectable unbalanced voltage is _________.

Ans: (0.17 to 0.23)

44. In the circuit diagram, shown in the figure, S1 was closed and S2 was open for a very long time. At t = 0, S­1 is opened and S2 is closed. The voltage across the capacitor, in volt, at t = 5 μs is _______

Ans: (1.43 to 1.63)

45. The block diagram of a closed-loop control system is shown in the figure. The values of k and kp are such that the system has a damping ratio of 0.8 and an undamped natural frequency ωn of 4 rad/s respectively. The value of kp will be ___________.

Ans: (0.32 to 0.4)

46. Assuming the op-amp shown in the figure to be ideal, the frequency at which the magnitude of Vo will be 95% of the magnitude of Vin is ____________kHz.

Ans: (2.9 to 3)

47. The following table lists an nth order polynomial f(x) = anxn + an – 1 xn – 1 +…+a1x + a0 and the forward differences evaluated at equally spaced values of x. The order of the polynomial is

(A)  1

(B)  2

(C)  3

(D)  4

Ans: (D)

48. Consider two discrete-time signals:

x1(n) = {1, 1} and x2(n) = {1, 2}, for n = 0.1.

The Z-transform of the convoluted sequence x(n) = x1(n) * x2(n) is

(A)  1 + 2z1 + 3z2

(B)  z2 + 3z + 2

(C)  1 + 3z1 + 2z2

(D)  z2 + 3z3 + 2z4

Ans: (C)

49. In the a.c. bridge, shown in the figure, R = 103Ω and C = 10−7 F. If the bridge is balanced at a frequency ω0, the value of ω0 in rad/s is ________.

Ans: (10000)

50. The junction semiconductor temperature sensor shown in the figure is used to measure the temperature of hot air. The output voltage Vo is 2.1V. The current output of the sensor is given by I = TμA where T is the temperature in K. Assuming the opamp to be ideal, the temperature of the hot air in ℃ is approximately ___________.

Ans: (76 to 78)

51. In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by Am(t) = 100 cos (ωct) + 50 cos(ωmt) cos (ωct), where ωc is the carrier frequency and ωm is the modulation frequency. The power carried by the sidebands in % of total power is ________%

Ans: (11 to 11.2)

52. The angle between two vectors  and  in radian is _____.

Ans: (0.65 to 0.8)

53. Quantum efficiency of a photodiode (ratio between the number of liberated electrons and the number of incident photons) is 0.75 at 830 nm. Given Plank’s constant h = 6.624 × 10−34 J, the charge of an electron e = 1.6 × 10−19 C and the velocity of light in the photodiode Cm = 2 × 108 m/s. For an incident optical power of 100 μW at 830 n, the photocurrent in μA is _______.

Ans: (74.5 to 75.5)

54. The two inputs A and B are connected to an R-S latch via two AND gates as shown in the figure. If A = 1 and B = 0, the output  is

(A)  00

(B)  10

(C)  01

(D)  11

Ans: (B)

55. The Laplace transform of a causal signal y(t) is   The value of the signal y(t) at t = 0.1 s is _______ unit.

Ans: (−2.4 to −2.0)

56. The event would have been successful if you ______ able to come.

(A)  are

(C)  have been

(D)  would have been

Ans: (B)

57. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

(A)  2, Red

(B)  2, 3, Red

(C)  2, blue

(D)  2, red, blue

Ans: (C)

58. What is the value of x when

(A)  1

(B)  −1

(C)  −2

(D)  Cannot be determined

Ans: (B)

59. There was no doubt that their work was thorough.

Which of the words below is closest in meaning to the underlined word above?

(A)  Pretty

(B)  Complete

(C)  Sloppy

(D)  Haphazard

Ans: (B)

60. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

(A)  1/9

(B)  2/9

(C)  1/3

(D)  4/9

Ans: (B)

61. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

(A) The centre operates on a first-come-first-served basis but with variable service times, depending on specific customer needs.

(B) Customers were served in an arbitrary order since they took varying amounts of time for service completion in the centre.

(C) Since some people came out within a few minutes of entering the centre. The system is likely to operate on a last-come-first-served basis.

(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Ans: (A)

62. The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (D)

63. A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri, Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok.

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

i. Pelling is at a higher elevation than Kalimpong

ii. Kalimpong is at a lower elevation than Darjeeling

iii. Kalimpong is at a higher elevation than siliguri

iv. Siliguri is at a lower elevation than Gangtok

(A)  Only ii

(B)  Only ii and iii

(C)  Only ii and iv

(D)  Only iii and iv

Ans: (C)

64. P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats.

Which of the following must necessarily be true?

(A) P is immediately to the right of R

(B) T is immediately to the left of P

(C) T is immediately to the left of P or P is immediately to the right of Q

(D) U is immediately to the right of R or P is immediately to the left of T

Ans: (C)

65. Budhan covers a distance of f19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

(A)  1

(B)  4

(C)  5

(D)  6

Ans: (D)

## Gate 2017 Geology and Geophysics Question Paper 4th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Geology and Geophysics 4th Feb 2017

Subject Name: Geology and Geophysics

Duration : 180

Total Marks: 100

1. Which one of the following is a continental hotspot?

(A)  Reunion

(B)  Macdonald

(C)  Hawaii

(D)  Afar

Ans: (D)

2. The diagram given below shows a Mohr circle for two-dimensional stress with points numbered as shown. The mean stress and the maximum shear stress are given by which one of the following number pairs?

(A)  1, 2

(B)  1, 3

(C)  1, 4

(D)  2, 3

Ans: (B)

3. Which type of fault is developed in the setting shown in the figure below? Velocity vectors on either side of the fault are given in the figure.

(A)  Normal

(B)  Dextral strike-slip

(C)  Sinistral strike-slip

(D)  Thrust

Ans: (A)

4. The age of most of the bituminous coal seams of India is

(A)  Silurian.

(B)  Miocene.

(C)  Carboniferous.

(D)  Permian.

Ans: (D)

5. The time equivalent of the time-stratigraphic team ‘Series’ is

(A)  Epoch.

(B)  Period.

(C)  Age.

(D)  Stage.

Ans: (A)

6. Match the following stratigraphic units of India (Group-I) with their age (Group-II)

Group-I                                                  Group-II

(P) Barakar Formation                            (1) Miocene

(Q) Warakali (Varkala) Formation       (2) Cretaceous

(R) Bagh Beds                                           (3) Proterozoic

(S) Bhander Limestone                           (4) Eocene

(5) Permian

(A)  P-5, Q-1, R-2, S-3

(B)  P-1, Q-4, R-2, S-5

(C)  P-5, Q-4, R-2, S-3

(D)  P-2, Q-3, R-1, S-4

Ans: (A)

7. Universal Transverse Mercator (UTM) is a type of

(A)  conical projection

(B)  gnomonic projection

(C)  orthogonal projection

(D)  cylindrical projection

Ans: (D)

8. The groundwater flow equation  where h refers to the hydraulic head and x, y, z are coordinates, is valid when the flow condition is

(A)  steady state in isotropic media.

(B)  unsteady state in isotropic media.

(C)  steady state in anisotropic media.

(D)  unsteady state in anisotropic media.

Ans: (A)

9. Los Angeles abrasion test was conducted for a granite aggregate with an initial weight of 4800 grams. After the test, the aggregate weighed 3504 grams. The Los Angeles abrasion value is _______%

Ans: (27)

10. Brightness temperature is a function of surface temperature and

(A)  transmittance.

(B)  reflectance.

(C)  refractive index.

(D)  emissivity.

Ans: (D)

11. Which one of the following minerals has poor cleavage in all directions?

(A)  Fluorite

(B)  Orthoclase

(C)  Quartz

(D)  Muscovite

Ans: (C)

12. The figure below shows the intercepts of the plane HKL with the crystallographic axes a, b, c. The Miller index of the plane HKL is

(A)  (243)

(B)  (342)

(C)  (436)

(D)  (634)

Ans: (B)

13. Match the rocks listed in Group-I with the corresponding general rock classification listed in Group-II.

Group-I                           Group-II

P. Granite                  1. Extrusive igneous rock

Q. Basalt                   2. Biochemical sedimentary rock

R. Gneiss                  3. Intrusive igneous rock

S. Sandstone            4. Metamorphic rock

5. Clastic sedimentary rock

(A)  P-1; Q-3; R-5; S-2

(B)  P-4; Q-5; R-1; S-2

(C)  P-3; Q-1; R-4; S-5

(D)  P-3; Q-4; R-1; S-5

Ans: (C)

14. Which one of the following oceanic ridges is known to be aseismic?

(A)  Carlsberg

(B)  Mid Atlantic

(C)  Ninety East

(D)  Southwest Indian

Ans: (C)

15. Isogonic lines are contours of equal magnetic

(A)  inclination.

(B)  declination.

(C)  total field intensity.

(D)  horizontal field intensity.

Ans: (B)

16. Match the geophysical terms in Group-I with their corresponding units of measurements in Group-II

Group-I                                     Group-II

P. Transit time                           1. mGal

Q. Conductivity                         2. Nano Tesla

R. Gravity anomaly                  3. Siemens

S. Magnetic field intensity      4. millivolt

5. microsecond per feet

(A)  P-5; Q-4; R-2; S-1

(B)  P-5; Q-4; R-3; S-2

(C)  P-5; Q-3; R-1; S-2

(D)  P-4; Q-3; R-2; S-1

Ans: (C)

17. The Maxwell’s equation based on Ampere’s law is

(A)

(B)

(C)

(D)

Ans: (B)

18. The normal gravity formula (for e.g. GRS80) is a function of

(A)  geocentric latitude.

(B)  geodetic latitude.

(C)  longitude.

(D)  altitude.

Ans: (B)

19. A seismic reflection survey was carried out over a subsurface consisting of a stack of horizontal isotropic layers. In the common midpoint (CMP) domain, the moveout (traveltime v/s offset) curve for any primary reflection event is best approximated by

(A)  an ellipse.

(B)  a parabola.

(C)  a circle.

(D)  a hyperbola.

Ans: (D)

20. Assertion(a) : Magnetic stripes are observed around mid-oceanic ridge regions.

Reason (R): The earth’s magnetic field undergoes reversals of polarity.

(A)  (a) is true but (r) is false.

(B)  (a) is false but (r) is true.

(C)  Both (a) and (r) are true and (r) is one of the correct reasons for (a).

(D)  Both (a) and (r) are true but (r) is not the correct reason for (a).

Ans: (C)

21. A seismic gap refers to a

(A)  time gap between two great earthquakes.

(B)  distance gap between the epicenters of two great earthquakes.

(C)  segment of an active belt where a historical great earthquake has not occurred.

(D)  wide gap in the earth created by a great earthquake.

Ans: (C)

22. The travel time difference between the arrival times of a shear wave (S) and primary wave (P) observed on a seismogram recorded at an epicentral distance of 100 km from a near surface earthquake is ______s.

(Assume the average P and S wave velocities to be 6.0 km/s and 3.5 km/s, respectively).

Ans: (11.8 to 12.0)

23. The percentage increase in P-wave velocity (km/s) across the Mohorovicic discontinuity from the lower crust to the upper mantle beneath a carton is approximately________(%)

Ans: (12 to 22)

24. Which one amongst the following logging tools has the largest depth of investigation?

(A)  Density

(B)  Laterolog 3

(C)  Laterolog 8

(D)  Neutron

Ans: (B)

25. The most abundant radioactive isotope in the continental crust is

(A)  40K

(B)  232Th

(C)  235U

(D)  238U

Ans: (A)

Geology (Part B) (Section-1)

26. Stylolitic foliation developed during diagenetic processes is typically

(A)  parallel to bedding.

(B)  perpendicular to bedding.

(C)  oblique to bedding.

(D)  vertical.

Ans: (A)

27. A coal seam with an attitude 090°, 50°S outcrops at an elevation of 1400 m in an area that has flat topography. A vertical exploratory drill hole will intersect the seam

(A)  north of the outcrop at elevations greater than 1400 m.

(B)  north of outcrop at elevations less than 1400 m.

(C)  south of the outcrop at elevations less than 1400 m.

(D)  south of the outcrop at elevations greater than 1400 m.

Ans: (C)

28. Earthquakes result in the formation of which one of the following features?

(A)  Porphyroblast

(B)  Porphyroclast

(C)  Pseudotachylite

Ans: (C)

29. In a bilaterally symmetrical brachiopod fossil, the angle between the hinge line and the median line changes to 45° after deformation. The shear strain observed in the deformed fossil is _______.

Ans: (1)

30. The empirical probability distribution of gold (Au) grades shows a unimodal distribution with mode = 2 g/t, median = 3 g/t, and mean = 5 g/t. This probability distribution is

(A)  positively skewed.

(B)  negatively skewed.

(C)  normally distributed.

(D)  platykurtic.

Ans: (A)

31. A limb of a non-plunging fold with an attitude 070°, 40°S is rotated about is fold axis 30° clockwise (looking towards ENE). The plunge amount of the pole to the fold limb after rotation is ______ degrees.

Ans: (20)

32. The Bulk Silicate Earth (BSE) is best approximated by the average

(A)  enriched upper mantle composition.

(B)  mantle and continental crust composition.

(C)  depleted mantle composition.

(D)  primitive upper mantle composition

Ans: (B)

33. Which one of the following is the stable mineral assemblage in metamorphism of a rock with politic bulk composition under granulite facies?

(A)  staurolite + muscovite + sillimanite + K-feldspar

(B)  phengite + garnet + chloritoid + biotite

(C)  gamet + orthopyroxene + clinopyroxene + plagioclase

(D)  gamet + cordierite + K-fledspar + sillimanite

Ans: (D)

34. The given P-T diagram shows four distinct metamorphic paths designated as 1, 2, 3 and 4. Which one of these P-T paths represents crustal thickening in a collisional tectonic setting?

(A)  1

(B)  2

(C)  3

(D)  4

Ans: (B)

35. The pressure on a rock overlain by a 7 km thick basaltic crust (ρ = 3100 kg m3) is _____ kilobar.

(Use g = 9.8 ms2; 105 Pa = 1 bar)

Ans: (2.0 to 2.2)

36. The given T-X diagram shows the phase relations in olivine solid solution at 1 bar pressure. If ‘P’ is the initial position of melt, the proportion of melt at 1500℃ is ______%.

Ans: (32 to 34)

37. Fluorite crystal (CaF2) adopts face-centered cubic structure with lattice parameter a = 5.463Å. If the ionic radius of anion (F) is 1.71 Å, the ionic radius of cation (Ca2+) is _______Å.

Ans: (2.1 to 2.2)

38. The diagram below shows the interference figure of a mineral. The mineral is

(A)  uniaxial positive.

(B)  biaxial negative.

(C)  uniaxial negative

(D)  biaxial positive.

Ans: (C)

39. The standard thermodynamic data for enstatite (Mg2Si2O6) and forsterite (Mg2SiO­4) is given in the table below. The Gibb’s free energy of the reaction Mg2SiO4 + SiO2 = Mg2­Si2O6 at 600 K and 1 bar is _____ J.

(Assuming Cp = 0 for all minerals in the reaction)

Ans: (−5300 to −4700)

40. The modal abundance in an ultramafic rock and the partition coefficients of lutetium (Lu) in clinopyroxene, orthopyroxene, olivine and plagioclase are tabulated below. The bulk distribution coefficient of lutetium (D­Lu) in the ultramafic rock is _____

Ans: (0.39 to 0.41)

41. Match the following classical ore deposits (Group-I) with their associated ore minerals (Group-II)

Group-I                                              Group-II

P. Sudbury type deposit                     1. Molybdenite

Q. Mississippi valley type deposit    2. Uraninite and chalcopyrite

R. Climax type deposit                       3. Pentlandite

S. IOCG type deposit                          4. Psilomelane

5. Sphalerite and Galena

(A)  P-4; Q-3; R-2; S-1

(B)  P-3; Q-5; R-1; S-2

(C)  P-5; Q-2; R-4; S-1

(D)  P-3; Q-5; R-2; S-4

Ans: (B)

42. Which one of the following microfossils is commonly used in biostratigraphic correlation of Palaeozoic marine strata?

(A)  Angiosperm pollen

(B)  Diatoms

(C)  Dinoflagellates

(D)  Chitinozoans

Ans: (D)

43. Given below are pairs of “living fossils”. Which one of the following is a brachiopod-molusc pair?

(A)  Lingula, Nautihus

(B)  Ginkgo, Metasequia

(C)  Syntexis, Notiothauma

(D)  Coelacanths, Sikhotealinia

Ans: (A)

44. Match the sedimentary rocks and their features listed in Group I with depositional environments listed in Group II.

Group I

(P) Sandstone with herring-bone cross bedding

(Q) Chalk with coccolith

(R) Well sorted arenite with large cross bedding (5-10 m thick)

(S) Poorly sorted sediments with faceted and striated pebbles

Group II

(1) Eolian

(2) Glacial

(3) Sabhka

(4) Tidal

(5) Pelagic

(A)  P-2; Q-1; R-4; S-5

(B)  P-4; Q-5; R-1; S-2

(C)  P-4; Q-1; R-2; S-5

(D)  P-5; Q-1; R-2; S-3

Ans: (B)

45. Arrange the following stratigraphic formations sequentially from older to younger.

(P) Jodhpur Sandstone

(Q) Cambay Shale

(R) Kajrahat Limestone

(S) Tipam Sandstone

(A)  P, R, Q, S

(B)  R, Q, P, S

(C)  P, S, R, Q

(D)  R, P, Q, S

Ans: (D)

46. 2 g air dried coal contains 0.2 g moisture, 0.3 g ash and 0.5 g volatile matter. The volatile matter content in the coal in dry mineral matter free (d.m.f.) basis is _______%.

(mineral matter content = 1.1 × ash content)

Ans: (33.5 to 34.5)

47. The approximate temperature for ‘oil window’ ranges from

(A)  30℃ to 50℃

(B)  60℃ to 160℃

(C)  180℃ to 250℃

(D)  260℃ to 350℃

Ans: (B)

48. Which one of the following biopolymers is the major source of liquid hydrocarbons?

(A)  Lignin

(B)  Proteins

(C)  Lipids

(D)  Carbohydrates

Ans: (C)

49. The hydraulic conductivity (K) of an isotropic aquifer is 10 m/day. If the hydraulic head within the aquifer drops 4 m over a distance of 750 m, the groundwater flow velocity within the aquifer is ______ m/day.

(Up to third decimal place)

Ans: (0.05 to 0.055)

50. Drainage network of a watershed ordered as per the Strahler method is given  below. Maximum observed bifurcation ratio for the given network is _____.

Ans: (2.55 to 2.65)

51. In a vertical aerial photo, the top and bottom of a tower built on a flat terrain is displaced by 2 mm. In the photograph, the distance between top of the tower and nadir point is 100 mm. The flying height of the aircraft was 3000 m above the ground. The estimated height of the tower is _____m.

Ans: (60)

52. Brazilian test was conducted on a rock sample having radius of 27 mm and thickness of 22 mm. The failure load was 5 kN. The tensile strength of the rock is ______ N/mm2.

Ans: (2.50 to 3.00)

53. The average assay (a) and area of influence (A) of a placer gold deposit of uniform thickness sampled at four locations W, X, Y and Z are given below. The weighted average assay of the ore body is ______ g/t.

Ans: (21.00 to 22.00)

54. The minimum and maximum values of the digital number (DN) of a remote sensing image are 8 and 32 respectively. The digital data was linearly stretched between 0 and 255 by using min-max linear stretching method. The post stretched integer DN value of a pixel with an original DNA value of 27 will be _______.

Ans: (201 to 204)

55. The length and width of concave and convex sides of a landslide is shown in the figure below. The Dilation Index of the landslide is ______.

Ans: (2)

Geophysics (Part B) (Section-2)

56. Which one of the following seismic phases is observable in the P-wave shadow zone?

(A)  P

(B)  PmP

(C)  PcS

(D)  PKiKP

Ans: (D)

57. Consider a geological body buried at the equator at a certain depth. If the same body were to be buried at the North pole at the same depth, how would the gravity and magnetic field responses measured overt the body differ? Assume the same magnetic susceptibility and density contrasts. (Consider only geomagnetic induction).

(A)  Both gravity and magnetic field responses do not change.

(B)  Both gravity and magnetic field responses change significantly.

(C)  Gravity field response changes significantly but magnetic field response does not change

(D)  Gravity field response does not change but magnetic field response changes significantly.

Ans: (D)

58. Given the Bouguer density of 2.8 g/cc, the Bouguer correction for a gravity station at an elevation of 30 m above the datum is ____ mGals.

(Use π = 3.14).

Ans: (3.3 to 3.7)

59. Given the following data for a resistivity sounding experiment over a two-layered half-space, the resistivity transform for the top layer is ______Ωm

(Data : resistivity of top layer ρ1 = 10 Ωm, resistivity of half space ρ2 = 100 Ωm, thickness of top layer h1 = 10 m and current electrode spacing AB/2 = 5 m).

Ans: (9.7 to 10.8)

60. The ratio of eccentricity to the polar flattening of an ellipsoidal Earth with equatorial radius ‘e’ and polar radius ‘p’ can be expressed as

(A)

(B)

(C)

(D)

Ans: (C)

61. The vertical field intensity anomaly ∆z due to a vertically polarized vertical dyke is given by

where M is the magnitude of intensity of magnetization. All relevant parameters are provided in the figure below. The dyke has 1% magnetite (magnetic susceptibility of magnetite = 0.5 SI unit) distributed homogeneously. Then, the magnitude of peak vertical field intensity over the dyke is _______nT.

Ans: (76 to 84)

62. In magneto-telluric (MT) experiment over a homogeneous and isotropic half-space, the apparent resistivity is 50 Ωm for an electric field intensity of 12 mV/km and time period of 10 s. Then the magnetic field strength is _____ nT.

Ans: (2.3 to 2.5)

63. The apparent resistivity for Wenner and Schlumberger configurations in an electrical sounding experiment is the same for a certain electrode spacing ‘a’ (Wenner configuration). Given the current electrode spacing of 18 m and the potential electrode spacing of 2 m for a Schlumberger configuration, the value of ‘a’ is ______m.

Ans: (19 to 21)

64. In a time-domain (T-D) induced polarization experiment with a steady voltage of 10 mV during the current flow interval, the voltage decay after the current cut-off is given by v(t) = 4.0e3t mV. The chargegability after current cut-off between t1 = 1 s and t2 = 4 s is _____ms.

Ans: (0.56 to 0.62)

65. Which one of the following statements is TRUE for a near surface earthquake occurring in a homogeneous, isotropic Earth?

(A)  Rayleigh waves are generated.

(B)  Love waves are generated.

(C)  Shear waves are split.

(D)  P waves undergo refraction.

Ans: (A)

66. A dynamic range of 60 dB in power corresponds to an increase in amplitude by a factor of ______.

Ans: (100)

67. The slope of the Wadati plot obtained using the P and S arrival times of local earthquake is 1.0. The corresponding Vp/Vs ratio of the subsurface medium is ______.

Ans: (2)

68. The beach ball figure given below depicts the focal mechanism of an earthquake. The shaded and unshaded portions indicate compressional and dilatational quadrants, respectively. FP1 is the fault plane solution. The focal mechanism and FP1 represent

(A)  a thrust fault with strike 45° and dip 30° with the tension axis in the compression quadrant.

(B)  a normal fault with strike 45° and dip 30° with the tension axis in the compression quadrant.

(C)  a thrust fault with strike 225° and dip 60° with the pressure axis in the compression quadrant.

(D)  a normal fault with strike 225° and dip 60° with the pressure axis in the compression quadrant.

Ans: (A)

69. The characteristic log responses of a thick coal seam are

(A)  low transit time, low resistivity and high gamma ray count.

(B)  low transit time, high resistivity and low gamma ray count.

(C)  high transit time, high resistivity and low gamma ray count.

(D)  high transit time, low resistivity and high gamma ray count.

Ans: (C)

70. The SP response of a thick, clean sandstone bed is −54 mV. Given the mud filtrate resistivity to be 0.45 Ωm at a formation temperature (Tf) of 130℉ and the coefficient, K = 77.29, the formation water resistivity is _____Ω

Ans: (0.08 to 0.10)

71. Which one of the following log responses is TRUE for a porous and permeable sandstone bed, when the resistivity of the mud filtrate used is equal to the resistivity of the formation water?

(A)  A large negative SP is observed.

(B)  A large positive SP is observed.

(C)  LLs and LLm logs show appreciably large separation.

(D)  LLm and LLd logs overlap with each other.

Ans: (D)

72. The number of half-lives (T1/2) required for a certain amount of radioactive isotope in a rock to reduce to 3% of its original amount is ________.

Ans: (5.05 to 5.07)

73. VLF fields can be measured over continental distances (r) because

(A)  the magnetic field decreases at the rate 1/r and the output power at the transmitting station is 1 to 10 kW

(B)  the magnetic field decreases at the rate 1/r3 and the output power at the transmitting station is 1 to 10 kW.

(C)  the magnetic field decreases at the rate 1/r and the output power at the transmitting station is  to 1000 kW.

(D)  the magnetic field decreases at the rate 1/r2 and the output power at the transmitting station is 100 to 1000 kW.

Ans: (C)

74. Convolution of two box car functions of different widths yields a

(A)  step function.

(B)  trapezoidal function.

(C)  box car function.

(D)  sinc function.

Ans: (B)

75. Assuming the Z-transform to be defined with Z as the unit delay operator, the pole of the infinite sequence  is at Z= ______.

Ans: (2)

76. Normal moveout (NMO) correction was applied to seismic data in the common midpoint (CMP) domain. The frequency distortion due to “NMO stretch” is highest for

(A)  larger offsets of deeper reflections.

(B)  smaller offsets of shallower reflections.

(C)  larger offsets of shallower reflections.

(D)  smaller offsets of deeper reflections.

Ans: (C)

77. Consider a hypothetical zero-offset seismic reflection survey acquired over a reflector whose dip is 30°. The velocity of the medium above the reflector is 2 km/s and the trace spacing is 25 m. The maximum unaliased frequency in the data is _____ Hz.

(Hint : The difference in traveltime between adjacent traces should be less than or equal to half a cycle.)

Ans: (40)

78. In statistical wavelet deconvolution, the reflectivity series is assumed to be a random sequence. Then, the autocorrelation of the wavelet is

(A)  a scaled version of the autocorrelation of the seismic trace.

(B)  a random sequence.

(C)  zero.

(D)  dirac-delta function.

Ans: (A)

79. A vector field u is expressed by its Helmoholtz decomposition as u = ∇ϕ + ∇ × ψ, with  and ψ = zy2I + xzj + x2 The magnitude of the divergence of the vector field u at (1, 1, 1) is _______.

Ans: (1)

80. In the figure shown below, a ray corresponding to a P-wave is incident on the interface between layer 1 and layer 2 at an angle of 30°. The P-wave velocity is 1 km/s, 1.2 km/s and 1.5 km/s in layer 1, layer 2 and the half space, respectively. The emergence angle of the ray into the half space is _____ degrees.

Ans: (48 to 49)

81. How do the P-wave velocity (VP), S-wave velocity (VS), and Poisson’s ratio (σ) change from a water saturated sandstone to a gas saturated sandstone?

(A)  VP increases, VS decreases and σ increases.

(B)  VP decreases, VS remains the same and σ decreases.

(C)  VP decreases, VS increases and σ decreases.

(D)  VP, VS and σ all remain constant.

Ans: (B)

82. Consider a vertical Seismic Profiling (VSP) data acquisition experiment as shown in the figure below. The subsurface consists of a horizontal layer of 2 km thickness underlain by a semi-infinite half-space. The P-wave velocities (VP) in the first layer and the half-space are 2.0 km/s and 2.5 km/s, respectively. The vertical well has a string of receivers (denoted by inverted triangles) spaced 10 m apart, with the shallowest receiver at a depth of 0.5 km and the deepest receiver at a depth of 1.5 km. The source (denoted by star) is placed 0.5 km from the well head. The traveltime of the primary reflections event at the deepest receiver is ______s.

Ans: (1.20 to 1.35)

83. Which one of the following sets of vectors {v1, v2, v3} is linearly dependent?

(A)  v1 = (0, −1, 3) v2 = (2, 0, 1), v3 = (−2, −1, 3)

(B)  v1 =(2, −2, 0), v2 = (0, 1, −1), v3 = (0, 4, 2)

(C)  v1 = (2, 6, 2), v2 = (2, 0, −2), v3 = (0, 4, 2)

(D)  v1 = (1, 4, 7), v2 = (2, 5, 8), v3 = (3, 6, 9)

Ans: (D)

84. The condition number for the matrix   is ___.

Ans: (1.5)

85. Match the items listed in Group I with their respective analytical expressions in Group II.

(A)  P-2, Q-3, R-4, S-1

(B)  P-2, Q-4, R-1, S-3

(C)  P-4, Q-2, R-5, S-3

(D)  P-4, Q-3, R-1, S-5

Ans: (B)

General Aptitude

86. The ways in which this game can be played ______ potentially infinite.

(A)  is

(B)  is being

(C)  are

(D)  are being

Ans: (C)

87. If you choose plan P, you will have to _____ plan Q, as these two are mutually______.

(A)  forgo, exclusive

(B)  forget, inclusive

(C)  accept, exhaustive

Ans: (A)

88. If a and b are integers and a – b is even, which of the following must always be even?

(A)  ab

(B)  a2 + b2 + 1

(C)  a2 + b + 1

(D)  ab – b

Ans: (D)

89. A couple has 2 children. The probability that both children are boys if the older one is a boy is

(A)  1/4

(B)  1/3

(C)  1/2

(D)  1

Ans: (C)

90. P looks at Q while Q looks at R. P is married, R is not. The number of pairs of people in which a married person is looking at an unmarried person is

(A)  0

(B)  1

(C)  2

(D)  Cannot be determined

Ans: (B)

91. “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 sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lives 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.”

Which of the following is closest in meaning to ‘cleaving’?

(A)  deteriorating

(B)  arguing

(C)  departing

(D)  splitting

Ans: (D)

92. X bullocks and Y tractors take 8 days to plough a field. If we halve the number bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take X bullocks alone to plough the field?

(A)  30

(B)  35

(C)  40

(D)  45

Ans: (A)

93. There are 4 women P, Q, R, S and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?

(A)  74

(B)  76

(C)  78

(D)  80

Ans: (C)

94. All people in a certain island are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identify. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

Which one of the following can be logically inferred from the above?

(A)  Both P and Q are knights

(B)  P is a knight; Q is a knave

(C)  Both P and Q are knaves

(D)  The identities of P, Q cannot be determined

Ans: (D)

95. In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10℃) and a month is summer (average temperature 30℃)

Consider the following statements based on the data shown above :

i. Over the given months, the difference between the maximum and the minimum pollutants concentrations is the same in both winter and summer.

ii. There are at least four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.

Which one of the following options is correct?

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (B)

## Gate 2017 Ecology and Evolution Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Ecology and Evolution 5th Feb 2017

Subject Name: Ecology and Evolution

Duration : 180

Total Marks: 100

1. The larvae of the monarch butterfly feed exclusively on milkweed plants. These larvae are relatively less susceptible to predation because they are:

(A)  Chemically protected

(B)  Highly aggressive

(C)  Protected by spines

(D)  Visually cryptic

Ans: (A)

2. Which one of the following evolutionary processes best describes Red Queen dynamics?

(A)  Co-evolution

(B)  Convergent evolution

(C)  Divergent evolution

(D)  Parallel evolution

Ans: (A)

3. Social behaviours can evolve to increase or decrease the fitness of the recipient of the behavior. A behavior is considered to be spiteful, when the fitness impact on the actor is _____, while the fitness impact on the recipient is _____.

(A)  negative; negative

(B)  negative; positive

(C)  positive; negative

(D)  positive; positive

Ans: (A)

4. Which of the following set of animals belongs to the group Afrotheria?

(A)  Elephant, dugong, elephant shrew, kangaroo rat

(B)  Elephant, hyrax, elephant shrew, dugong

(C)  Elephant, pika, hyrax, aardvark

(D)  Elephant shrew, dugong, aardvark, pika

Ans: (B)

5. What genetic markers are required to determine paternity in birds?

(A)  Microsatellites

(B)  Mitochondrial DNA

(C)  X chromosome markers

(D)  Z chromosome markers

Ans: (A)

6. Species 1 and 2 are sympatric, but species 2 has a wider physiological tolerance than species 1. The two species simultaneously invade a new environment that has an average temperature of 22 degrees C. What are the expected outcomes for species 1 and 2?

(A)  Both species will survive in the long term

(B)  Neither species will survive in the long term

(C)  Species 1 will outcompete species 2

(D)  Species 2 will outcompete species 1

Ans: (D)

7. Plants have evolved many morphological adaptations to extreme environmental conditions. Which of the following is NOT an adaptation to desert life?

(A)  Dense coat of hairs or spines

(B)  High density of stomata

(C)  Photosynthetic stem

(D)  Succulent or thick leaves

Ans: (B)

8. When large mammals walk in the forest and trample small plants, those plants die. This interspecies relationship is a form of :

(A)  Amensalism

(B)  Commensalism

(C)  Mutualism

(D)  Parasitism

Ans: (A)

9. The population of a widely distributed species gets divided into two subpopulations due to the appearance of a mountain barrier. Eventually these subpopulations evolve into two separate species. This is a case of :

(A)  Allopatric speciation

(B)  Parapatric speciation

(C)  Peripatric speciation

(D)  Sympatric speciation

Ans: (A)

10. In a population, the frequency of genotypes at a locus are A1A1 = 0.16, A1A2 = 0.48, A2A2 = 0.36. The probability of fixation of the A1 allele by genetic drift is _______.

Ans: (0.39 to 0.40)

11. The percent sequence divergence in the mitochondrial cytochrome b gene between two species was found to be 5%. Much of this divergence in the coding region would be contributed by changes at the :

(A)  First position of the codon

(B)  Second position of the codon

(C)  Third position of the codon

(D)  Intron

Ans: (C)

12. In haplo-diploid insects, males are haploid and females are diploid. A female, who is heterozygous for a recessive red-eye colour mutation, mates with a wild-type black-eyed male. What would be the percentage of eye colour phenotypes among their daughters?

(A)  100% red-eye

(B)  100% black-eye

(C)  50% red-eye

(D)  66.7% black-eye

Ans: (B)

13. What is relationship between effective population size (Ne) and total population size (N) of any naturally occurring eukaryotic population?

(A)  Ne is greater than N

(B)  Ne is less than N

(C)  Ne is always equal to N

(D)  Ne is unrelated to N

Ans: (B)

14. The figure below represents the phylogenetic relationship of taxa P-S. Assuming that the branch lengths are proportional to divergence time, which among the following species pairs would be expected to show the most post-zygotic isolation?

(A)  P & S

(B)  Q & R

(C)  R & P

(D)  S & R

Ans: (B)

15. Members of which of the following animal phyla are exclusively marine?

(A)  Cnidaria

(B)  Echinodermata

(C)  Mollusca

(D)  Porifera

Ans: (B)

16. Some amphibians, such as axolotl larvae, rarely metamorphose into an adult form in spite of being sexually mature. This phenomenon of retention of larval characters in the adult form is known as :

(A)  Neoteny

(B)  Ontogeny

(C)  Pedogenesis

(D)  Polyphenism

Ans: (A)

17. Plants are classified into the following major categories : division, class, , order and family. These four categories generally have specific suffixes. Which among the following describes the correct order of specific suffixes for the categories of division, class, order and family respectively?

(A)  −ales, −opsida, −phyta, −aceae

(B)  −opsida, −phyta, −aceae, −ales

(C)  −phyta, −ales, −opsida, −aceae

(D)  −phyta, −opsida, −ales, −aceae

Ans: (D)

18. The Indian cricket team captain has lost the coin toss for nine consecutive games. Assuming that an unbiased coin is being used throughout the tournament, the chance that the Indian captain will win the toss on the 10th game is ______.

Ans: (0.499 to 0.501)

19. Consider the function y = ex. The slope of this function at x = 10 is

(A)  0

(B)  10

(C)  e10

(D)  10 e10

Ans: (C)

20. Which of the following best demonstrates the phenomenon of a sign stimulus as defined in classical ethology? A male stickleback fish performing an aggressive display when presented with :

(A)  A diamond-shaped model with the lower half painted red

(B)  A life-like model of a male stickleback fish with a red  belly

(C)  A mirror

(D)  A video-recording of another male stickleback fish with a red belly

Ans: (A)

21. Eating puffer fish can sometimes be fatal for human beings. This is because puffer fish carry a potent toxin known as :

(A)  Botulinum toxin

(B)  Bungarotoxin

(C)  Conotoxin

(D)  Tetrodotoxin

Ans: (D)

22. The ‘Selfish Herd’ hypothesis for group behavior predicts :

(A)  Competition among individuals for central positions in groups

(B)  Competition among individuals for peripheral positions in groups

(C)  Competition for food among individuals in groups

(D)  Co-operative defence against predators

Ans: (A)

23. Birds that inhabit forests typically produce calls in the form of low-pitched whistles. The most likely reason is that low-pitched whistles :

(A)  Area easy to localize

(B)  Experience high levels of scattering

(C)  Transmit over greater distances

(D)  Travel faster than high-pitched whistles

Ans: (C)

24. At mid-latitudes, which of the following biomes is associated with hot dry summers and cool rainy winters?

(A)  Boreal Forests

(B)  Chapparal Forests

(C)  Temperate Broadleaf Deciduous Forests

(D)  Temperate Grasslands

Ans: (B)

25. Rafflesia arnoldii produces one of the largest flowers on earth and is typically pollinated by :

(A)  Bats

(B)  Bees

(C)  Birds

(D)  Flies

Ans: (D)

26. Lantana camara is an invasive weed introduced into India from South America. If you characterize the genetic variation of this species in both its native and introduced populations, the South American population is expected to have :

(A)  higher number of alleles per locus than the Indian population

(B)  higher homozygosity than the Indian population

(C)  lower number of alleles per locus than the Indian population

(D)  lower genetic diversity than the Indian population

Ans: (A)

27. Which of the following combination of properties of neuronal circuits mediating escape behavior in animals would make them most effective at evading predators?

(A)  large-diameter axons and chemical synapses

(B)  Large-diameter axons and electrical synapses

(C)  Small-diameter axons and chemical synapses

(D)  Small-diameter axons and electrical synapses

Ans: (B)

28. An experimentalist rejects a null hypothesis because she finds a p-value to be 0.01. This implies that :

(A)  There is a 1% chance that the alternative hypothesis explains the data

(B)  There is a 1% chance that the null hypothesis explains the data

(C)  There is a 99% chance that the alternative hypothesis explains the data

(D)  There is a 99% chance that the null hypothesis explains the data

Ans: (B)

29. A student counts every individual blackbuck in two grasslands. He finds 2100 and 2300 blackbuck in the two areas. Which statistical test is required to establish that these two population sizes are different?

(A)  Chi-square test

(B)  F-test

(C)  No test is required

(D)  Student’s t-test

Ans: (C)

30. The plot below shows the fitness of two traits as a function of relative frequency of trait-1 in the population. The solid line represents the fitness of trait-1 and the dotted line represents the fitness of trait-2. Which of the following is most likely to be TRUE?

(A)  Either Trait-1 or Trait-2 will take over the population

(B)  Only Triat-1 will take over the population

(C)  Trait-1 and Trait-2 will always reach a coexistence equilibrium

(D)  Trait-1 and Trait-2 will oscillate over time

Ans: (A)

31. The following figure shows the phylogeny of insect species 1-5. Each of these 5 insect species harbours a specific bacterial endosymbiont. S R, Q, T and P are the endosymbiont bacteria associated with insect species 1, 2, 3, 4 and 5, respectively.

Which one of the following symbiont phylogenetic trees suggests host shift by these endosymbionts?

(A)

(B)

(C)

(D)

Ans: (C)

32. P to T are islands of different sizes at different distances from the mainland, where the distance x < y < z. The area of island P > Q > R = S = T. Assuming that there is migration only from the mainland to islands and not between islands, which of the following is NOT true about species richness on these islands?

(A)  P > Q > R

(B)  R > S > T

(C)  Q > T > S

(D)  S < Q < P

Ans: (C)

33. The frequency of an allele at a locus on the non-recombining region of the Y chromosome in humans is 0.3. If the population size is N and the sex ratio is 1 : 1, what is the number of copies of the alleles in the population ?

(A)  0.3 N/4

(B)  0.3 N/2

(C)  0.3 N

(D)  0.6 N

Ans: (B)

34. The species compositions of three areas, P, Q and R are shown below :

P : Cobra, Gecko, Crow, Viper

Q : Viper, Tiger, Salamander, Fish

R : Salamander, Viper, Frog, Chameleon

Based on the relationship between species, one can determine the phylogenetic diversity of each region. Which of the following captures the order of phylogenetic diversity of these regions?

(A)  Q > P = R

(B)  Q = R > P

(C)  Q > R > P

(D)  R > Q > P

Ans: (C)

35. Recent paleogenomic studies indicate that some groups of living humans have Neanderthal genes in their genomes. What is the best explanation for this phenomenon?

(A)  Modern humans descended directly from Neanderthals

(B)  Neanderthals are still living among us

(C)  Some genes in modern humans has reverted to Neanderthal-like sequences

(D)  Some ancestors of living humans hybridized with the Neanderthals

Ans: (D)

36. A population grows as per the equation dn/dt = rn (1 – n/1000) where n is the population density, r is the intrinsic growth rate and 1000 is the carrying capacity. The growth rate of the population is maximum at a population density o f _________

Ans: (499.9 to 500.1)

37. An ecology exam paper has a large number of multiple choice questions with five options each, of which only one is correct. An unprepared student picks one of the five given options randomly, and attempts all questions. A correct answer yields one mark whereas a wrong answer yields negative x mark(s). To ensure that an unprepared student most likely gets zero marks, the value of x must be _______(write only the magnitude, not the sign).

Ans: (0.249 to 0.251)

38. Increasing atmospheric CO2 concentration is likely to benefit C3 plants more than C4 plants because :

(A)  C4 photosynthesis is inhibited by increasing CO2

(B)  Carboxylation increase relative to oxygenation in C3 plants

(C)  Oxygenation is suppressed in C4 plants

(D)  Transpiration increases with increasing Co2 in C4 plants

Ans: (B)

39. In meta communities composed of species A and B, the rates of colonization of habitat patches by A and C are CA and CB. The rates of extinction for species A and B in the absence of competition, are EA and EB. Species A is the superior competitor within any given patch. Which one of the following conditions is necessary to allow the continued persistence of species B?

(A)  EA > EB

(B)  CB/EB > CA/EA

(C)  CB­/EB < CA/EA

(D)  CB > CA

Ans: (B)

40. Batesian and Mullerian mimicry are effective anti-predatory defences because predators show :

(A)  Habituation

(B)  Imprinting

(C)  Learning by negative reinforcement

(D)  Learning by positive reinforcement

Ans: (C)

41. A species possesses ten types of olfactory receptors (encoded by ten unique gene sequences) but i s able to perceptually distinguish a hundred different odorants. This is possible because each olfactory receptor type :

(A)  binds to a subset of the 100 odorant molecules with unequal affinities

(B)  binds to all 100 types of odorant molecules with equal affinity

(C)  changes its specificity in relation to the odorant molecule

(D)  is specific and binds only one species of odorant molecule

Ans: (A)

42. Among vertebrates, male-only parental care is more commonly found among fishes and amphibians than birds and mammals. The most likely reason for this is because fishes and amphibians are characterized by :

(A)  External fertilization

(B)  Moist skin

(C)  Poikilothermy

(D)  Sexual dimorphism

Ans: (A)

43. Guppies are fish that typically have blue, red and yellow spots on their bodies. In an experiment, one group of guppies was subjected to treatment X, where they were maintained and allowed to breed for several generations in ponds containing their natural predator species. A second group of fish was subjected to treatment Y, where they were maintained and allowed to breed for the same number of generations in ponds from which all predators were removed. After several generations, it was found that guppies subjected to treatment X had lost their blue spots, whereas those subjected to treatment Y showed an increase in the number of blue spots. Based on these observations, which one of t he following statements can be rejected?

(A)  Blue spots on guppies are subject to natural selection

(B)  Blue spots on guppies may be subject to sexual selection

(C)  Blue spots are likely to make guppies more conspicuous to predators

(D)  Blue spots are likely to make guppies less conspicuous to predators

Ans: (D)

44. Which of the following is NOT a plausible explanation for the evolution of seed dispersal mechanisms in plants?

(A)  Long-distance dispersal benefits the dispersal agent

(B)  Seed dispersal agents carry seeds to areas favourable for germination

(C)  Seeds falling close to the parent plant have a higher risk of predation

(D)  The area close to the parent plant is not optimal because of competition with kin

Ans: (A)

45. Which of the following evolutionary changes was NOT associated with the colonization of land by plants?

(A)  Acquisition of dynein-mediated transport

(B)  Acquisition of Jasmonic acid signaling

(C)  Acquisition of vasculature

(D)  Acquisition of seed desiccation tolerance

Ans: (A)

46. For a given low population size, which of these plant species are more likely to experience Allee effects?

(A)  Asexual plants

(B)  Bisexual plants

(C)  Dioecious plants

(D)  Monoecious plants

Ans: (C)

47. Which of the following combinations of leaf traits is most likely to be observed in terrestrial plant communities that occur in low-nutrient environment with herbivory?

(A)  High levels of protein and high levels of chemical defences

(B)  High levels of protein and low levels of chemical defences

(C)  Low levels of protein and high levels of chemical defences

(D)  Low levels of protein and low levels of chemical defences

Ans: (C)

48. Which of the following sets of parameters form the basis of Holdridge’s lifezone classification?

(A)  Altitude, Mean Annual Biotemperature, Annual Precipitation

(B)  Annual Precipitation, Mean Annual Biotemperature, Length of dry season

(C)  Potential Evapotranspiration, Annual Maximum Temperature, Annual Precipitation

(D)  Potential Evapotranspiration Ratio, Mean Annual Biotemperature, Annual Precipitation

Ans: (D)

49. The Annual Net Primary Productivity (ANPP) of ecosystems varies with the type of biome. Which of the following represents the correct order of ANPP values?

(A)  Temperate Broadleaf Forest > Tropical Moist Forest > Boreal Forest > Savanna

(B)  Tropical Moist Forest > Savanna > Temperate Broadleaf Forest > Boreal Forest

(C)  Tropical Moist Forest > Temperate Broadleaf Forest > Boreal Forest > Savanna

(D)  Tropical Moist Forest > Temperate Broadleaf Forest > Savanna > Boreal Forest

Ans: (D)

50. Which of these communities (R1, R2, R3, and R4) each with 80 species and represented  by their Species Rank-Abundance curves, is likely to have the highest value of Shannon’s index of species diversity?

(A)  R1

(B)  R2

(C)  R3

(D)  R4

Ans: (A)

51. In any experimental design, we prefer a large sample size because :

(A)  It reduces errors in the estimation of the mean effect

(B)  It reduces the possibility of outliers

(C)  It reduces type-I errors

(D)  It reduces variability between different data points

Ans: (A)

52. In haplo-diploid insects, males are haploid and females are diploid. For a haplo-diploid species, assume that each individual mates only once. The minimum coefficient of relatedness between two female cousins, whose maternal grandmother is the same, is ________(enter answer to 4 decimal places).

Ans: (0.185 to 0.190)

53. Match the scientists with the concept or theories they are most famously associated with :

(A)  P – i; Q – iii; R – iv; S – ii

(B)  P – iv; Q – iii; R – ii; S – i

(C)  P – iv; Q – iii; R – i; S – ii

(D)  P – iv; Q – i; R – ii; S – iii

Ans: (C)

54. Which of the following graphs best represents the function given by the following equation :

(A)

(B)

(C)

(D)

Ans: (A)

55. On the semi-arid plateaus of the Western Ghats, raptors, lizards and grasshoppers dominate the community of animals. Raptors prey primarily on lizards, which prey primarily on grasshoppers. If raptor density declines significantly, which of the following is expected?

(A)  Both grasshopper and plant densities will increase

(B)  Only grasshopper density will increase

(C)  Plant density will increase

(D)  Plant density will decrease

Ans: (C)

56. She has a sharp tongue and it can occasionally turn ______

(A)  hurtful

(B)  left

(C)  methodical

(D)  vital

Ans: (A)

57. I ____ make arrangements had I ____ informed earlier.

(A)  could have, been

(B)  would have, being

(D)  had been, been

Ans: (A)

58. 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%

Which of the following statements is correct?

(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.

Ans: (D)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

(A)  120

(B)  144

(C)  160

(D)  212

Ans: (B)

60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions 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

iv. All benches are chairs.

(A)  Only i

(B)  Only ii

(C)  Only ii and iii

(D)  Only iv

Ans: (B)

61. ‘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 multilation will have in the respective section, and ultimately on Asia, you will not find 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

Ans: (D)

62. T.U.V.W.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

Ans: (A)

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

(A)  1440

(B)  1200

(C)  720

(D)  600

Ans: (A)

64. 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

Ans: (A)

65. A contour line joins 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

Ans: (C)

## Gate 2017 Electrical Engineering Question Paper 11th Feb 2017 Session 2 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electrical Engineering 11th Feb 2017 Session 2

Subject Name: Electrical Engineering

Duration : 180

Total Marks: 100

1. In the circuit shown, the diodes are ideal, the inductance is small, and Io ≠ Which one of the following statements is true?

(A) D1 conducts for greater than 180° and D2 conducts for greater than 180°

(B) D2 conducts for more than 180° and D2 conducts for 180°

(C) D1 conducts for 180° and D2 conducts for 180° .

(D) D1 conducts for more than 180° and D2 conducts for 180°

Ans: (A)

2. For a 3-input logic circuit shown below, the output Z can be expressed as

(A)

(B)

(C)

(D)

Ans: (C)

3. An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

(A)  1/2

(B)  4/9

(C)  5/9

(D)  6/9

Ans: (A)

4. When a unit ramp input is applied to the unity feedback system having closed loop transfer function  the steady state error will be

(A)

(B)

(C)

(D)

Ans: (D)

5. A three-phase voltage source inverter with ideal devices operating in o 180 conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is Vdc. The peak of the fundamental component of the phase voltage is

(A)

(B)

(C)

(D)

Ans: (B)

6. The figures show diagrammatic representations of vector fields  respectively. Which one of the following choices is true?

(A)

(B)

(C)

(D)

Ans: (C)

7. Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.

Ans: (0.9)

8. Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

(A) uniformly over the entire volume of the sphere

(B) uniformly over the outer surface of the sphere

(C) concentrated around the centre of the sphere

(D) along a straight line passing through the centre of the sphere

Ans: (B)

9. The transfer function C(s) of a compensator is given below.

The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is

(A)  0.1 < ω < 1

(B)  1 < ω < 10

(C)  10 < ω < 100

(D)  ω > 100

Ans: (A)

10. The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts.

For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2× 2. Which one of the following statements is true?

(A)  Both Ybus and Zbus are symmetric

(B)  Ybus is symmetric and Zbus­ is unsymmetric

(C)  Ybus is unsymmetric and Zbus is symmetric

(D)  Both Ybus and Zbus are unsymmetric

Ans: (D)

11. A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is

(A)  25

(B)  50

(C)  100

(D)  300

Ans: (C)

12. Let x and y be integers satisfying the following equations

2x2 + y2 = 34

x + 2y = 11

The value of (x + y) is ________.

Ans: (7)

13. Consider a function f(x, y, z) given by

f(x, y, z) = (x2 + y2 – 2z2) (y2 + z2)

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is ________

Ans: (40)

14. For the given 2-port network, the value of transfer impedance Z21 in ohms is_______

Ans: (3)

15. The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)

Ans: (100)

16. The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T1 and T2 are 90° and 270°, respectively.

The RMS value of the current through diode D3 in amperes is ________

Ans: (0)

17. In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100× If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.

Ans: (61)

18. A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

(A)  1500

(B)  1470

(C)  157

(D)  154

Ans: (C)

19. Two resistors with nominal resistance values R1 and R2 have additive uncertainties ∆R1 and ∆R2, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

(A)

(B)

(C)

(D)

Ans: (A)

20. The nominal- π circuit of a transmission line is shown in the figure.

Impedance  and reactance X = 3300Ω. The magnitude of the characteristic impedance of the transmission line, in Ω, is _______________. (Give the answer up to one decimal place.)

Ans: (406.2)

21. The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Which one of the following is TRUE about the frequency selectivity of these systems?

(A) All three are high-pass filters.

(B) All three are band-pass filters.

(C) All three are low-pass filters.

(D) P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter.

Ans: (B)

22. The mean square value of the given periodic waveform f (t) is_________

Ans: (6)

23. A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHZ. The frequency of the vertical input is

(A)  1.5 kHz

(B)  2 kHz

(C)  3 kHz

(D)  4.5 kHz

Ans: (D)

24. Let y2 – 2y + 1 = x and √x + y = 5. The value of x + √y equals ______. (Give the answer up to three decimal places)

Ans: (5.732)

25. If a synchronous motor is running at a leading power factor, its excitation induced voltage (E­f) is

(A)  equal to terminal voltage Vt

(B)  higher than the terminal voltage Vt

(C)  less than terminal voltage Vt

(D)  dependent upon supply voltage Vt

Ans: (B)

26. Which of the following systems has maximum peak overshoot due to a unit step input?

(A)

(B)

(C)

(D)

Ans: (C)

27. Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab = Dbc = Dca = 1m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω/ km (rounded off to three decimal places) is ________

Ans: (0.289)

28. Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger unit is _______ MW.

Ans: (400)

29. For the network given in figure below, the Thevenin‟s voltage Vab is

(A)  −1.5 V

(B)  −0.5 V

(C)  0.5 V

(D)  1.5 V

Ans: (A)

30. The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

(A) 1000 samples/s

(B) 1500 sample/s

(C) 2000 samples/s

(D) 3000samples/s

Ans: (B)

31. A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance Ra = 0.02Ω. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is

(A)  34.2 A

(B)  30 A

(C)  22 A

(D)  4.84 A

Ans: (B)

32. A cascade system having the impulse responses  is shown in the figure below, where symbol ↑ denotes the time origin.

The input sequence x (n) for which the cascade system produces an output sequence  is

(A)

(B)

(C)

(D)

Ans: (D)

33. For the circuit shown in the figure below, it is given that The transistor has β = 29 and VBE = 0.7 V when the B-E junction is forward biased.

For this circuit, the value of  is

(A)  43

(B)  92

(C)  121

(D)  129

Ans: (D)

34. A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ________ electrical degrees.

Ans: (12.7)

35. For the circuit shown below, assume that the OPAMP is ideal.

Which one of the following is TRUE?

(A)  Vo = vs

(B)  vo = 1.5vs

(C)  vo = 2.5vs

(D)  vo = 5vs

Ans: (C)

36. The root locus of the feedback control system having the characteristic equation s2 + 6Ks + 2s + 5 = 0 where K > 0, enters into the real axis at

(A)  s = −1

(B)  s = −√5

(C)  s = −5

(D)  s = √5

Ans: (B)

37. For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions

The minimum number of clock cycles after which the output Z would again become zero is ________

Ans: (6)

38. In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

(A)  1 nF

(B)  1 μF

(C)  1 mF

(D)  10 mF

Ans: (D)

39. In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is ________. (Give the answer up to one decimal place.)

Ans: (40)

40. In the circuit shown in the figure, the diode used is ideal. The input power factor is _______. (Give the answer up to two decimal places.)

Ans: (0.707)

41. Consider the system described by the following state space representation

If u(t) is a unit step input and  the value of output y(t) at t = 1 sec (rounded off to three decimal places) is ________

Ans: (1.2838)

42. A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R1 = 0.3Ω, R2 = 0.3Ω, X1 = 0.41Ω, X2 = 0.41Ω Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3-phase AC source is __________.

Ans: (71.04)

43. A 25 kVA, 400 V, ∆ – connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.

Ans: (−14.6)

44. If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA. Y− ∆ transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is_____.

Ans: (37.879)

45. For the balanced Y-Y connected 3-Phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

(A)  33∠−53.1°Ω

(B)  60∠53.1°Ω

(C)  60∠−53.1°Ω

(D)  180∠−53.1°Ω

Ans: (C)

46. A thin soap bubble of radius R = 1 cm, and thickness a = 3.3μm(a <<R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is 4πR2a and that of the drop is  The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.)

Ans: (10.03)

47. The value of the contour integral in the complex-plane

Along the contour |Z| = 3, taken counter-clockwise is

(A)  −18πi

(B)  0

(C)  14πi

(D)  48πi

Ans: (C)

48. Let

Consider the composition of f and g, i.e., (f ∘ g) (x) = f(g(x)). The number of discontinuities in (f ∘ g) present in the interval (−∞, 0) is:

(A)  0

(B)  1

(C)  2

(D)  4

Ans: (A)

49. A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω, and the shunt field resistance is 240Ω. The no load speed, in rpm, is ________.

Ans: (1241.82)

50. A 10 ½ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.

Ans: (10000)

51. A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y} , where var {.} denotes the variance, equals

(A)

(B)

(C)

(D)

Ans: (C)

52. The figure below shows a half-bridge voltage source inverter supplying an RL-load with  The desired fundamental frequency of the load voltage is 50 Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. M = 0.6. At 50 Hz, the RL-load draws an active power of 1.44 kW. The value of DC source voltage VDC in volts is

(A)  300√2

(B)  500

(C)  500√2

(D)  1000√2

Ans: (C)

53. The range of K for which all the roots of the equation s3 + 3s2 + 2s + K = 0 are in the left half of the complex s-plane is

(A)  0 < K < 6

(B)  0 < K < 16

(C)  6 < K < 36

(D)  6 < K < 16

Ans: (A)

54. The eigen values of the matrix given below are

(A)  (0, −1, −3)

(B)  (0, −2, −3)

(C)  (0, 2, 3)

(D)  (0, 1, 3)

Ans: (A)

55. A 3-phase 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25Ω and 3.925Ω If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.

Ans: (0.737)

56. There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W, Z is to the East of X and the West of V, W is to the West of Y. Which is the building in the middle?

(A)  V

(B)  W

(C)  X

(D)  Y

Ans: (A)

57. Saturn is _________ to be seen on a clear night with the naked eye.

(A) enough bright

(B) bright enough

(C) as enough bright

(D) bright as enough

Ans: (B)

58. Choose the option with words that are not synonyms.

(A)  aversion, dislike

(C) plunder, loot

(D) yielding, resistant

Ans: (D)

59. There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

(A)  1/5

(B)  7/30

(C)  1/4

(D)  4/15

Ans: (D)

60. A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

(A)  12

(B)  15

(C)  18

(D)  19

Ans: (B)

61. An air pressure contour line joins locations in a region having the same  atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

(A)  P

(B)  Q

(C)  R

(D)  S

Ans: (C)

62. There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

(A) The box labelled “Apples”

(B) The box labelled “Apples and Oranges”

(C) The box labelled “Oranges”

(D) Cannot be determined

Ans: (B)

63. “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”

The author’s belief that ideology is not as important as literature is revealed by the word:

(A)  ‘culture’

(B)  ‘seemingly’

(C)  ‘urgent’

(D)  ‘political’

Ans: (B)

64. X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number 3 X will have

(A)  90 digits

(B)  91 digits

(C)  92 digits

(D)  93 digits

Ans: (A)

65. The number of roots of ex + 0.5x2 – 2 = 0 in the range [−5, 5] is

(A)  0

(B)  1

(C)  2

(D)  3

Ans: (C)

## Gate 2017 Electrical Engineering Question Paper 11th Feb 2017 Session 1 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electrical Engineering 11th Feb 2017 Session 1

Subject Name: Electrical Engineering

Duration : 180

Total Marks: 100

1. Consider

Here,  represents the largest integer less than or equal to t and  denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

Ans: (0)

2. A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are Van = 220 sin (100 πt) V and ia = 10 sin(100 πt)A, respectively. Similarly for phase-b the instantaneous voltage and current are Vbn = 220 cos(100 πt) V and ib = 10 cos(100 πt) A, respectively.

The total instantaneous power flowing form the source to the load is

(A)  2200 W

(B)  2200 sin2 (100 πt) W

(C)  440 W

(D)  2200 sin(100 πt) cos (100 πt) W

Ans: (A)

3. A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30 Ω per phase. The load angle is 30°. The power delivered to the motor in kW is _______.

Ans: (835 to 842)

4. For a complex number z, is

(A)  −2i

(B)  −i

(C)  i

(D)  2i

Ans: (D)

5. Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?

(A) The particles will never collide

(B) All will collide together

(C) Proton and Neutron

(D) Electron and Neutron

Ans: (D)

6. Let z(t) = x(t) * y(t), where “ * ” denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).

(A)  c.x(ct) * y(ct)

(B)  x(ct) * y(ct)

(C)  c.x (t) * y(ct)

(D)  c.x(ct) * y(t)

Ans: (A)

7. A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are Y11 = −j12pu, Y22 = −j15pu and Y33 = −j7pu

The per unit values of the line reactances p, q and r shown in the figure are

(A) p = −0.2, q = −0.1, r = −0.5

(B) p = 0.2, q = 0.1, r = 0.5

(C) p = −5, q = −10, r = −2

(D) p = 5, q =10, r = 2

Ans: (B)

8. The equivalent resistance between the terminals A and B is ______ Ω.

Ans: (2.9 to 3.1)

9. The Boolean expression  simplifies to

(A)

(B)

(C)

(D)

Ans: (A)

10. The following measurements are obtained on a single phase load:

V = 220V ±1%, I = 5.0A ±1% and W = 555W±2%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ______.

Ans: (4)

11. The transfer function of a system is given by,  . Let the output of the system be vo(t) = Vm sin(ωt + φ) for the input vi(t) = Vm sin(ωt). Then the minimum and maximum values of φ (in radians) are respectively

(A)

(B)

(C)

(D)

Ans: (D)

12. The matrix  has three distinct eigenvalues and one of its eigenvectors is

Which one of the following can be another eigenvector of A?

(A)

(B)

(C)

(D)

Ans: (C)

13. For the power semiconductor devices IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?

(A) All of the four are majority carrier devices.

(B) All the four are minority carrier devices

(C)  IGBT and MOSFET are majority carrier devices, whereas Diode and Thyristor are minority carrier devices.

(D) MOSFET is majority carrier device, whereas IGBT, Diode, Thyristor are minority carrier devices.

Ans: (D)

14. Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30° is _______.

Ans: (1.01 to 1.06)

15. A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

(A) bend closer to the cylinder axis

(B) bend farther away from the axis

(C) remain uniform as before

(D) cease to exist inside the cylinder

Ans: (A)

16. Let  where R is the region shown in the figure and c = 6 × 10−4. The value of I equals ______.

Ans: (0.99 to 1.01)

17. Consider the system with following input-output relation y[n] = (1 + (−1)n)x[n] where, x[n] is the input and y[n] is the output. The system is

(A) invertible and time invariant

(B) invertible and time varying

(C) non-invertible and time invariant

(D) non-invertible and time varying

Ans: (D)

18. The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of

(A) 150 ns has to be inserted into the y-channel

(B) 150 ns has to be inserted into the x-channel

(C) 150 ns has to be inserted into both x and y channels

(D) 100 ns has to be inserted into both x and y channels

Ans: (A)

19. A 3-phase voltage source inverter is supplied from a 600V DC source as shown in the figure below. For a star connected resistive load of 20 Ω per phase, the load power for 120o device conduction, in kW is __________.

Ans: (8.5 to 9.5)

20. A closed loop system has the characteristic equation given by s3 + Ks2 + (K + 2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

(A) 0 < K < 0.5

(B) 0.5 < K < 1

(C) 0 < K < 1

(D) K > 1

Ans: (D)

21. A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is

(A)  1350

(B)  1650

(C)  1950

(D)  2250

Ans: (C)

22. For the circuit shown in the figure below, assume that diodes D1, D2 and D3 are ideal.

The DC components of voltages v1 and v2, respectively are

(A) 0 V and 1 V

(B) −0.5 V and 0.5 V

(C) 1 V and 0.5 V

(D) 1 V and 1 V

Ans: (B)

23. A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______

Ans: (14)

24. The power supplied by the 25 V source in the figure shown below is ________W.

Ans: (248 to 252)

25. In the converter circuit shown below, the switches are controlled such that the load voltage vo(t) is a 400 Hz square wave.

The RMS value of the fundamental component of vo(t) in volts is _______.

Ans: (196 to 200)

26. The output expression for the Karnaugh map shown below is

(A)

(B)

(C)

(D)

Ans: (D)

27. A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4Ω and 0.1 Ω The load torque varies as the square of the speed. The flux in the motor may be taken as being proportional to the armature current. To reduce the speed of the motor by 50% the resistance in ohms that should be added in series with the armature is _________.

Ans: (9.5 to 12)

28. The transfer function of the system Y(s)/U(s) whose state-space equations are given below is:

(A)

(B)

(C)

(D)

Ans: (D)

29. The load shown in the figure is supplied by a 400 V (line to line) 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three watt-meters W1, W2 and W3 read 577.35 W each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

(A)  W1 = 1732 and W2 = W3 = 0

(B)  W1 = 0, W2 = 1732 and W3 = 0

(C)  W1 = 866, W2 = 0, W3 = 866

(D)  W1 = W2 = 0 and W3 = 1732

Ans: (D)

30. Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

A1 , B1,C1, D1, A2, B2, C2 and D2 are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source VT and impedance ZT connected in series, then

(A)

(B)

(C)

(D)

Ans: (D)

31. The circuit shown in the figure uses matched transistors with a thermal voltage VT = 25mV. The base currents of the transistors are negligible. The value of the resistance R in kΩ that is required to provide 1μA bias current for the differential amplifier block shown is ______.

Ans: (170 to 174)

32. The figure below shows an uncontrolled diode bridge rectifier supplied form a 220 V, 50 Hz 1-phase ac source. The load draws a constant current Io= 14A. The conduction angle of the diode D1 in degrees is___________.

Ans: (220 to 230)

33. Consider the differential equation  with y(1) = 2π. There exists a unique solution for this differential equation when t belongs to the interval

(A)  (−2, 2)

(B)  (−10, 10)

(C)  (−10, 2)

(D)  (0, 10)

Ans: (A)

34. A separately excited DC generator supplies 150 A to a 145 V DC grid. The generator is running at 800 RPM. The armature resistance of the generator is 0.1 Ω . If the speed of the generator is increased to 1000 RPM, the current in amperes supplied by the generator to the DC grid is _______.

Ans: (548 to 552)

35. In the circuit shown below, the maximum power transferred to the resistor R is _______ W.

Ans: (3 to 3.1)

36. Let a causal LTI system be characterized by the following differential equation, with initial rest condition

Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

(A)  2e2tu(t) – 7e5tu(t)

(B)  −2e2tu(t) + 7e5tu(t)

(C)  7e2tu(t) – 2e5tu(t)

(D)  −7e2tu(t) + 2e5tu(t)

Ans: (B)

37. The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

(A)

(B)

(C)

(D)

Ans: (A)

38. The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for t ≥ 0, is

(A)  2.5e4t

(B)  5e4t

(C)  2.5e0.25t

(D)  5e0.25t

Ans: (A)

39. The bus admittance matrix for a power system network is

There is a transmission line, connected between buses 1 and 3, which is represented by the circuit shown in figure.

If this transmission line is removed from service, What is the modified bus admittance matrix?

(A)

(B)

(C)

(D)

Ans: (C)

40. In the system whose signal flow graph is shown in the figure, U1(s) and U2 (s) are inputs. The transfer function  is

(A)

(B)

(C)

(D)

Ans: (A)

41. For a system having transfer function  a unit input is applied at time t = 0. The value of the response of the system at t = 1.5 sec is _____.

Ans: (0.550 to 0.556)

42. The magnitude of magnetic flux density (B) in micro Teslas (μT) at the center of a loop of wire wound as a regular hexagon of side length 1m carrying a current (I=1A), and placed in vacuum as shown in the figure is __________.

Ans: (0.65 to 0.75)

43. The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sin δ, where δ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of δ as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is Pmax sinδ, the value of Pmax, in pu is ______.

Ans: (1.21 to 1.23)

44. A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Zm = (12.50 + j15.75)Ω (main winding), Za = (24.50 + j12.75)Ω (auxiliary windings). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.

Ans: (95 to 100)

45. A function f(x) is defined as  where x ∈ ℝ.

Which one of the following statement is TRUE?

(A) f(x) is NOT differentiable at x=1 for any values of a and b.

(B) f(x) is differentiable at x = 1 for the unique values of a and b

(C) f(x) is differentiable at x = 1 for all values of a and b such that a + b = e

(D) f(x) is differentiable at x = 1 for all values of a and b.

Ans: (A)

46. Consider a causal and stable LTI system with rational transfer function H(z). Whose corresponding impulse response begins at n = 0. Furthermore,  The poles of H(z) are   for k = 1, 2, 3, 4. The zeros of H(z) are all at z = 0. Let g[n] = jnh[n]. The value of g[8] equals

Ans: (0.06 to 0.65)

47. Only one of the real roots of f(x) = x6 – x – 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is ________.

Ans: (10)

48. Two parallel connected, three-phase, 50Hz, 11kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are 1Ω and 3Ω Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is ________.

Ans: (2.05 to 2.13)

49. The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero).

Ans: (0.1)

50. Let the signal  be passed through an LTI system with frequency response H(ω) , as given in the figure below

The Fourier series representation of the output is given as

(A)  4000 + 4000cos(2000πt) + 4000cos(4000πt)

(B)  2000 + 2000 cos(2000πt) + 2000 cos(4000πt)

(C)  4000 cos(2000 πt)

(D)  2000 cos(2000πt)

Ans: (C)

51. The logical gate implemented using the circuit shown below where. V1 and V2 are inputs (with 0 V as digital 0 and 5 V as digital 1) and VOUT is the output is

(A)  NOT

(B)  NOR

(C)  NAND

(D)  XOR

Ans: (B)

52. A load is supplied by a 230 V, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that 1 kW ≤ P ≤ 2kW and 1kVAR ≤ Q ≤ A capacitor connected across the load for power factor correction generates 1 kVAR reactive power. The worst case power factor after power factor correction is

(A)  0.447 lag

(B)  0.707 lag

(C)  0.894 lag

(D)  1

Ans: (B)

53. The input voltage VDC of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio D of the converter for which the magnitude of the steady state output voltage remains constant at 48 V is

(A)

(B)

(C)

(D)

Ans: (A)

54. A three-phase, three winding ∆/∆/Y (1.1 kV/6.6kv/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV winding and 300 kVA load at 0.6 power factor lag from the 400 V winding. The RMS line current in ampere drawn by the 1.1 kV winding from the mains is _______.

Ans: (623 to 627)

55. Consider the line integral  where z = x + iy. The line C is shown in the figure below.

The value of I is.

(A)

(B)

(C)

(D)

Ans: (B)

56. Research in the workplace reveals that people work for many

(A) money beside

(B) beside money

(C) money besides

(D) besides money

Ans: (D)

57. The probability that a k-digit number does NOT contain the digits 0.5, or 9 is

(A)  0.3k

(B)  0.6k

(C)  0.7k

(D)  0.9k

Ans: (C)

58. Find the smallest number y such that y × 162 is a perfect cube.

(A)  24

(B)  27

(C)  32

(D)  36

Ans: (D)

59. After Rajendra Chola returned from his voyage to Indoneisa, he _______ to visit the temple in Thanjavur.

(A)  was wishing

(B)  is wishing

(C)  wished

Ans: (C)

60. Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

(A) Rahul and Murali

(B) Srinivas and Anil

(C) Srinivas and Murali

(D) Srinivas and Rahul

Ans: (C)

61. Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

(A)  2

(B)  3

(C)  4

(D)  Cannot be determined

Ans: (A)

62. The expression  is equal to

(A)  the maximum of x and y

(B)  the minimum of x and y

(C)  1

(D)  none of the above

Ans: (B)

63. A contour line joins 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 25m intervals in this plot. If in a flood, the water level rises to 525m. Which of the villages P,Q,R,S,T get submerged?

(A)  P, Q

(B)  P, Q, T

(C)  R, S, T

(D)  Q, R, S

Ans: (C)

64. Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white, Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

(A)  21

(B)  18

(C)  16

(D)  14

Ans: (D)

65. “The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history.”

Which of the following statements best reflects the author’s opinion?

(A) Nationalists are highly imaginative.

(B) History is viewed through the filter of nationalism.

(C) Our colonial past never happened

(D) Nationalism has to be both adequately and properly imagined.

Ans: (B)

## Gate 2017 Electronics and Communication Engineering Question Paper 5th Feb 2017 Session 2 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electronics and Communication Engineering 5th Feb 2017 Session 2

Subject Name: Electronics and Communication Engineering

Duration : 180

Total Marks: 100

1. Consider the circuit shown in the figure.

The Boolean expression F implemented by the circuit is

(A)

(B)

(C)

(D)

Ans: (B)

2. An LTI system with unit sample response h[n] = 5δ[n] – 7δ[n – 1] + 7δ[n – 3] – 5δ[n – 4] is a

(A)  Low – pass filter

(B)  high – pass filter

(C)  band – pass filter

(D)  band – stop filter

Ans: (C)

3. In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V. The ratio is _______.

Ans: (0.19 to 0.21)

4. In a DRAM,

(A) periodic refreshing is not required

(B) information is stored in a capacitor

(C) information is stored in a latch

(D) both read and write operations can be performed simultaneously

Ans: (B)

5. Consider an n-channel MOSFET having width W, length L, electron mobility in the channel μn and oxide capacitance per unit are C0%. If gate-to-source voltage VGS = 0.7V, drain-to-source voltage VDS = 0.1V, (μnC0%) = 100μA/V2, threshold voltage VTH = 0.3 V and (W/L) = 50 then the transconductance gm(in mA/V) is _______.

Ans: (0.45 to 0.55)

6. Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.

For some charge placed on this structure, the potential and surface electric field on S1 are Va and Ea, and that on S2 are Vb and Eb, respectively, which of the following is CORRECT?

(A)  Va = Vb and Ea < Eb

(B)  Va > Vb and Ea > Eb

(C)  Va = Vb and Ea > Eb

(D)  Va > Vb and Ea = Eb

Ans: (C)

7. For the circuit shown in the figure, P and Q are the inputs and Y is the output.

The logic implemented by the circuit is

(A)  XNOR

(B)  XOR

(C)  NOR

(D)  OR

Ans: (B)

8. An n-channel enhancement mode MOSFET is biased at VGS > VTH and VDS > (VGS – VTH), where VGS is the gate-to-source voltage, VDS is the drain-to-source voltage and VTH is the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a

(A) voltage source with zero output impedance

(B) voltage source with non-zero output impedance

(C) current source with finite output impedance

(D) current source with infinite output impedance

Ans: (C)

9. A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10Ω, 5Ω, 2Ω are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ____________.

Ans: (2.12 to 2.16)

10. An npn bipolar junction transistor (BJT) is operating in the active region. If the reverse bias across the base – collector junction is increased, then

(A) the effective base width increases and common – emitter current gain increases

(B) the effective base width increases and common – emitter current gain decreases

(C) the effective base width decreases and common – emitter current gain increases

(D) the effective base width decreases and common – emitter current gain decreases

Ans: (C)

11. Consider the state space realization  with the initial condition  where u(t) denotes the unit step function. The value of   is ________.

Ans: (4.99 to 5.01)

12. The rank of the matrix  is _______.

13. A two – wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is ______________

Ans: (48.0 to 51.0)

14. The input x(t) and the output y (t) of a continuous-time system are related as  The system is

(A) Linear and time-variant

(B) Linear and time-invariant

(C) Non-linear and time-variant

(D) Non-linear and time-invariant

Ans: (B)

15. Which of the following statements is incorrect?

(A) Lead compensator is used to reduce the settling time.

(B) Lag compensator is used to reduce the steady state error.

(C) Lead compensator may increase the order of a system.

(D) Lag compensator always stabilizes an unstable system.

Ans: (D)

16. The residues of a function  are

(A)

(B)

(C)

(D)

Ans: (B)

17. A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is _______

Ans: (7)

18. The general solution of the differential equation  in terms of arbitrary constants K1 and K2 is

(A)

(B)

(C)

(D)

Ans: (A)

19. Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P?

(A)

(B)

(C)

(D)

Ans: (C)

20. The output V0 of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is ____________.

Ans: (3.15 to 3.21)

21. Consider the random process X(t) = U + Vt, where U is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is ____________

Ans: (2)

22. For the system shown in the figure, Y (s) / X (s) = __________.

Ans: (0.95 to 1.05)

23. The smaller angle (in degrees) between the planes x + y + z =1 and 2x – y + 2z = 0 is ________.

Ans: (54.0 to 55.0)

24. Consider the circuit shown in the figure. Assume base-to- emitter voltage VBE=0.8 V and common base current gain (α) of the transistor is unity.

The value of the collector- to – emitter voltage VCE (in volt) is _______.

Ans: (5.5 to 6.5)

25. In the figure, D1 is a real silicon pn junction diode with a drop of 0.7V under forward bias condition and D2 is a zener diode with breakdown voltage of -6.8 V. The input Vin(t) is a periodic square wave of period T, whose one period is shown in the figure.

Assuming 10τ << T.where τ is the time constant of the circuit, the maximum and minimum values of the output waveform are respectively,

(A) 7.5 V and –20.5V

(B) 6.1 V and –21.9V

(C) 7.5 V and –21.2 V

(D) 6.1 V and –22.6 V

Ans: (A)

26. If the vector  is irrotational, then the values of the constants k1, k2 and k3 respectively, are

(A) 0.3, –2.5, 0.5

(B) 0.0, 3.0, 2.0

(C) 0.3, 0.33, 0.5

(D) 4.0, 3.0, 2.0

Ans: (B)

27. The un-modulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduced to 40%, then the maximum un-modulated carrier power (in kW) that can be used without overloading the transmitter is ___________

Ans: (5.19 to 5.23)

28. Consider an LTI system with magnitude response

And phase response Arg {H(f)} = −2f.

If the input to the system is

Then the average power of the output signal y(t) is

Ans: (7.95 to 8.05)

29. A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV. EC – FF = 0.9 eV, where EC and EF are the conduction band minimum and the Fermi energy levels of Si, respectively. Oxide ∈r = 3.9, ∈0 = 8.85 × 1014 F/cm. oxide thickness tox = 0.1 μm and electronic charge q = 1.6 × 1019 If the measured flat band voltage of the capacitor is −1V, then the magnitude of the fixed charge at the oxide-semiconductor interface, in nC/cm2, is ______.

Ans: (6.85 to 6.95)

30. An electron (q1) is moving in free space with velocity 105 m/s towards a stationary electron (q2) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is _______×108

[Given, mass of electron m = 9.11 × 1031 kg, charge of electron e = −1.6 × 1019 C, and permittivity ε0 = (1/36π) × 109 F/m]

Ans: (4.55 to 5.55)

31. The values of the integrals  are

(A) same and equal to 0.5

(B) same and equal to –0.5

(C) 0.5 and – 0.5, respectively

(D) – 0.5 and 0.5, respectively

Ans: (C)

32. Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is _________.

Ans: (2.4 to 2.6)

33. Figure I shows a 4-bits ripple carry adder realized using full adders and Figure II shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure II are 20 ns, 15 ns and 10 ns respectively. Assume all the inputs to the 4-bit adder are initially reset to 0.

At t=0, the inputs to the 4-bit adder are changed to

X3X2X1X0 = 1100, Y3Y2Y1Y0 = 0100 and Z0 = 1.

The output of the ripple carry adder will be stable at t (in ns) = ___________

Ans: (70)

34. The permittivity of water at optical frequencies is 1.75 ε0 . It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5m, as shown in the figure. The critical angle is θc.

The value of d (in meter) is _____________

Ans: (4.2 to 4.4)

35. A unity feedback control system is characterized by the open-loop transfer function

The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below.

If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right –half of the s-plane is

(A)  0

(B)  1

(C)  2

(D)  3

Ans: (C)

36. The signal x(t) = sin(14000πt), where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :

What is the number of sinusoids in the output and their frequencies in kHz?

(A) Number = 1, frequency = 7

(B)  Number = 3, frequencies= 2,7,11

(C) Number = 2, frequencies = 2, 7

(D) Number = 2, frequencies = 2, 11

Ans: (B)

37. A unity feedback control system is characterized by the open-loop transfer function

The value of k for which the system oscillates at 2 rad/s is ________.

Ans: (0.74 to 0.76)

38. Consider the circuit shown in the figure.

The Thevenin equivalent resistance (in Ω ) across P – Q is _________.

Ans: (−1.01 to −0.99)

39. The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = [sin(t)/πt]u(t), where u(t) is a unit step function, the system output y(t) as t → ∞ is ______.

Ans: (0.45 to 0.55)

40. An integral I over a counter clock wise circle C is given by . If C is defined as |z| = 3, then the value of I is

(A)  −πi sin(1)

(B)  −2πi sin(1)

(C)  −3πi sin(1)

(D)  −4πi sin(1)

Ans: (D)

41. Consider a binary memory less channel characterized by the transition probability diagram shown in the figure.

The channel is

(A)  Lossless

(B)  Noiseless

(C)  Useless

(D)  Deterministic

Ans: (C)

42. An abrupt pn junction (located at x = 0) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the x-direction is E(x). Which of the following figures represents the electric field profile near the pn junction?

(A)

(B)

(C)

(D)

Ans: (A)

43. A second – order LTI system is described by the following state equations,

Where x1 (t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t) = x1(t). The system is

(A) Undamped (oscillatory)

(B) Under damped

(C) Critically damped

(D) Over damped

Ans: (D)

44. Consider the parallel combination of two LTI systems shown in the figure.

The impulse responses of the systems are

h1(t) = 2δ(t + 2) – 3δ(t + 1)

h2(t) = δ(t – 2)

If the input x(t) is a unit step signal, then the energy of y(t) is ____________.

Ans: (7.0)

45. Assuming that transistors M1 and M2 are identical and have a threshold voltage of 1V, the state of transistors M1 and M2 are respectively.

(A) Saturation, Saturation

(B) Linear, Linear

(C) Linear, Saturation

(D) Saturation, Linear

Ans: (C)

46. A programmable logic array (PLA) is shown in the figure.

The Boolean function F implemented is

(A)

(B)

(C)

(D)

Ans: (C)

47. A modulating signal given By x(t) = 5 sin(4π103t – 10π cos 2π103t)V is fed to a phase modulator with phase deviation constant kp = 0.5 rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________

Ans: (69.9 to 70.1)

48. The minimum value of the function in the interval −100 ≤ x ≤ 100 occurs at x = _____.

Ans: (−100.01 to −99.99)

49. The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0. The current i(t) (in ampere) at t = 0.5 seconds is ________

Ans: (8.0 to 8.3)

50. In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors Q1, Q2….., Q32 are identical in all respects and have infinitely large values of common – emitter current the relation IC = IS exp ((VBE/VT), where Is is the saturation current. Assume that the voltage VP shown in the figure is 0.7 V and the thermal voltage VT = 26m V.

The output voltage Vout(in volts) is __________.

Ans: (1.1 to 1.2)

51. The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input „In‟ and an output „Out‟. The initial state of the FSM is S0.

If the input sequence is 10101101001101, starting with the left-most bit, then the number times „Out‟ will be 1 is __________.

Ans: (4)

52. Standard air – filled rectangular waveguides of dimensions a = 2.29 cm and b= 1.02 cm are designed for radar applications. It is desired that these waveguides operate only in the dominatnt TE10 mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is

(A) 8.19 GHz ≤ f ≤ 13.1 GHz

(B) 8.19 GHz ≤ f ≤ 12.45 GHz

(C) 6.55 GHz ≤ f ≤ 13.1 GHz

(D) 1.64 GHz ≤ f ≤ 10.24 GHz

Ans: (B)

53. For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (JL) is 2.5 mA/cm2 and the open-circuit voltage (Voc) is 0.451 V. Consider thermal voltage (VT) to be 25 mV. If the intensity of the incident light is increased by 20 times, assuming that the temperature remains unchanged V (in volts) will be _______.

Ans: (0.51 to 0.54)

54. In the circuit shown, transistors Q1 and Q2 are biased at a collector current of 2.6mA. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of 26 mV, the magnitude of voltage gain V0/Vs in the mid-band frequency range is _____________ (up to second decimal place).

Ans: (49.0 to 51.0)

55. Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double that of T1. Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage  of T2 is double that of T1, where VGS and VTH are the gate – to – source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T1 are ID1 and gm1 respectively, the corresponding values of these two parameters for T2 are

(A)  8ID1 and 2gm1

(B)  8ID1 and 4gm1

(C)  4ID1 and 4gm1

(D)  4ID1 and 2gm1

Ans: (B)

56. The ninth and the tenth of this month are Monday and Tuesday ___________.

(A)  figuratively

(B)  retrospectively

(C)  respectively

(D)  rightfully

Ans: (C)

57. 500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186). Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A)  37

(B)  43

(C)  47

(D)  53

Ans: (D)

58. It is _________ to read this year’s textbook __________ the last year’s.

(A) easier, than

(B) most easy, than

(C) easier, from

(D) easiest, from

Ans: (A)

59. Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?

(A) 8km, East

(B) 12 km, North

(C) 6km, East

(D) 10km, North

Ans: (A)

60. A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking beer. What must be checked to ensure that the rule is being followed?

(A) Only P’s drink

(B) Only P’s drink and S’s age

(C) Only S’s age

(D) Only P’s drink, Q’s drink and S’s age

Ans: (B)

61. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A) X is the mother-in-law of R

(B) P and R are not married to each other

(C) P is a son of X and Y

(D) Q cannot be married to R

Ans: (D)

62. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A)  781

(B)  791

(C)  881

(D)  891

Ans: (C)

63. A contour line joins 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 25m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A)  P to Q

(B)  P to R

(C)  P to S

(D)  P to T

Ans: (B)

64. 1200 men and 500 women can build a bridge in 2weeks. 900men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A)  3000

(B)  3300

(C)  3600

(D)  3900

Ans: (C)

65. “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.”

Which of the following statements best reflects the author’s opinion?

(A) An intimate association does not allow for the necessary perspective.

(B) Matters are recorded with an impartial perspective.

(C) An intimate association offers an impartial perspective.

(D) Actors are typically associated with the impartial recording of matters.

Ans: (A)

## Gate 2017 Electronics and Communication Engineering Question Paper 5th Feb 2017 Session 1 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electronics and Communication Engineering 5th Feb 2017 Session 1

Subject Name: Electronics and Communication Engineering

Duration : 180

Total Marks: 100

1. 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

Ans: (C)

2. 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

Which one of the following statements is true about the system?

(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

Ans: (A)

3. Consider the following statement about the linear dependence of the real valued functions y1 = 1, y2 = x and y3 = x2, over the field of real numbers.

I. y1, y2 and y3 are linearly independent on −1 ≤ x ≤ 0

II. y1, y2 and y3 are linearly dependent on 0 ≤ x ≤ 1

III. y1, y2 and y3­ are linearly independent on 0 ≤ x ≤ 1

IV. y1, y2 and y3 are linearly dependent on −1 ≤ x ≤ 0

Which one among the following is correct?

(A) Both I and II are true

(B) Both I and III are true

(C) Both II and IV are true

(D) Both III and IV are true

Ans: (B)

4. Consider the 5 × 5 matrix

It is given that A has only one real eigen value. Then the real eigen value of A is

(A)  −2.5

(B)  0

(C)  15

(D)  25

Ans: (C)

5. The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is V(ℓ) = e−−γℓ +jωt volts, Where ℓ is the distance along the length of the cable in meters. γ = (0.1 + j40)m−1 is the complex propagation constant, and ω = 2π × 109 rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.

Ans: (0.85 to 0.88)

6. 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

Ans: (A)

7. The rank of the matrix  is

(A)  0

(B)  1

(C)  2

(D)  3

Ans: (C)

8. For a narrow base PNP BJT, the excess minority carrier concentration (∆nE for emitter, ∆pB for base. ∆nC for collector) normalized to equilibrium minority carrier concentration (nE0 for emitter, pB0 for base, nC0 for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?

(A) Forward active

(B) Saturation

(C) Inverse active

(D) Cutoff

Ans: (C)

9. The Miller effect in the context of a Common Emitter amplifier explains

(A) an increase in the low-frequency cutoff frequency

(B) an increase in the high-frequency cutoff frequency

(C) a decrease in the low-frequency cutoff frequency

(D) a decrease in the high-frequency cutoff frequency

Ans: (D)

10. Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output latch in percentage is ___________.

Ans: (2.9 to 30.1)

11. Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?

(A)

(B)

(C)

(D)

Ans: (A)

12. 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”

Ans: (B)

13. 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) __________.

Ans: (0.027 to 0.028)

14. A periodic signal x(t) has a trigonometric Fourier series expansion

If x(t) = −x – (t) = −x(t – π/ω0), we can conclude that

(A)  an are zero for all and bn are zero for n even

(B)  an are zero for all n and bn are zero for n odd

(C)  an are zero for n even and bn zero for n odd

(D)  an are zero for n odd and bn are zero for n even

Ans: (A)

15. The open loop transfer function

Where p is an integer, is connected in unity feedback configuration as shown in figure.

Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.

Ans: (0.99 to 1.01)

16. An n+ − n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of ND1 = 1 × 1018 cm3 and ND2 = 1 × 1015 cm3 corresponding to the n+ and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic carrier concentration to be ni = 1 × 1010 cm3. What is the magnitude of the built-in potential of this device?

(A)  0.748V

(B)  0.460V

(C)  0.288V

(D)  0.173V

Ans: (D)

17. For the operational amplifier circuit shown, the output saturation voltages are ±15V. The upper and lower threshold voltages for the circuit are, respectively.

(A)  +5V and −5V

(B)  +7V and −3V

(C)  +3V and −7V

(D)  +3V and −3V

Ans: (B)

18. In the circuit shown, the positive angular frequency ω (in radians per second) at which magnitude of the phase difference between the voltages V­1 and V2 equals  is________.

Ans: (0.9 to 1.1)

19. In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is inter symbol interference zero?

(A)

(B)

(C)

(D)

Ans: (B)

20. Consider a stable system with transfer function

Where b1,….,bp and a1,….aq are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to −60 dB decade as ω→∞. A possible pair of values for p and q is

(A) p = 0 and q = 3

(B) p =1and q = 7

(C) p = 2 and q = 3

(D) p = 3 and q = 5

Ans: (A)

21. 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

Ans: (C)

22. Let (X1 ,X2) be independent random variables. X1 has been 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 _______.

Ans: (0)

23. Consider the following statements for continuous-time linear time invariant (LTI) systems.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.

II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

(A) Both I and II are true

(B) Both I and II are not true

(C) Only I is true

(D) Only II is true

Ans: (D)

24. Which one of the following statements about differential pulse code modulation (DPCM) is true?

(A) The sum of message signal sample with its prediction is quantized

(B) The message signal sample is directly quantized, and its prediction is not used

(C) The difference of message signal sample and a random signal is quantized

(D) The difference of message signal sample with its predictions is quantized

Ans: (D)

25. Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

(A) increases by a factor of 2

(B) decrease by a factor 2

(C) remains unchanged

(D) decreases by a factor of √2

Ans: (C)

26. Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of Newton-Rapson’s method (up to two decimal places) is ________.

Ans: (0.65 to 0.72)

27. In binary frequency shift keying (FSK), the given signal waveform are

u0(t) = 5 cos(20000πt); 0≤t ≤ T, and

u1(t) = 5 cos(22000πt); 0≤t≤T

Where T is the bit-duration interval and t is in seconds. Both u0(t) and u1(t) are zero outside the interval 0 ≤ t ≤ T. With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u0(t) and u1(t) uncorrelated is

(A)  0.25 ms

(B)  0.5 ms

(C)  0.75 ms

(D)  1.0 ms

Ans: (B)

28. For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector current are equal. Given that VT = 25 mV, VBE = 0.7V, and  the BJT output resistance r0 is practically infinite. Under these conditions, the midband voltage gain magnitude. Ac = |Vo/Vi|V/V, is ____________.

Ans: (127.0 to 129.0)

29. The figure shows an RLC circuit exited by the sinusoidal voltage 100cos (3t) volts, where t is in seconds. The ratio  is _________.

Ans: (2.55 to 2.65)

30. Which one of the following is the general solution of the first order differential equation  where x, y are real?

(A)  y = 1 + x + tan1 (x + c), where c is a constant

(B)  y = 1 + x + tan(x + c), where c is a constant

(C)  y = 1 – x + tan1(x + c), where c is a constant

(D)  y = 1 – x + tan(x + c), where c is a constant

Ans: (D)

31. A linear time invariant (LTI) system with the transfer function is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed loop system is stable for

(A)  K > 1.5

(B)  1 < K < 1.5

(C)  0 < K < 1

(D)  no positive value of K

Ans: (A)

32. Let  where x, y, z are real, and let C be th straight line segment from point A : (0, 2, 1) to point B : (4, 1, −1). The value of I is _______.

Ans: (−11.1 to −10.9)

33. As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentration of ND1 = 1014 cm−3 and ND2 = 1016 cm−3 in the n-regions of the diodes, and uniform acceptor doping concentration of NAl = 1014 cm−3 and NA2 = 1016 cm−3 in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is >> built-in potentials of the diodes, the ratio C2/C1 of their reverse bias capacitances for the same applied reverse bias, is __________.

Ans: (10.0 to 10.0)

34. An optical fiber is kept along the The refractive indices for the electric fields along  directions in the fiber are nx = 1.5000 and ny = 1.5001, respectively (nx ≠ ny due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5μm. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeter, is ___________.

Ans: (0.36 to 0.38)

35. 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 of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _______.

Ans: (31)

36. Which one of the following options correctly describes the locations of the roots of the equations s4 + s2 + 1 = 0 on the complex plane?

(A) Four left half plane (LHP) roots

(B) One right half plane (RHP) root, one LHP root and two roots on the imaginary axis

(C) Two RHP roots and two LHP roots

(D) All four roots are on the imaginary axis

Ans: (C)

37. The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n = 1 × 1016 cm−3 and electronic charge q = 1.6 × 10−19 C. If a bias of 5V is applied across a 1 μm region of this semiconductor, the resulting current density in this region, in kA/cm2, is ________.

Ans: (1.5 to 1.7)

38. For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage Vtn = 1V and its transconductance parameter  Neglect channel length modulation and body bias effects. Under these conditions, the drain current ID in mA is _________.

Ans: (1.9 to 2.1)

39. Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response

As shown in Figure (b). The output of the lowpass filter is Y(t).

Let E be the expectation operator and consider the following statements.

I. E(X(t)) = E(Y(t))

II. E(X2(t)) = E(Y2(t))

III. E(Y2(t)) = 2

Select the correct option:

(A) only I is true

(B) only II and III are true

(C) only I and II are true

(D) only I and III are true

Ans: (A)

40. As shown a uniformly doped Silicon (Si) bar of length L = 0.1 μm with a donor concentration ND = 1016 cm−3 is illuminated at x = 0 such that electron and hole pairs are generated at the rate of   where GL0 = 1017 cm−3 s−1. Hole lifetime is 10−4 s, electronic charge q = 1.6 × 10−19 C, hole diffusion coefficient Dp = 100 cm2/s and low level injection condition prevails. Assuming linearly decaying steady state excess hole concentration that goes to 0 at x = L, the magnitude of the diffusion current density at x = L/2, in A/cm2, is _______.

Ans: (15.9 to 16.1)

41. The Nyquist plot of the transfer function  does not encircle the point (1 + j0) for K = 10 but does encircle the point (−1 + j0) for K = 100. Then the closed loop system (having unity gain feedback) is

(A) stable for K = 10 and stable for K = 100

(B) stable for K = 10 and unstable for K = 100

(C) unstable for K = 10 and stable for K =100

(D)  unstable for K = 10 and unstable for K = 100

Ans: (B)

42. In the figure shown, the npn transistor acts as a switch

For the input Vin(t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage saturation VCE(sat) = 0.2 V and base-to-emitter voltage VBE = 0.7V. The minimum value of the common-base current gain (α) of the transistor for the switching should be _______.

Ans: (0.89 to 0.91)

43. A three dimensional region R of finite volume is described by x2 + y2 ≤ z3; 0 ≤ z ≤ 1, Where x, y, z are real. The volume of R(up to two decimal places) is _________.

Ans: (0.70 to 0.85)

44. The expression for an electric field in free space is

where x, y, z represent the spatial coordinates, t represents time, and ω, k are constants. This electric field

(A) does not represent a plane wave

(B) represents a circular polarized plane wave propagating normal to the z-axis

(C) represents an elliptically polarized plane wave propagating along x-y plane.

(D) represents a linearly polarized plane wave

Ans: (C)

45. A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are QAQB = 00, 01, 10 and 11.

Assume that XIN = 1is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state QAQB = 00 and clocked, after a few clock cycles, it starts cycling through

(A)  all of the four possible states if XIN = 1

(B)  three of the four possible states if XIN = 1

(C)  only two of the four possible states if XIN = 1

(D)  only two of the four possible states is XIN = 0

Ans: (D)

46. Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t)

I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6π rad/s

For the three statements above, which one of the following is correct?

(A) only II and III are true

(B) only I and III are true

(C) only III is true

(D) only I is true

Ans: (B)

47. A 4-bit shift register circuit configured for right-shift operation, i.e, Din → A, A → B, B → C, C → D, is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is _______.

Ans: (10.0 to 10.0)

48. Let  for real x. From among the following choose the Taylor series approximation of f(x) around x = 0, which included all powers of x less than or equal to 3.

(A)    1 + x + x2 + x3

(B)

(C)

(D)

Ans: (C)

49. The following FIVE instructions were executed on an 8085 microprocessor.

MVI A, 33H

MVI B, 78H

CMA

ANI 32H

The Accumulator value immediately after the execution of the fifth instruction is

(A)  00H

(B)  10H

(C)  11H

(D)  32H

Ans: (B)

50. In the circuit shown, the voltage VIN(t) is described by:

Where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is ___________.

Ans: (0.30 to 0.40)

51. A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ ϕ ≤ π. Here the angle θ(0 ≤ θ < π) is measured from the z-axis, and the angle ϕ(0 ≤ ϕ ≤ 2π) is measured from the x-axis in the x-y plane.

(A)  θ = 90°, ϕ = 45°

(B)  θ = 45°, ϕ = 90°

(C)  θ = 90°, ϕ = 135°

(D)  θ = 45°, ϕ = 135°

Ans: (A)

52. The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, Ao = 105V/V and an open-loop cut-off frequency fc = 8Hz. The voltage gain of the amplifier at 15 kHz, in V/V is _______.

Ans: (43.3 to 45.3)

53. Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by and h[n] = 0 for n < 0 and n > 2.

Let H(ω) be the discrete-time Fourier system transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H(ω0) = 0 and 0 < ω0 < π, the value of ω0 (in radians) is equal to ________.

Ans: (2.05 to 2.15)

54. Which one of the following gives the simplified sum of products expression for the Boolean function F = m0 + m2 + m3 + m5, where m0, m­2, m3 and m5 are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

(A)

(B)

(C)

(D)

Ans: (B)

55. A continuous time signal x(t) = 4 cos (200 πt) + 8 cos (400 πt), 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 _______.

Ans: (7.90 to 8.10)

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

(A)   hurtful

(B)   left

(C)   methodical

(D)   vital

Ans: (A)

57. 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

(iv) All benches are chairs

(A) only (i)

(B) only (ii)

(C) only (ii) and (iii)

(D) only (iv)

Ans: (B)

58. 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

Ans: (B)

59. 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%.

Which of the following statement is correct?

(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

Ans: (D)

60. I ________ made arrangements had I _________informed earlier.

(A) could have, been

(B) would have, being

(D) had been, been

Ans: (A)

61. “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

Ans: (D)

62. 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

Ans: (A)

63. 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

Ans: (C)

64. 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

Ans: (A)

65. 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

Ans: (A)

## Gate 2017 Chemistry Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Chemistry 5th Feb 2017

Subject Name: Chemistry

Duration : 180

Total Marks: 100

1. Consider N particle at temperature T, pressure P, volume V and chemical potential μ having energy E. The parameters that are kept constant for a canonical ensemble are

(A)  N, V, T

(B)  N, V, E

(C)  N, P, T

(D)  μ, V, T

Ans: (A)

2. For ortho-hydrogen, the nuclear wave function and the rotational quantum number, respectively, are

(A)  antisymmetric and even

(B)  symmetric and odd

(C)  symmetric and even

(D)  antisymmetric and odd

Ans: (B)

3. m1 and m2 are the slopes (dp/dT) of the solid-liquid equilibrium lines in the P-T phase diagrams of H2O and CO2, respectively. For P < 10 atm, the values of m1 and m2 are

(A)  m1 > 0 and m2 > 0

(B)  m1 > 0 and m2 < 0

(C)  m1 < 0 and m2 < 0

(D)  m­1 < 0 and m2 > 0

Ans: (D)

4. The rate constant of reaction is 1.25 × 104 mol L1 s1. If the initial concentration of the reactant is 0.250 mol L1, the total time (in seconds) required for complete conversion is _______

Ans: (1999 to 2001)

5. Consider the ideal gas of volume V at temperature T and pressure P. If the entropy of the gas is S, the partial derivative (∂P/∂S)V is equal to

(A)  (∂T/∂P)S

(B)  (∂T/∂V)P

(C)  −(∂T/∂V)S

(D)  (∂T/∂S)P

Ans: (C)

6. The wavelength associated with a particle in one-dimensional box of length L is (n refers to the quantum number)

(A)  2L/n

(B)  L/n

(C)  nL

(D)  L/2n

Ans: (A)

7. The dependence of rate constant k on temperature T (in K) of a reaction is given by the expression

ln k = [(−5000 K)/T] + 10

The activation energy of the reaction (in kJ mol1 is ______ (up to two decimal places)

Ans: (41.50 to 41.60)

8. The lowest energy of a quantum mechanical one-dimensional simple harmonic oscillator is 300 cm1. The energy (in cm1) of the next higher level is ______

Ans: (899 to 901)

9. The electronic ground state term for the chromium ion in [Cr(CN)6]4 is

(A)  3F

(B)  3H

(C)  3G

(D)  5D

Ans: (B)

10. The  ions exhibit intense ligand to metal charge transfer transition. The wavelengths of this transition follow the order

(A)

(B)

(C)

(D)

Ans: (C)

11. The lanthanide ion that exhibits color in aqueous solution is

(A)  La(III)

(B)  Eu(III)

(C)  Gd(III)

(D)  Lu(III)

Ans: (B)

12. The hapticity of cycloheptatriene, (C7H8), in Mo(C7H8)(CO)3 is___________

Ans: (6)

13. The Vo-o resonance Raman stretching frequency (in cm1) of the O2 coordinated to iron centre in oxy-hemoglobin nearly

(A)  1100

(B)  850

(C)  1550

(D)  1950

Ans: (A)

14. The energy band diagram fro magnesium is (The hatched an unhatced regions in the figure correspond to filled and unfilled regions of the band, respectively.)

(A)

(B)

(C)

(D)

Ans: (D)

15. P, F and I represent primitive, face-centered and body-centered lattices, respectively. The lattice types of NaCl and CsCl, respectively, are

(A)  F and I

(B)  F and P

(C)  I and P

(D)  P and I

Ans: (B)

16. The characteristic feature of an electron spin resonance (ESR) spectrum of frozen aqueous solution of CuSO4∙5H2O at 77 K is

(A)  g > g

(B)  g < g

(C)  g = g

(D)  gx ≠ gy ≠ gz

Ans: (A)

17. The most suitable reagent for the following transformation is

(A)  Li/Liq. NH3

(B)  PtO2/H2

(C)  LiAlH4

(D)  B2H6

Ans: (A)

18. The major products M and N formed in the following reactions are

(A)

(B)

(C)

(D)

Ans: (C)

19. The 13C NMR spectrum of acetone-d6 has a signal at 30 ppm as a septel in the intensity ratio

(A)  1 : 6 : 15 : 20 : 15 : 6 : 1

(B)  1 : 3 : 6 : 7 : 6 : 3 : 1

(C)  1 : 2 : 3 : 5 : 3 : 2 : 1

(D)  1 : 3 : 7 : 10 : 7 : 3 : 1

Ans: (B)

20. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Ans: (D)

21. The major product obtained in the following reaction is

(A)

(B)

(C)

(D)

Ans: (B)

22. In the two reaction sequence given below, the starting bis-sulfone acts as

(A)  a dienophile and synthetic equivalent of acetylene

(B)  a dienophile and synthetic equivalent of ethylene

(C)  a dipolarophile and synthetic equivalent of acetylene

(D)  a dipolarophile and synthetic equivalent of ethylene

Ans: (A)

23. The major product formed in the following photochemical reaction is

(A)

(B)

(C)

(D)

Ans: (B)

24. The product formed in the following reaction is

(A)

(B)

(C)

(D)

Ans: (D)

25. The number of possible stereoisomers for cyclononene is _______

Ans: (3)

26. The mobility of a univalent ion in aqueous solution is 6.00 × 108 m2 s1 V1 at 300 K. Its diffusion coefficient at 300 K is X × 109 m2 s1. The value of X is __________ up to two decimal places)

Ans: (1.50 to 1.60)

27. For the following consecutive first order reactions

the time (in seconds) required for Y to reach its maximum concentration (assuming only X is present at time t = 0) is ___________(up to two decimal places)

Ans: (1.50 to 1.60)

28. Under physiological conditions, the conversion of CO2 to bicarbonate ion by carbonic anhydrase enzyme (MW = 30,000 g mol1) has a turnover number of 4.00 × 105 s1. The minimum amount of enzyme (in μg) required to convert 0.44 g of CO2 to bicarbonate ions in 100 seconds is ______ (up to two decimal places)

Ans: (7.40 to 7.60)

29. Assume 1,3,5-hexatriene to be a linear molecule and model the π electrons as particles in a one-dimensional box of length 0.70 nm. The wavelength (in nm) corresponding to the transition from the ground-state to the first excited-state is _________

Ans: (225 to 240)

30. The standard Gibbs free energy change of the reaction shown below is −7 kJ mol1.

Sn(s) + Pb2+ = Sn2+ + Pb(s)

Given that E°(Pb2+/Pb) is −0.126 V, the value of E°(Sn2+/Sn) in V is ______ (up to two decimal places)

Ans: (−0.15 to −0.13)

31. The dissociative chemiosorption of X2(g) on a metal surface follows Langmuir adsorption isotherm. The ratio of the rate constants of the adsorption and desorption processes is 4.0 atm1. The fractional surface coverage of X(adsorbed)at 1.0 atm pressure is ________ (up to two decimal places)

Ans: (0.65 to 0.70)

32. The ionic activity coefficients of Ca2+ and F are 0.72 and 0.28, respectively. The mean activity coefficient of CaF2 is _______(up to two decimal places)

Ans: (0.36 to 0.40)

33. The angle of orientation (in degrees) of the angular momentum vector with respect to z-axis for I = 2 and ml = +2 state of H-atom is ______(up to two decimal places)

Ans: (33.30 to 36.90)

34. The Gibbs free energy of mixing is denoted as ∆Gmix. 1.0 mole of He, 3.0 moles of Ne and 2.0 moles of Ar are mixed at the same pressure and temperature. Assuming ideal gas behavior, the value of ∆Gmix/RT is ______ (up to two decimal places)

Ans: (−6.10 to −6.05)

35. Ψ = [cϕ1 – (1/√3)ϕ2] represents a normalized molecular orbital constructed from two different atomic orbitals ϕ1 and ϕ2 that form an orthonormal set. The value of |c| is _________(up to two decimal places)

Ans: (0.80 to 0.84)

36. In cyclophosphazenes, (NPX2)3 (X = F, Cl, Br and Me), the s strength of P−N π-bond varies with X in the order

(A)  F > Cl > Br > Me

(B)  Me > F > Cl > Br

(C)  Br > Cl > F > Me

(D)  Me > Br > Cl > F

Ans: (A)

37. The structure type and shape of the polyhedral (skeletal) framework of the carbonate, Me2C2B10H10, respectively, are

(A)  nido and dodecahedron

(B)  closo and icosahedron

(C)  nido and icosahedron

(D)  closo and dodecahedron

Ans: (B)

38. If ∆o is the octahedral splitting energy and P is the electron pairing energy, then the crystal-field stabilization energy (CFSE) of [Co(NH3)6]2+ is

(A)  −0.8 ∆0 + 2P

(B)  −0.8 ∆0 + 1P

(C)  −0.8 ∆0

(D)  −1.8∆0 + 3P

Ans: (C)

39. The rates of substitution for the following reaction vary with L in the order

(A)

(B)

(C)

(D)

Ans: (D)

40. The product formed in the reaction of MeMn(CO)5 with 13CO is

(A)  (Me13CO)Mn(CO)5

(B)  (MeCO)Mn(CO)5

(C)  (MeCO)Mn(CO)4(13CO)

(D)  (Me13CO)Mn(CO4)(13CO)

Ans: (C)

41. For the following three alkenes, 1, 2,  and 3, the rates of hydrogenation using Wilkinson’s catalyst at 25℃ vary in the order

(A)  1 > 3 > 2

(B)  1 > 2 > 3

(C)  2 > 1 > 3

(D)  2 > 3 > 1

Ans: (B)

42. 210Bi undergoes β decay to 1/8 of its initial amount in 15 days. The time required for its decay 1/4 of its initial amount is _______ days (up to two decimal places).

Ans: (9.90 to 10.10)

43. The metal ion and the macrocyclic skeleton present in the green pigment of plants, respectively, are

(A)  Mg(II) and chlorin

(B)  Mg(II) and corrin

(C)  Mn(II) and chlorin

(D)  Mg(II) and porphine

Ans: (A)

44. The spinel structure of MgAl2O4 has cubic close packed arrangement of oxide ions. The fractions of the octahedral and tetrahedral sites occupied cations, respectively, are

(A)  1/8 and 1/2

(B)  1/4 and 1/2

(C)  1/2 and 1/4

(D)  1/2 and 1/8

Ans: (D)

45. The diffusion limiting current (Id) at a dropping mercury electrode for an aqueous Mg(II) solution of concentration ‘c’ (mol L1) is 300 μ If ‘c’ is increased by 0.1 mol L1, Id increases to 900 μA. The value of ‘c’ (in mol L1) is _______ (up to two decimal places)

Ans: (0.04 to 0.05)

46. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Ans: (C)

47. The product formed in the following photochemical reaction is

(A)

(B)

(C)

(D)

Ans: (D)

48. Among the following decahydroquinoline toluenesulfonates (Ts), the one that yields 9-methylamino-E-non-5-enal as a major product upon aqueous solvolysis is

(A)

(B)

(C)

(D)

Ans: (C)

49. The product obtained in the following solvolysis reaction is

(A)  a racemic mixture of trans 1,2-diacetoxycyclohexane

(B)  enantimerically pure trans 1,2-diacetoxycyclohexane

(C)  racemic cis 1,2-diacetoxycyclohexane

(D)  a mixture of cis and trans 1, 2-diacetoxycyclohexane

Ans: (A)

50. The spectroscopic data for an organic compound with molecular formula C10H12O2 are given below. IR band around 1750 cm11H NMR δ3 (m, 5H) 5.85 (Q, 1H, J = 7.2 Hz), 2.05 (s, 3H), 1.5 (d, 3H, J = 7.2 Hz) ppm. The compound is

(A)  methyl 2-phenylpropionate

(B)  1-(phenylethyl) acetate

(C)  2-(phenylethyl) acetate

(D)  methyl 3-phenylpropionate

Ans: (B)

51. The structure of the intermediate [P] and major product Q formed in the following reaction sequence are

(A)

(B)

(C)

(D)

Ans: (B)

52. Hydration of fumaric acid gives malic acid as shown below. Assume that addition of water takes place specifically from A face or B face. The correct statement pertaining to stereochemistry of malic acid formed is

(A)  addition specifically from A face gives S isomer of malic acid

(B)  addition specifically from B face gives S isomer of malic acid

(C)  addition specifically from A face gives R isomer of malic acid

(D)  addition specifically from B face gives a racemic mixture of malic acid

Ans: (A)

53. Hydroboration of 2-butyne with (C6H11)2BH yields the intermediate U, which on treatment with I2 and NaOMe at −78℃, gives product V. The structures of U and V are

(A)

(B)

(C)

(D)

Ans: (D)

54. The structures of the major products W and X in the following synthetic scheme are

(A)

(B)

(C)

(D)

Ans: (D)

55. The major products Y and Z in the following reaction sequence are

(A)

(B)

(C)

(D)

Ans: (A)

56. She has a sharp tongue and it occasionally turn _______

(A)  hurtful

(B)  left

(C)  methodical

(D)  vital

Ans: (A)

57. I_____ made arrangements had I _______ informed earlier.

(A)  could have, been

(B)  would have, being

(D)  had been, been

Ans: (A)

58. 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%.

Which of the following statements is correct?

(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.

Ans: (D)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represents this as a slice of a pie chart is

(A)  120

(B)  144

(C)  160

(D)  212

Ans: (B)

60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions 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

iv. All benches are chairs

(A)  Only i

(B)  Only ii

(C)  Only ii and iii

(D)  Only iv

Ans: (B)

61. ‘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 sections, and ultimately on Asia, you will not find it in these page; 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

Ans: (D)

62. 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

Ans: (A)

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

(A)  1440

(B)  1200

(C)  720

(D)  600

Ans: (A)

64. 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

Ans: (A)

65. A contour line joins 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

Ans: (C)

## Gate 2017 Computer Science and Information Technology Question Paper 11th Feb 2017 Session 2 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Computer Science and Information Technology 11th Feb 2017 Session 2

Subject Name: Computer Science and Information Technology

Duration : 180

Total Marks: 100

1. Consider the set X={a, b,c,d,e} under the partial ordering

R={(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)}.

The Hasse diagram of the partial order (X, R) is shown below.

The minimum number of ordered pairs that need to be added to R to make (X, R) a lattice is ________.

Ans: (0)

2. Which of the following statements about parser is/are CORRECT?

I. Canonical LR is more powerful than SLR.

II. SLR is more powerful than LALR

III. SLR is more powerful than Canonical LR.

(A)  I only

(B)  II only

(C)  III only

(D)  II and III only

Ans: (A)

3. Match the following:

(A) P-(ii), Q-(iv), R-(i), S-(iii)

(B) P-(ii), Q-(i), R-(iv), S-(iii)

(C) P-(ii), Q-(iv), R-(iii), S-(i)

(D) P-(iii), Q-(iv), R-(i), S-(ii)

Ans: (A)

4. Let L1, L2 be any two context free languages and R be any regular language. Then which of the following is/are CORRECT ?

(A) I, II and IV only

(B) I and III only

(C) II and IV only

(D) I only

Ans: (B)

5. G is undirected graph with n vertices and 25 edges such that each vertex of G has degree at least 3. Then the maximum possible value of n is ___________.

Ans: (16)

6. Let p, q, r denote the statements “It is raining ,“ It is cold”, and “ It is pleasant,” respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by

(A)  (¬p ⋀  r) ⋀ (¬r→p ⋀ q))

(B)  (¬p ⋀ r) ⋀ ((p ⋀ q)→¬r )

(C)  (¬p ⋀ r) ⋀ ((p ⋀ q)→¬r )

(D)  (¬p ⋀ r ) ⋀ (r→(p ⋀ q))

Ans: (A)

7. The Breadth First Search (BFS) algorithm has been implemented using the queue data structure. Which one of the following is a possible order of visiting the nodes in the graph below?

(A)  MNOPQR

(B)  NQMPOR

(C)  QMNROP

(D)  POQNMR

Ans: (D)

8. Let  be two matrices.

Then the rank of P + Q is _________.

Ans: (2)

9. Consider socket API on a Linux machine that supports connected UDP sockets. A connected UDP socket is a UDP socket on which connect function has already been called. Which of the following statements is/are CORRECT ?

I. A connected UDP socket can be used to communicate with multiple peers simultaneously.

II. A process can successfully call connect function again for an already connected UDP socket.

(A)  I only

(B)  II only

(C)  Both I and II

(D)  Neither I nor IIs

Ans: (B)

10. The minimum possible number of states of a deterministic automaton that accepts the regular language

L = {w1aw2|w1, w2 ∈ {a, b}*, |w1| = 2,|w2| ≥ 3} is ______.

Ans: (8)

11. Consider the following tables T1 and T2.

In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in table T1 on-delete set NULL and on-update cascade. In order to delete record  from table T1, the number of additional records that need to be deleted from table T1 is ______________.

Ans: (0)

12. Which of the following is/are shared by all the threads in a process ?

I. Program counter          II. Stack

III. Address space            IV. Registers

(A)  I and II only

(B)  III only

(C)  IV only

(D)  III and IV only

Ans: (B)

13. A circular queue has been implemented using a single linked list where each node consists of a value and a single pointer pointing to the next node. We maintain exactly two external pointers FRONT and REAR pointing to the front node and the rear node of the queue, respectively. Which of the following statements is/are CORRECT for such a circular queue, so that insertion and deletion operation can be performed in O (1) time ?

I. Next pointer of front node points to the rear node.

II. Next pointer of rear node points to the front node.

(A)  I only

(B)  II only

(C)  Both I and II

(D)  Neither I nor II

Ans: (B)

14. Given the following binary number in 32-bit (single precision) IEEE-754 format:

00111110011011010000000000000000

The decimal value closest to this floating- point number is

(A)  1.45 × 101

(B)  1.45 × 10−1

(C)  2.27 × 101

(D)  2.27 × 101

Ans: (C)

15. An ER model of a database consists of entity types A and B. These are connected by a relationship R which does not have its own attribute. Under which one of the following conditions, can the relational table for R be merged with that of A?

(A) Relationship R is one-to-many and the participation of A in R is total

(B) Relationship R is one-to-many and the participation of A in R is partial

(C) Relationship R is many-to one and the participation of A in R is total

(D) Relationship R is many-to one and the participation of A in R is partial

Ans: (C)

16. Match the algorithms with their time complexities:

(A) P-(iii),Q-(iv), R-(i), S-(ii)

(B) P-(iv),Q-(iii), R-(i), S-(ii)

(C) P-(iii),Q-(iv), R-(ii), S-(i)

(D) P-(iv),Q-(iii), R-(ii), S-(i)

Ans: (C)

17. Match the following according to input (from the left column) to the complier phase (in the right column) that processes it.

(A) P-(ii),Q-(iii), R-(iv), S-(i)

(B) P-(ii),Q-(i), R-(iii), S-(iv)

(C) P-(iii),Q-(iv), R-(i), S-(ii)

(D) P-(i),Q-(iv), R-(ii), S-(iii)

Ans: (C)

18. Consider the following statements about the routing protocols, Routing Information Protocol (RIP) and Open Shortest Path First (OSPF) in an IPv4 network.

I. RIP uses distance vector routing

II. RIP packets are sent using UDP

III. OSPF packets are sent using TCP

IV. OSPF operation is based on link-state routing

Which of the statements above are CORRECT?

(A) I and IV only

(B) I, II and III only

(C) I, II and IV only

(D) II, III and IV only

Ans: (C)

19. If  and  then the constants R and S are respectively

(A)

(B)

(C)

(D)

Ans: (C)

20. In a file allocation system, which of the following allocation schemes(s) can be used if no external fragmentation is allowed?

I. Contiguous     II. Linked       III. Indexed

(A) I and III only

(B) II only

(C) III only

(D) II and III only

Ans: (D)

21. Consider a quadratic equation x2 – 13x + 36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = ___________.

Ans: (8)

22. Identify the language generated by the following grammar, where S is start variable.

S → XY

X → aX|a

Y → aYb|∈

(A)  {ambn| m ≥ n, n > 0}

(B)  {ambn|m ≥ n, n ≥ 0}

(C)  {ambn|m > n, n ≥ 0}

(D)  {ambn|m > n, n > 0}

Ans: (C)

23. The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is

(A)  571244

(B)  736251

(C)  571247

(D)  136251

Ans: (D)

24. Consider the following function implemented in C:

void printxy (int x, int y) {

int *ptr ;

x = 0;

ptr = &x;

y = * ptr;

* ptr = l;

print f (“%d, %d,” x, y);

}

The output of invoking printxy (l, l) is

(A)  0, 0

(B)  0, 1

(C)  1, 0

(D)  1, 1

Ans: (C)

25. The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is _________.

Ans: (9)

26. Consider a binary code that consists of only four valid code words as given below:

00000,01011,10101,11110

Let the minimum Hamming distance of the code be p and the maximum number of erroneous bits that can be corrected by the code be q. Then the values of p and q are

(A) p = 3 and q = 1

(B) p = 3 and q = 2

(C) p = 4 and q = 1

(D) p = 4 and q = 2

Ans: (A)

27. A system shares 9 tape drives. The current allocation and maximum requirement of tape drives for three processes are shown below:

Which of the following best describes current state of the system ?

(B) Safe, Not Deadlocked

(C) Not Safe, Deadlocked

(D) Not Safe, Not deadlocked

Ans: (B)

28. Two transactions T1 and T2 are given as

T1 : r1 (X) w1 (X) r1 (Y) w1 (Y)

T2 : r2 (Y) w2 (Y) r2 (Z) w2 (Z)

where ri(V) denotes a read operation by transaction Ti on a variable V and wi(V)  denotes a write operations by transaction Ti on a variable V. The total number of conflict serializable schedules that can be formed by T1 and T2 is _____________.

Ans: (54)

29. If w, x, y, z are Boolean variables, then which one of the following is INCORRECT ?

(A)    wx +w(x + y) + x(x + y)=x + wy

(B)

(C)

(D)  (w + y)(wxy + wyz) = wxy + wyz

Ans: (C)

30. Consider the following C Program.

# include <stdio.h>

#include< string.h>

#int main ( ) {

char* c = “GATECSIT2017”;

char* p = c;

printf(“%d”, (int) strlen (c+2[p]-6[p]-1));

return 0;

}

The output of the program is _______________.

Ans: (2)

31. P and Q are considering to apply for a job. The probability that P applies for the job is   The probability that P applies for the job given that Q applies for the job is  and the probability that Q applies for the job given that P applies for the job  Then the probability that P does not apply for the job given that Q does not apply for the job is

(A)

(B)

(C)

(D)

Ans: (A)

32. If the characteristics polynomial of 3× 3 matrix M over R ( the set of real numbers) is λ3 – 4λ2 + aλ + 30, a ∈ R, and one eigenvalue of M is 2, then the largest among the absolute values of the eigenvalues of M is ________.

Ans: (5)

33. Consider the following expression grammar G:

E → E – T|T

T → T + F|F

F → (E) |id

Which of the following grammars is not left recursive, but is equivalent to G?

(A)

(B)

(C)

(D)

Ans: (C)

34. In a two-level cache system, the access times of L1 and L2 caches are 1 and 8 clock cycles, respectively. The miss penalty from L2 cache to main memory is 18 clock cycles . The miss rate of L1 cache is twice that of L2. The average memory access time (AMAT) of this cache system is 2 cycles. This miss rates of L1 and L2 respectively are :

(A) 0.111 and 0.056

(B) 0.056 and 0.111

(C) 0.0892 and 0.1784

(D) 0.1784 and 0.0892

Ans: (A)

35. Consider two hosts X and Y, connected by a single direct link of rate 106 bits/sec. The distance between the two hosts is 10,000 km and the propagation speed along the link is 2 × 108 m/sec. Host X sends a file of 50,000 bytes as one large message to host Y continuously. Let the transmission and propagation delays be p milliseconds and q milliseconds, respectively . Then the values of p and q are

(A) p = 50 and q = 100

(B) p = 50 and q = 400

(C) p = 100 and q = 50

(D) p = 400 and q = 50

Ans: (D)

36. Consider the recurrence function

Then T(n) in terms of θ notation is

(A)  θ(log log n)

(B)  θ(log n)

(C)  θ(√n)

(D) θ(n)

Ans: (B)

37. If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X+2)2] equals ______.

Ans: (54)

38. Consider the following C function

int fun (int n) {

int i, j;

for (i = 1; i < = n; i++) {

for (j = 1 ; j < n ; j+=i) {

printf (“%d %d , i, j ) ;

}

}

}

Time complexity of fun in terms of θ notation is

(A)  θ(n√n)

(B)  θ(n2)

(C)  θ(n log n)

(D)  θ (n2 log n)

Ans: (C)

39. The pre-order transversal of a binary search tree is given by 12, 8, 6, 2, 7, 9, 10, 16, 15, 19, 17, 20. Then the post-order traversal of this tree is:

(A) 2,6,7,8,9,10,12,15,16,17,19,20

(B) 2,7,6,10,9,8,15,17,20,19,16,12

(C) 7,2,6,8,9,10,20,17,19,15,16,12

(D) 7,6,2,10,9,8,15,16,17,20,19,12

Ans: (B)

40. Consider the C program fragment below which is meant to divide x by y using repeated subtractions. The variables x, y, q and r are all unsigned int.

while (r >= y) {

r = r – y;

q = q +1;

}

Which of the following conditions on the variables x, y, q and r before the execution of the fragment will ensure that the loop terminates in a state satisfying the condition x = = (y*q + r)?

(A) (q = = r) && (r = =0)

(B) (x > 0) && (r = =x) && (y > 0)

(C) (q = = 0) && (r = = x) && (y > 0)

(D) (q = = 0) && (y > 0)

Ans: (C)

41. A message is made up entirely of characters from the set X= {P,Q,R,S,T}. The table of probabilities for each of the characters is shown below:

If a message of 100 characters over X is encoded using Huffman coding, then the expected length of the encoded message in bits is_____

Ans: (225)

42. The next state table of a 2-bit saturating up-counter is given below.

The counter is built as a synchronous sequential circuit using T flip-flops. The expression for T1 and T0 are

(A)

(B)

(C)

(D)

Ans: (B)

43. Consider the set of processes with arrival time (in milliseconds). CPU burst time (in milliseconds), and priority (0 is the highest priority) shown below. None of the processes have I/O burst time.

The average waiting time (in milliseconds) of all the processes using preemptive priority scheduling algorithm is __________

Ans: (29)

44. For any discrete random variable X, with probability mass function P(X = j) = pj, pj ≥ 0, j ∈ {0,….. N} and  define the polynomial function g For a certain discrete random variable Y, there exists a scalar β ∈ [0, 1] such that gY (z) = (1 – β+ βz)n. The expectation of Y is

(A)  Nβ(1 – β)

(B)  Nβ

(C)  N(1 – β)

(D)  Not expressible in terms of N and β alone

Ans: (B)

45. The read access times and the hit ratios for different caches in a memory hierarchy are as given below.

The read access time of main memory is 90 nanoseconds. Assume that the caches use the referred word-first read policy and the write back policy. Assume that all the caches are direct mapped caches. Assume that the dirty bit is always 0 for all the blocks in the caches. In execution of a program, 60% of memory reads are for instruction fetch and 40% are for memory operand  fetch. The average read access time in nanoseconds (up to 2 decimal places) is______.

Ans: (4.72)

46. If the ordinary generating function of a sequence  then a3 – a0 is equal to ______.

Ans: (15)

47. Consider the following snippet of a C program. Assume that swap (&x, &y) exchanges the contents of x and y.

int main ( ) {

int array[]={3,5,1,4,6,2};

int done =0 ;

int i ;

while (done = = 0) {

done = 1;

for (i = 0; i <=4; i ++) {

if (array [i] < array [i +1]) {

swap (& array [i], &array [i+1]);

done = 0;

}

}

for (i = 5 ; i > =1; i –) {

if (array [i] > array [ i-1]) {

swap ( & array [i] , &array [i-1]);

done = 0;

}

}

}

printf ( “ %d “ , array [3] );

}

The output of the program is ____________.

Ans: (3)

48. Consider the following C program.

# include <stdio.h>

int main ( ) {

int m = 10;

int n, n1;

n = ++m;

n1 = m++;

n–;

–n1;

n – = nl;

printf (“%d”, n) ;

return 0;

}

The output of the program is ______________.

Ans: (0)

49. Consider the following database table named top _scorer.

Consider the following SQL query:

SELECT ta.player FROM top _scorer AS ta

WHERE ta.goals > ALL (SELECT tb. goals

FROM top _ scorer AS tb

WHERE tb.country = ‘Spain’)

AND ta.goals > ANY (SELECT tc. goals

FROM top_ scorer AS tc

WHERE tc.country = ‘Germany’)

The number of tuples returned by the above SQL query is ___________.

Ans: (7)

50. Given f (w, x, y, z) = ∑m (0,1,2,3,7,8,10) + ∑d (5,6,11,15), where d represents the don’t care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w, x, y, z) ?

(A)

(B)

(C)

(D)

Ans: (A)

51. In a B+ tree, if the search –key value is 8 bytes long, the block size is 512 bytes and the block pointer size is 2 bytes, then maximum order of the B+ tree is _______________.

Ans: (52)

52. Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Let L (M) be the language accepted by a Turning machine M. Which of the following decision problems are undecidable ?

I. Given a regular expression R and a string w, is w ∈ L(R)?

II. Given a context-free grammar G, L(G) = ∅

III. Given a context-free grammar G, is L(G) = ∑* for some alphabet ∑?

IV. Given a Turning machine M and a string w, is w ∈ L(M)?

(A) I and IV only

(B) II and III only

(C) II, III and IV only

(D) III and IV only

Ans: (D)

53. Consider a machine with a byte addressable main memory of 232bytes divided into blocks of size 32 bytes. Assume that a direct mapped cache having 512 cache lines is used with this machine. The size of the tag field in bits is ______.

Ans: (18)

54. Let δ denote that transition function and   denote the extended transition function of the ∈ − NFA whose transition table is given below:

Then  (q2, aba) is

(A)  ∅

(B)  {q0, q1, q3}

(C)  {q0, q1, q2}

(D)  {q0, q2, q3}

Ans: (C)

55. Consider the following languages.

L1 = {ap|p is a prime number}

L2 = {anbmc2m|n ≥ 0, m ≥ 0}

L3 = {anbnc2n|n ≥ 0}

L4 = {anbn|n ≥ 1}

Which of the following are CORRECT ?

I. L1 is context-free but not regular.

II. L2 is not context-free.

III. L3 is not context-free but recursive.

IV. L4 is deterministic context-free.

(A) I ,II and IV only

(B) II and III only

(C) I and IV only

(D) III and IV only

Ans: (D)

56. There are 3 red socks, 4 green socks and 3 blue socks, you choose 2 socks. The probability that they are of the same colour is ___________.

(A)  1/5

(B)  7/30

(C)  1/4

(D)  4/15

Ans: (D)

57. Choose the option with words that are not synonyms.

(A)  aversion, dislike

(C)  plunder, loot

(D)  yielding, resistant

Ans: (D)

58. There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the west of W. Z is to the East of X and the West of V. W is to the West of Y. Which is the building in the middle ?

(A)  V

(B)  W

(C)  X

(D)  Y

Ans: (A)

59. A test has twenty questions worth 100 marks in total. There are two types of questions, multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

(A)  12

(B)  15

(C)  18

(D)  19

Ans: (B)

60. Saturn is ____ to be seen on a clear night with the naked eye.

(A)  enough bright

(B)  bright enough

(C)  as enough bright

(D)  bright as enough

Ans: (B)

61. “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”

The author’s belief that ideology is not as important as literature is revealed by the word:

(A)  ‘culture’

(B)  ‘seemingly’

(C)  ‘urgent’

(D)  ‘political’

Ans: (B)

62. X is a 30 digit number starting with the digit 4 followed by the digit 7, then the number X3 will have

(A)  90 digits

(B)  91 digits

(C)  92 digits

(D)  93 digits

Ans: (A)

63. There are three boxes, one contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

(A) The box labelled ‘Apples’

(B) The box labelled ‘Apples and Oranges’

(C) The box labelled ‘Oranges’

(D) Cannot be determined

Ans: (B)

64. An air pressure contour line joins locations in a region having the same atmospheric pressure . The following is an air contour plot of a geographical region . Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

(A)  P

(B)  Q

(C)  R

(D)  S

Ans: (C)

65. The number of roots of ex + 0.5x2 – 2 = 0 in the range [−5, 5] is

(A)  0

(B)  1

(C)  2

(D)  3

Ans: (A)