GATE Entrance Paper 2019 | ENTRANCE INDIA

GATE Exam 2019 Life Sciences (XL) Question Paper With Answer Key

June 7, 2023December 15, 2019 by suresh84

General Aptitude Set-4

Q.1 – Q. 5 carry one mark each.

1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.

Which one of the following choices CANNOT fill the given blank?

(A) will be

(B) were to be

(D) might be

Answer: (B)

2. A final examination is the _______ of a series of evaluations that a student has to go through.

(A) culmination

(B) consultation

(D) insinuation

Answer: (A)

3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .

(A) JDE

(B) JED

(D) JCD

Answer: (B)

4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

(A) 6

(B) 7

(D) 9.5

Answer: (Marks to All)

5. Are there enough seats here? There are _______people here than I expected.

(A) many

(B) most

(D) more

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.

(A) 37.50

(B) 35.70

(D) 10.00

Answer: (A)

7. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is_____.

(A) 13.50

(B) 14.5

(D) 16.50

Answer: (B)

8. While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattan penthouses with clinking ice cubes. This was, till an eminent Caribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”.

The writer of this passage is surprised by the creative writing assignments of his students, because ______ .

(A) Some of the students had written stories set in foreign places

(B) None of the students had written stories set in India

(D) Some of the students had written about ice cubes and cowboys

Answer: (B)

9. Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?

(A) 16.24

(B) 23.97

(D) 38.74

Answer: (B)

10. X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television.

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

(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television

(B) Non-members prefer to watch cable television

(D) The X is cancelling accounts of non-members

Answer: (A)

GATE Exam 2019 Engineering Sciences (XE) Question Paper With Answer Key

June 7, 2023December 15, 2019 by suresh84

General Aptitude Set-4

Q.1 – Q. 5 carry one mark each.

1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.

Which one of the following choices CANNOT fill the given blank?

(A) will be

(B) were to be

(D) might be

Answer: (B)

2. A final examination is the _______ of a series of evaluations that a student has to go through.

(A) culmination

(B) consultation

(D) insinuation

Answer: (A)

3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .

(A) JDE

(B) JED

(D) JCD

Answer: (B)

4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

(A) 6

(B) 7

(D) 9.5

Answer: (Marks to All)

5. Are there enough seats here? There are _______people here than I expected.

(A) many

(B) most

(D) more

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.

(A) 37.50

(B) 35.70

(D) 10.00

Answer: (A)

(A) 13.50

(B) 14.5

(D) 16.50

Answer: (B)

The writer of this passage is surprised by the creative writing assignments of his students, because ______ .

(A) Some of the students had written stories set in foreign places

(B) None of the students had written stories set in India

(D) Some of the students had written about ice cubes and cowboys

Answer: (B)

(A) 16.24

(B) 23.97

(D) 38.74

Answer: (B)

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

(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television

(B) Non-members prefer to watch cable television

(D) The X is cancelling accounts of non-members

Answer: (A)

Engineering Sciences

Engineering Mathematics XE-A

XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each.

1. Let 𝑋 be the Poisson random variable with parameter 𝜆 = 1. Then, the probability

(2 ≤ 𝑋 ≤ 4) equals

(A) 19/24e

(B) 17/24e

(D) 11/24e

Answer: (B)

2. For the series which of the following statements is NOT correct?

(A) The series converges at 𝑥 = −3

(B) The series converges at 𝑥 = −1

(D) The series converges at 𝑥 = 1

Answer: (D)

3. Let is the complex conjugate of 𝑧. Then, it is differentiable on

(A) |𝑧| > 1

(B) |𝑧| < 1

(D) the entire complex plane ℂ

Answer: (C)

4. If the transformation (𝑥, 𝑡) = 𝑒^𝑥𝑣(𝑥, 𝑡) reduces the partial differential equation then f(x) equals

(A) −𝑒⁻^𝑥

(B) 𝑒⁻^𝑥

(D) 2𝑒⁻^𝑥

Answer: (A)

5. The value of 𝛼 for which the system of equations

𝑥 − 𝑦 − 3𝑧 = 3

2𝑥 + = 0

−2𝑦 − 7 = 𝛼

has a solution is ______.

Answer: (6 to 6)

6. The value of the line integral where 𝛾 is the circle 𝑥² + 𝑦² = 1 oriented counter clockwise, is ______.

Answer: (3 to 3)

7. Let 𝑦₁(𝑥) and 𝑦2(𝑥) be two linearly independent solutions of the differential equation is ______.

Answer: (0 to 0)

8. If is the matrix where 𝒗₁, 𝒗₂ and 𝒗₃ are linearly independent eigenvectors of the matrix 𝑄, then the sum of the absolute values of all the elements of the matrix 𝑃⁻¹𝑄𝑃 is

(A) 6

(B) 10

(D) 22

Answer: (B)

9. If (𝑥) = 𝑎𝑥³ + 𝑏𝑥² + 𝑐𝑥 + 𝑑 is the polynomial obtained by Lagrange interpolation satisfying 𝑃(0) = −8, 𝑃(1) = −7, 𝑃(2) = −6 and 𝑃(4) = 20, then the value of 𝑎 − 𝑏 + 𝑐 is

(A) 1

(B) 3

(D) 7

Answer: (D)

10. The number of critical points of the function (𝑥, 𝑦) = 𝑥³ + 3𝑥𝑦² − 15𝑥 − 12𝑦 at which there is neither maximum nor minimum is_____.

Answer: (2 to 2)

11. Let and 𝛾 is the circle |𝑧| = 2 oriented counter clockwise. Then, the value of 𝐼 rounded off to one decimal place is _______.

Answer: (6.0 to 6.2)

XE : B Fluid Mechanics

XE -B: Q. 1 – Q. 9 carry one mark each

1. For stable equilibrium of a floating body, which one of the following statements is correct?

(A) Centre of gravity must be located below the centre of buoyancy.

(B) Centre of buoyancy must be located below the centre of gravity.

(D) Centre of gravity must be located below the metacentre.

Answer: (D)

2. If 𝑢 and 𝑣 are the velocity components in the x- and y-directions respectively, the z-component of vorticity 𝜔_𝑧 at a point in a flow field is

Answer: (B)

3. In which one of the following devices the difference between static and total pressure is used to determine the flow velocity?

(A) Piezometer

(B) Pitot static tube

(D) Venturimeter

Answer: (B)

4. A golf ball is dimpled to make the flow turbulent and consequently to reduce the drag. Turbulent flow reduces the drag on the golf ball because

(A) skin friction coefficient is lower in a turbulent flow.

(B) skin friction coefficient is higher in a turbulent flow.

(D) turbulent flow has a higher tendency to separate.

Answer: (C)

5. For a steady laminar incompressible boundary layer flow over a sharp-edged flat plate at zero incidence,

(A) the edge of the boundary layer is a streamline.

(B) the edge of the boundary layer is a pathline.

(D) the skin friction coefficient remains constant all along the plate.

Answer: (C)

6. The power input 𝑃 to a centrifugal pump is a function of the volume flow rate 𝑄, impeller diameter 𝐷, rotational speed Ω, fluid density 𝜌, dynamic viscosity 𝜇, and surface roughness 𝜖. To carry out a dimensional analysis using Buckingham’s 𝜋 theorem, which one of the following sets can be taken as the set of repeating variables?

(A) 𝑄, Ω, 𝐷

(B) 𝑄, 𝜖, 𝐷

(D) 𝐷, 𝜌, Ω

Answer: (D)

7. Consider the two-dimensional laminar flow of water (𝜇 = 0.001 N.s/m²) between two infinitely long parallel plates 0.1 m apart as shown in the figure below. The velocity profile at any location is given by (𝑦) = 100(0.1𝑦 − 𝑦²) m/s where y is in m. The magnitude of shear stress (in N/m2, rounded off to 2 decimal places) acting on the bottom plate is ______

Answer: (0.01 to 0.01)

8. The maximum velocity in a fully developed laminar incompressible flow through a circular pipe of constant cross-sectional area is 6 m/s. The average velocity (in m/s) of the flow is ______

Answer: (3 to 3)

9. The theoretical discharge for the flow through an orificemeter is 40 m³/s. If the measured discharge in an experiment is 32 m3/s, then the discharge coefficient (rounded off to one decimal place) is _______

Answer: (0.8 to 0.8)

XE – B: Q. 10 – Q. 22 carry two marks each.

10. Consider the flow between two infinitely long parallel plates of large width separated by a distance 2H. The upper plate is moving with a constant velocity U while the lower plate is stationary. The volumetric flow rate per unit width of the plate is

(A) 0.25 𝑈𝐻

(B) 0.5 𝑈𝐻

(D) 2 𝑈𝐻

Answer: (C)

11. The velocity field in Cartesian coordinates in a two-dimensional steady incompressible flow of a fluid with density 𝜌 is 𝐕 = 𝑥𝐢 − 𝑦𝐣. Assuming no body and line forces, the magnitude of pressure gradient ∇𝑝 at point (1,1) is

(A) √2 𝜌

(B) 𝜌

(D) 𝜌/2

Answer: (A)

12. A two-dimensio nal velocity field in Cartesian coordinates is defined by 𝐕 = 𝑦𝐢 − 𝑥𝐣. This flow is

(A) compressible and rotational

(B) compressible and irrotational

(D) incompressible and irrotational

Answer: (C)

13. Assertion [a]: The streamlines in a free vortex flow are concentric circles.

Reasoning [r]: There exists only radial component for the velocity field in a free vortex flow.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(D) [a] is false but [r] is true

Answer: (C)

14. The velocity components in Cartesian coordinates in a two-dimensional incompressible flow are = 𝑒^𝑦 cos(𝑥) and 𝑣 = 𝑒^𝑦 sin(𝑥). The magnitude of total acceleration at the point (−1,1) is

(A) 0

(B) 1

(D) 𝑒²

Answer: (D)

15. For steady laminar flow at zero incidence over a flat plate, the component of velocity parallel to the plate in the boundary layer is given by 𝑢(𝑦) = 𝑎 + 𝑏𝑦 + 𝑐𝑦², where 𝑦 is the distance measured normal to the flat plate. If 𝜇 is the coefficient of dynamic viscosity, 𝑈 is the velocity parallel to the wall at the edge of the boundary layer and 𝛿 is the boundary layer thickness, the wall shear stress is given by

(A) 𝜇𝑈/𝛿

(B) 2𝜇𝑈/𝛿

(D) 3𝜇𝑈/𝛿

Answer: (B)

16. A fluid with constant density of 1 kg/m3 flows past a semi-cylindrical structure with a freestream velocity of 2 m/s as shown in the figure below. The difference in static pressure between points P and Q is 10 N/m². If the gravitational acceleration g is 10 m/s² and the flow is assumed to be potential, what is the radius r (in m) of the semi-cylindrical structure?

(A) 1

(B) 0.8

(D) 0.4

Answer: (D)

17. The mercury manometer shown in the figure below is connected to a water pipe at one end while the other end is open to the atmosphere. The density of water is 1000 kg/m³, the specific gravity of mercury is 13.6 and the gravitational acceleration g is 10 m/s². The gauge pressure 𝑝 (in kN/m², rounded off to 2 decimal places) in the water pipe is______

Answer: (33.25 to 33.75)

18. Water (𝜌 = 1000 kg/m³, 𝜇 = 0.001 N.s/m²) flows through a smooth circular pipe of radius 0.05 m. If the flow Reynolds number is 1000, then the pressure drop (in N/m2, rounded off to 2 decimal places) over a length of 5 m will be ________

Answer: (0.15 to 0.17)

19. A uniform flow with a velocity of 2 m/s in the x-direction approaches a line source placed on the x-axis at a distance of 0.1 m from the origin. If the origin is the stagnation point in the resulting flow, the strength of the source (in m²/s, rounded off to 2 decimal places) is ______

Answer: (1.25 to 1.27 OR 0.20 to 0.20)

20. In a steady incompressible flow of a fluid past a smooth stationary sphere, the drag force 𝐹 depends on the flow velocity 𝑈, diameter 𝐷, and the dynamic viscosity 𝜇 and density 𝜌 of the fluid. Experiments are conducted on the same sphere at the same flow velocity using two different fluids. The density of the second fluid is two times that of the first fluid. The dynamic viscosity of the second fluid is 𝑛 times that of the first fluid. If the non-dimensional force 𝐹/(𝜌𝑈²𝐷²) remains the same in both the experiments, the value of 𝑛 is_______

Answer: (2 to 2)

21. An incompressible fluid flows past a flat plate as shown in the figure below with a uniform inlet velocity profile 𝑢 = 𝑈 and a parabolic exit velocity profile 𝑢 = 𝑈(2𝜂 − 𝜂²), where 𝑢 is the component of velocity parallel to the wall, 𝑦 is the normal distance from the plate and 𝜂 = 𝑦/𝛿. If the volume flow rate across the top surface of the control volume (CV) is 𝑄 = 𝑝𝑈𝛿 per unit width (perpendicular to the x-y plane) of the plate, the value of 𝑝 (rounded off to 2 decimal places) is _______

Answer: (0.32 to 0.34)

22. A jet engine is to be tested on a thrust stand as shown in the figure below. The conditions prevailing in a typical test are as follows: Axial intake air velocity = 100 m/s; axial exhaust gas velocity = 250 m/s; intake cross-sectional area = 1 m²; intake static pressure = −22 kPa (gauge); exhaust static pressure = 0 kPa (gauge); mass flow rate through the engine = 100 kg/s. The anchoring force (in kN) in axial direction on the thrust stand is_______

Answer: (37 to 37)

XE C : Materials Science

XE (C): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. On decreasing the objective aperture size in an optical microscope

(A) the spherical aberration increases

(B) the depth of field increases

(D) the astigmatism increases

Answer: (B)

2. Pilling-Bedworth ratios for oxides of some metals are given in the table.

Based on the criterion of Pilling-Bedworth ratio alone, which one of the following metals will be most protected from high temperature oxidation?

(A) Li

(B) Ce

(D) W

Answer: (B)

3. In NaCl, the substitution of a Na⁺ ion by a Ca²⁺ ion would most probably lead to

(A) the formation of a Na⁺ vacancy

(B) the creation of a Cl^‾ interstitial

(D) the formation of a Na⁺ and Cl^‾ vacancy pair

Answer: (A)

4. Which one of the following is time-independent?

(A) Elastic def ormation

(B) Anelastic deformation

(D) Creep deformation

Answer: (A)

5. Copper is diffused into aluminium at 400 °C for 100 hours to obtain a certain concentration at a given depth. In another experiment conducted at 500°C, to achieve the same concentration of copper at the same depth, the time required in hours is

(Given: Diffusion coefficients of copper in aluminium at 400 °C and 500 °C are 5 × 10 ⁻¹⁴ m² s⁻¹ and 6 × 10⁻¹³ m² s⁻¹, respectively)

(A) 7.33

(B) 8.33

(D) 10.33

Answer: (B)

6. If carbon (C) in iron (Fe) is 6 percent by weight, then its atomic percent is approximately

(Given: atomic weight C = 12, Fe = 56)

(A) 13

(B) 23

(D) 50

Answer: (B)

7. GaAs has advantage over silicon when used in intergrated circuits at low power because it has

(A) larger band gap

(B) more than one element

(D) higher hole mobility

Answer: (C)

8. Glass transition temperature of a polymer can be determined by

(A) Thermo-gravimetric analysis

(B) Raman spectroscopy

(D) Differential scanning calorimetry

Answer: (D)

9. The maximum wavelength of radiation to which Germanium (Ge) is opaque will be

(Given: energy gap of Ge = 0.67 eV, Planck’s constant h = 6.63 × 10⁻³⁴ J s, velocity of light c = 3×108 m s⁻¹ and 1 eV = 1.6×10⁻¹⁹ J )

(A) 0.8 µm

(B) 1.8 µm

(D) 4.8 µm

Answer: (B)

10. An alternating copolymer has number-averaged molecular weight of 105 g mol⁻¹ anddegree of polymerization of 2210. If one of the repeat units is ethylene, the other one is

(Given: atomic weight of H = 1, C = 12, F = 19 and Cl = 35.5)

(A) −CH₂−CH(CH₃)−

(B) −CH₂−CHCl−

(D) −CH₂−CH(C₆H₅)−

Answer: (B)

11. Match the sintering processes in column I with the most suitable products in column II.

(A) P-4; Q-1; R-2; S-3

(B) P-3; Q-2; R-1; S-4

(D) P-2; Q-3; R-1; S-4

Answer: (B)

12. Which one of the following conditions will NOT favour the separation of impurities in zone refining process?

(A) Increase in the gap between solidus and liquidus lines

(B) Increase in the solubility of impurities in solid as compared to that in liquid phase

(D) Low cooling rate of melt

Answer: (B)

13. A monochromatic X-ray beam of wavelength 0.154 nm is incident on a cubic crystal having lattice parameter a = 0.245 nm. The diffraction angle (2θ) for the first order reflection from a set of planes represented by the schematic plane below is _____degrees. (round off to 1 decimal place)

Answer: (100.0 to 102.0)

14. Nickel corrodes at 298 K in a solution of 0.06 M nickel chloride having pH 4. Assuming complete dissociation of nickel chloride, the partial pressure of hydrogen required to stop the corrosion of nickel is ______ atm. (round off to the nearest integer)

(Given: Standard reduction potential of nickel = ̶ 0.25 V, Faraday’s constant = 96500 C mol⁻¹, Universal gas constant = 8.314 J K⁻¹mol⁻¹)

Answer: (45 to 52)

15. The potential energy, U(r), of a pair of atoms spaced at a distance r in a solid is given by

The equilibrium distance between the atom pair is ______nm.

(round off to 2 decimal places)

(Given: Constants A = 6×10⁻²⁰ J nm³, B = 2.1×10⁻²² J nm⁷)

Answer: (0.28 to 0.32)

16. Tensile true stress – true strain curve for plastic region of an alloy is given by

𝜎 (MPa) = 600 𝜀^𝑛.

When true strain is 0.05, the true stress is 350 MPa. For the same alloy, when engineering strain is 0.12 then the engineering stress is______ MPa. (round off to the nearest integer)

Answer: (360 to 364)

17. Box-S has 2 white and 4 black balls and box-T has 5 white and 3 black balls. A ball is drawn at random, from the box-S and put in box-T. Subsequently, the probability of drawing a white ball from box-T is ________. (round off to 2 decimal places)

Answer: (0.58 to 0.61)

18. The zero point energy of an electron in a box of 0.2 nm width is _____ eV.

(round off to 1 decimal place)

(Given: Planck’s constant = 6.63×10⁻³⁴ J s, electron mass = 9.11×10⁻³¹ kg and 1 eV = 1.6×10⁻¹⁹ J )

Answer: (9.2 to 9.6)

19. The de Broglie wavelength of an electron accelerated across a 300 kV potential in an electron microscope is _______ ×10⁻¹² m. Ignore relativistic effects.

(round off to 2 decimal places)

(Given: Planck’s constant = 6.63×10⁻³⁴ J s, electron rest mass = 9.11×10⁻³¹ kg, electron charge = 1.6×10⁻¹⁹ C)

Answer: (2.10 to 2.35)

20. A stress of 17 MPa is applied to a polymer serving as a fastener in a complex assembly. At constant strain the stress drops to 16.6 MPa after 100 hours. The stress on the polymer must remain above 14.5 MPa in order for the assembly to function properly. The expected life of the assembly is ______ hours. (round off to the nearest integer)

Answer: (666 to 670)

21. A piezoelectric material has a Young’s modulus of 72 GPa. The stress required to changethe polarization from 640 to 645 C m m⁻³ is _____ MPa. (round off to the nearest integer)

Answer: (560 to 565)

22. An iron bar magnet having coercivity of 7000 A m⁻¹ is to be demagnetized. The bar is introduced fully inside a 0.25 m long solenoid having 150 turns of wire. The electric current required to generate the necessary magnetic field is ________ A.

(round off to 1 decimal place)

Answer: (11.0 to 12.5)

XE – D : Solid Mechanics

XE -D: Q. 1 – Q. 9 carry one mark each

1. For a pinned-pinned slender column of length L, with uniform circular cross section, and with second moment of cross sectional area I, the critical buckling load is Pcr. For a similar column, made of same material, having length 2L and second moment of cross sectional area 4I, the critical buckling load is

(A) 4Pcr

(B) 2Pcr

(D) 0.5Pcr

Answer: (C)

2. Two rods P and Q of uniform circular cross section are made of same material and are subjected to identical uniaxial tensile load. The length of rod P is twice the length of rod Q and the diameter of rod P is also twice the diameter of rod Q. The ratio of elastic strain energy stored in rod P to that stored in rod Q is

(A) 4:1

(B) 2:1

(D) 1:2

Answer: (D)

3. The frame comprises members ABC, CD, and BEDF. This frame is fixed at A, and the connections between the three members are pins. Load P is applied at F. Which of the following statements is TRUE?

(A) ABC and CD are two-force members

(B) CD is the only two-force member

(D) ABC is the only two-force member

Answer: (B)

4. When two spheres moving in a horizontal plane collide obliquely, which one of the following statements is ALWAYS TRUE?

(A) Energy of the two-sphere system is conserved

(B) Linear momentum of the two-sphere system is conserved along the normal to the plane of impact

(D) Linear momentum of each individual sphere is NOT conserved along the horizontal tangent to the plane of impact

Answer: (B)

5. In a bending moment diagram of a simply supported beam, discontinuity in the bending moment occurs

(A) at the point of application of a couple

(B) at the point of application of a concentrated force

(D) at a point where shear force is zero

Answer: (A)

6. For a solid circular shaft fixed at one end and a torque applied at the other end, which one of the following is TRUE?

(A) Every cross section of the shaft is subjected to the same internal torque

(B) The internal torque gradually increases from one end of the shaft to the other end

(D) No cross section of the shaft rotates relative to another cross section

Answer: (A)

7. Flexural stress occurs in a straight beam when

(A) it is subjected to pure torsion

(B) it is subjected to axial loads

(D) it is subjected to combined axial and torsional loads

Answer: (C)

8. The bending moment at a point in a beam changes its sign. Which one of the following is ALWAYS TRUE?

(A) The slope of the beam changes its sign at that point

(B) The deflection of the beam changes its sign at that point

(D) The curvature of the beam changes its sign at that point

Answer: (D)

9. The state of stress at a point in a body under plane stress condition is given as 𝜎 = 5 MPa, 𝜎_𝑦 = ̶ 1 MPa and 𝜏^𝑥𝑦 = 4 MPa. If one of the principal stresses at that point is 7 MPa, thenthe other non-zero principal stress (in MPa) is _______

Answer: (-3.0 to -3.0)

XE -D: Q. 10 – Q. 22 carry two marks each.

10. A massless rod of length L having a concentrated mass m attached at its mid-point is held at rest between the smooth ground and the smooth wall when it makes an acute angle 𝜃₀ with the ground as shown. The rod is then released. The acceleration due to gravity is 𝑔. At an instant when the angle between the rod and ground is θ, the velocity of the mass m is

Answer: (B)

11. A cantilever beam of constant cross section is subjected to a positive moment M and a positive axial force F as shown. The normal stress due to the axial force F is 200 MPa and the maximum compressive stress due to the moment M is 100 MPa. If the point A is located on the top surface and the point B is located on the centroidal axis of the beam, the stress elements at these points are (with stresses shown in MPa)

(A)

(B)

(C)

(D)

Answer: (A)

12. The block of mass m = 10 kg is held in place along the incline by the force F applied via a pulley arrangement as shown. The coefficient of static friction between the block and incline is 0.65. The range of F (in N) for which the block will remain at rest is (use acceleration due to gravity 𝑔 = 10 m/s²)

(A) 6.3 to 106.30

(B) 0 to 106.30

(D) 53.15 to 106.30

Answer: (C)

13. The frame shown comprises members ABC, BE, BF, and DEF. It is pin supported at A and D. Members BE and BF are pin connected to ABC and DEF. The vertical load P is applied at C. The force in the member BF is

(A) compressive P

(B) tensile P

(D) tensile 2P

Answer: (D)

14. A simply supported beam is subjected to a concentrated force P = 48000 N at the mid-span as shown. The flexural rigidity of the beam is EI = 11 × 106 N-m². The curvature of the beam between points Q and R is given as κ = (𝑃𝑥⁄2𝐸𝐼). The magnitude of deflection (in mm) of the beam at 𝑥 = 0.5 m is

(A) 0.5

(B) 1.0

(D) 2.0

Answer: (A)

15. The shear force (V) diagram for a cantilever beam under certain loads applied at points B and C is shown. The magnitude of applied force at B (FB), and the magnitude of applied force at C (FC), are

(A) F_B = 500 N F_C = 300 N

(B) F_B = 200 N F_C = 300 N

(D) F_B = 300 N F_C = 500 N

Answer: (A)

16. A bar of length 1 m, having a uniform area of cross section 1000 mm², is fixed at one end and subjected to a uniaxial tensile load of 200 kN at the other end. Along with the tensile load, the rod also experiences a uniform temperature rise ΔT = 100 °C. The material of the rod has a Young’s modulus E = 200 GPa and coefficient of thermal expansion α = 1×10^{̶ 5}/ °C. The elongation of the rod (in mm) is ______

Answer: (2.0 to 2.0)

17. A solid rod, with uniform circular cross section, of length 1000 mm and diameter 100 mm is subjected to a uniaxial tensile load. As a result, the increase in length of the rod is observed to be 1 mm while the reduction in diameter of the rod is observed to be 0.03 mm. If the Young’s modulus of the material of the rod is 260 GPa, the shear modulus (in GPa) of the material of the rod is _______

Answer: (100 to 100)

18. A spherical pressure vessel has inner diameter of 4 m and wall thickness of 10 mm. It is made of a steel having tensile yield strength of 200 MPa. Neglecting radial stress and using the maximum shear stress theory, the maximum value of gauge pressure (in MPa) that the wall of the pressure vessel can withstand is _____ (rounded off to two decimal places)

Answer: (1.90 to 21.0)

19. Two solid shafts P and Q made of same material transmit equal torque. Shaft P has a uniform circular cross section of area A and shaft Q has a uniform circular cross section of area 4A. If the maximum torsional shear stress developed in shaft P is 160 MPa, the maximum torsional shear stress developed (in MPa) in shaft Q is _______

Answer: (19.0 to 21.0)

20. The slotted arm AB rotates in the horizontal plane about point A at a constant angular speed 𝜔 = 10 rad/sec. The particle P is released from rest, in the frictionless slot, at a distance of 2 m from end A. The magnitude of the velocity of the particle (in m/s) just before it hits end B is ______ (rounded off to two decimal places)

Answer: (52.00 to 54.00)

21. The uniform pendulum rod, having mass 10 kg and length 𝐿 = 5 m, is attached to a viscous damper having damping coefficient c. Use acceleration due to gravity 𝑔 = 10 m/s². The least value of c (in N-s/m) such that small motions of the pendulum rod decay without oscillations is ______

Answer: (102.0 to 106.0)

22. A beam having a constant solid rectangular cross section is subjected to pure bending. The longitudinal strain at a point A on the cross section is 3.0 × 10⁻⁵. If the Young’s modulus of the material of the beam is 200 GPa, the maximum tensile stress (in MPa) is ______

Answer: (10.0 to 10.0)

XE-E

XE-E: Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each. Notations used:

c_p: Specific heat at constant pressure; c_v: Specific heat at constant volume; h: Specific enthalpy; s: Specific entropy; v: Specific volume; P: Pressure; V: Volume; T: Temperature; R: Gas constant; R_u : Universal Gas constant

1. One kg of an ideal gas (molecular weight = X) occupies a certain volume V at temperature T and pressure 𝑃1. Four kgs of another ideal gas (molecular weight = 2X) is added to the first gas keeping the volume V and temperature T same as before. The final pressure is

(A) 2 𝑃₁

(B) 3 𝑃₁

(D) 5 𝑃₁

Answer: (B)

2. Which of the following is an intensive thermodynamic property?

(A) Enthalpy

(B) Internal energy

(D) Pressure

Answer: (D)

3. A thermodynamic process for a substance is represented as a constant pressure process on a P-V diagram, and a constant temperature process on a T-V diagram. Which of the following statements is TRUE?

(A) The substance is an ideal gas.

(B) The substance is a van der Waals gas.

(D) Such a process is not possible.

Answer: (C)

4. Addition of a reheat process to a simple Rankine cycle will always

(A) increase both efficiency and work output of the cycle.

(B) increase efficiency but not necessarily work output of the cycle.

(D) decrease both efficiency and work output of the cycle.

Answer: (C)

5. A Carnot cycle implemented using an ideal gas in a piston-cylinder system will have

(A) work transfer in two parts of the cycle and heat transfer in the other two parts of the cycle.

(B) work transfer in all four parts of the cycle and heat transfer in two parts of the cycle.

(D) work transfer in all four parts of the cycle and heat transfer in all four parts of the cycle.

Answer: (B)

6. The “degrees of freedom” for a pure substance at its triple point is

(A) 3

(B) 2

(D) 0

Answer: (D)

7. The differential of the Gibbs function (g) for a simple compressible system can be represented as 𝑑𝑔 = 𝑣 𝑑𝑃 − 𝑠 𝑑𝑇. Using the appropriate Maxwell relation derived from the above equation, the quantity, for an ideal gas is

(A) R/T

(B) R/P

(D) T/R

Answer: (B)

8. A Carnot engine receives 2000 kJ heat from a source at 1200 K and rejects 500 kJ heat to sink. The sink temperature (K) is ______.

Answer: (300 to 300)

9. A closed vessel contains a pure substance with 0.1 m3 of saturated liquid and 0.9 m³ of saturated vapor. The specific volume of the liquid and vapor phases are 0.000843 m³/kg and 0.02671 m³/kg respectively. The percentage of vapor in the mixture on mass basis (rounded off to two decimal places) is _____.

Answer: (22.00 to 22.30)

10. A gas obeys the van der Waals equation of state where a and b are van der Waals constants. The compressibility factor in the limit of high specific volume (𝑏 ≪ 𝑣) is

Answer: (A)

11. Consider the thermodynamic relation, For a certain gas, if the isobaric thermal expansion coefficient, (where T is the temperature measured in K), then the value of is,

(A) 0

(B) 1

(D) 𝑣/T

Answer: (A)

12. A piston-cylinder system has an initial volume of 0.1 m³ and contains an ideal gas ( 𝑣 = 0.74 kJ/kg.K, 𝑅 = 0.288 kJ/kg.K) at 1.5 bar and 298 K. The piston is moved to compress the gas until the pressure and temperature reach 10 bar and 423 K respectively. During this process, 20 kJ of work is done on the gas. The magnitude of heat transfer (kJ) during this process is

(A) 134.8

(B) 36.2

(D) 3.8

Answer: (D)

13. A reversible cyclic device absorbs 400 kJ/s heat from a reservoir maintained at 265 K and rejects heat to another reservoir at 298 K. The magnitude of the rate of work done (kW) by the device is

(A) 849.81

(B) 449.81

(D) 49.81

Answer: (D)

14. In a reversible process, an ideal gas (cp = 1.04 kJ/kg.K, R = 0.297 kJ/kg.K) at 293 K, is compressed in a cylinder from 100 kPa to 500 kPa. During this compression process, the relation between pressure and volume is expressed as, 𝑃𝑣^1.3 = constant.

In the following options, mark the closest value for the entropy change per kilogram (J/kg.K).

(A) −91

(B) 91

(D) 864

Answer: (A)

15. The sublimation pressure of water vapor at 233 K is 13 Pa. Assume the water vapor to behave as an ideal gas (R = 0.46 kJ/kg.K), and the latent heat of sublimation is 2840 kJ/kg. The sublimation pressure of water vapor at 213 K, (rounded off to 2 decimal places), is _______ Pa.

Answer: (1.05 to 1.15)

16. In a heating and humidification process, dry air (d.a) with relative humidity of 10% at ambient temperature of 10°C, is mixed with superheated steam at temperature ‘T’. The resultant mixture is at 25°C with relative humidity of 50%. The total pressure before and after the process remains the same at 102 kPa. The saturated pressure of water vapor (v) at 10°C and 25°C are 1.2281 kPa, and 3.1698 kPa, respectively. The specific humidity in grams of water vapour per kg of dry air, can be calculated using where 𝑝_𝑣and 𝑝_𝑑_._𝑎 are the partial pressures of water vapour and dry air respectively. The quantity of steam in grams (rounded off to 2 decimal places) added per kg of dry air is _______

Answer: (8.50 to 9.50)

17. In a vapor compression system, a refrigerant leaves the evaporator and enters the compressor in saturated vapor condition at 0°C. The specific enthalpies of the saturated liquid and the saturated vapor at 0°C are 50 kJ/kg and 250 kJ/kg, respectively. The refrigerant leaves the compressor with a specific enthalpy of 300 kJ/kg. From the exit of the condenser, the refrigerant is throttled to the evaporator pressure. If the coefficient of performance (COP) of the refrigerator is 2.8 then the dryness fraction of the refrigerant entering the evaporator is_________.

Answer: (0.3 to 0.3)

18. Hot air, assumed as an ideal gas (cp = 1000 J/kg.K, γ = 1.4) enters a gas turbine at 10 bar, 1000 K and leaves at a pressure of 5 bar. Subsequently it expands in a nozzle to a pressure of 1 bar. Assume both these processes to be reversible and adiabatic. If the inlet velocity of the air to the nozzle is negligible, the final velocity (m/s, rounded off to 1 decimal place) of air at the exit of the nozzle is _______.

Answer: (770.0 to 785.0)

19.

The “T-s diagram” for a thermodynamic process is shown in the figure. The heat transferred (kJ/kg) during the reversible process 1-3 is ______ .

Answer: (255 to 255)

20. In a simple Rankine cycle, superheated steam enters the turbine at 100 bar, 500°C (h = 3375.1 kJ/kg, s = 6.5995 kJ/kg.K) at a rate of 1000 kg/s. It expands isentropically in the turbine to the condenser pressure. The temperature in the condenser is 30°C (h_f = 125.74 kJ/kg, s_f = 0.4368 kJ/kg.K, h_g = 2555.6 kJ/kg, s_g = 8.4520 kJ/kg.K). Saturated water from the condenser is pumped back to the boiler. Neglecting the pump work, the efficiency (in percentage, rounded off to 1 decimal) of the cycle is ________.

Answer: (41.0 to 43.5)

21. A rigid, adiabatic container has two parts (A) and (B) separated by a piston. Initially, part (A) is filled with 1 kg of an ideal gas (c_v = 750 J/kg.K, R = 500 J/kg.K) at 1 bar, 600 K. The part (B) is filled with 1 kg of the same ideal gas at 2 bar, 400 K. The piston is now removed. In the final state, the pressure (bar, rounded off to two decimal places) will be ________ .

Answer: (1.25 to 1.25)

22. In a steady flow process, superheated steam at 70 bar and 450°C, is throttled to 30 bar in an insulated valve, at a rate of 2 kg/s. The changes in the kinetic energy and potential energy during the process are assumed to be zero. The rate of entropy generation (kJ/s.K rounded off to three decimal places) during the throttling process is _____.

The thermodynamic property data for superheated steam at 70 bar and 450°C:

h = 3288.3 kJ/kg, s = 6.6353 kJ/kg.K

The thermodynamic property data for superheated steam at 30 bar are given in the following table.

Answer: (0.700 to 0.750)

XE-F: Polymer Science and Engineering

XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each. XE (B to H): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. The functionality of allyl alcohol (CH₂=CH-CH₂OH) for condensation reaction with terephthalic acid is

(A) 0

(B) 1

(D) 3

Answer: (B)

2. Which of the following polymers can be synthesized by ring opening polymerization?

(A) Poly(vinyl alcohol)

(B) Nylon 66

(D) Poly(ε-caprolactone)

Answer: (D)

3. The weather resistant polymer among the following is

(A) natural rubber

(B) styrene butadiene rubber

(D) silicone rubber

Answer: (D)

4. If a combination of sodium and naphthalene is used to initiate polymerization of styrene, then the most likely mechanism of polymerization is

(A) free radical

(B) cationic

(D) olefin metathesis

Answer: (C)

5. Hypalon is the trade name for

(A) chlorosulfonated polyethylene

(B) chlorinated polyethylene

(D) cross-linked polyethylene

Answer: (A)

6. The copolymer(s) among high density polyethylene (HDPE), low density polyethylene (LDPE) and linear low density polyethylene (LLDPE) is/are

(A) LDPE only

(B) LLDPE only

(D) HDPE and LDPE

Answer: (B)

7. The polymer which lacks the ability to exhibit tacticity among the following is

(A) polypropylene

(B) polystyrene

(D) poly(methyl methacrylate)

Answer: (C)

8. The correct order of glass transition temperature (Tg) for the polymers listed below is

(PC = polyca polycarbonate; PET = poly(ethylene terephthalate); PE = polyethylene; PP = polypropylene)

(A) PC > PE T > PP > PE

(B) PC > PET > PE > PP

(D) PET > PC > PP > PE

Answer: (A)

9. Polystyrene coffee cup can be most economically manufactured by

(A) thermoforming

(B) injection molding

(D) blow molding

Answer: (A)

10. Match the following rubber additives to their function:

(A) P-4, Q-1, R-3, S-2

(B) P-3, Q-1, R-4, S-2

(D) P-4, Q-2, R-3, S-1

Answer: (B)

11. Match the following polymers with their characteristic infrared (IR) stretching frequency:

(A) P-2, Q-3, R-1, S-4

(B) P-2, Q-1, R-4, S-3

(D) P-4, Q-1, R-2, S-3

Answer: (D)

12. Match the following products to the most suitable polymer for their manufacture:

(A) P-3, Q-2, R-1, S-4

(B) P-3, Q-4, R-2, S-1

(D) P-2, Q-3, R-1, S-4

Answer: (B)

13. The order of limiting oxygen index for the following polymers is (polypropylene = PP; PTFE=polytetrafluoroethylene; PVC=poly(vinyl chloride)

(A) PP < PTFE < Nylon 6 < PVC

(B) PP < PVC < Nylon 6 < PTFE

(D) PP < Nylon 6 < PTFE < PVC

Answer: (C)

14. Match the following plastic additives to their function:

(A) P-3, Q-1, R-2, S-4

(B) P-3, Q-4, R-1, S-2

(D) P-4, Q-3, R-1, S-2

Answer: (D)

15. Match the material classification in Column A with the appropriate one in Column B: (PS=polystyrene, PPO=polyphenylene oxide, PDMS=poly(dimethyl siloxane), PP=polypropylene, PE=polyethylene, PP-g-MA= maleic anhydride grafted PP)

(A) P-3, Q-4, R-2, S-1

(B) P-4, Q-3, R-2, S-1

(D) P-4, Q-3, R-1, S-2

Answer: (A)

16. A linear amorphous polymer has a T_g of +10 °C. At 28 °C, it has a melt viscosity of 4 × 10⁸poise. The viscosity of the polymer at its T_g is _____ × 10¹³ poise (round off to one decimal place).

Answer: (1.2 to 1.4)

17. A polypropylene (PP) bar with a 10 mm × 10 mm square section is 225 mm long. The modulus of PP bar is 861 MN m⁻². It is pinned at both ends and an axial compressive load of 140 N is applied. The strain due to the applied load experienced by the PP bar is ______% (round off to two decimal places).

Answer: (0.15 to 0.17)

18. In a unidirectional carbon fibre/vinyl ester composite, the ratio of the moduli of the carbon fibre to that of vinyl ester is 35 and the fibres take up 50% of the cross-section. The percentage of applied force taken up by the fibres is ______% (round off to one decimal place).

Answer: (97.0 to 97.5)

19. A 3 mm thick layer of softened poly(methyl methacrylate) at 190 °C is sandwiched between two flat parallel plates. A shear stress of 100 kPa is applied to the softened polymer. Assuming the softened polymer as a Newtonian fluid with an apparent viscosity of 3.9 × 10⁴ Pa s, the relative sliding velocity between the two plates is _____ mm s⁻¹ (round off to one decimal place).

Answer: (7.6 to 7.8)

20. For AIBN initiated polymerization of styrene, if both the monomer and initiator concentration are doubled, then the rate of polymerization increases by a factor of ______ (round off to two decimal places).

Answer: (2.80 to 2.84)

21. If 49 moles of hexamethylene diamine is reacted with 50 moles of adipic acid to prepare Nylon 66, then the number average molecular weight, of the resulting polymer at 99.5% conversion (ignoring contribution from end groups) is _____ g mol⁻¹ (round off to 2 decimal places).

Answer: (7497.72 to 7517.72)

22. A single screw extruder is to be used to manufacture a nylon rod of 0.5 cm diameter at a production rate of 2.5 cm s⁻¹. The density of solid nylon and nylon melt are 1.140 g cm-3 and 0.790 g cm⁻³, respectively. The melt flow rate through the die is____ cm³ s⁻¹ (round off to two decimal places).

Answer: (0.69 to 0.73)

XE-G: Food Technology

Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. Colloidal stability of milk casein is because of the highly hydrated carbohydrate residues in______.

(A) α_s1 casein

(B) α_s2 casein

(D) κ casein

Answer: (D)

2. Rice bran is stabilized prior to oil extraction to protect it from the activity of ______.

(A) Polyphenol oxidase

(B) Peroxidase

(D) Lipoxygenase

Answer: (C)

3. Sticking of powder to wall of the chamber during spray drying of fruit juice is due to _____.

(A) Low glass transition temperature of the compounds in juice

(B) High glass transition temperature of the compounds in juice

(D) Presence of gums in feed material

Answer: (A)

4. Thearubigins and theaflavins in black tea are formed by the oxidation and dimerization of ______.

(A) Quercetin

(B) Catechins

(D) Kaempferol

Answer: (B)

5. Ratio of Schmidt number to Lewis number is ______.

(A) Prandtl number

(B) Reynolds number

(D) Sherwood number

Answer: (A)

6. ‘Red dog’ is one of the byproducts during milling of .

(A) Corn

(B) Rice

(D) Wheat

Answer: (D)

7. An ice cream mix of 870 g L⁻¹ has been used to prepare ice cream which yielded a finished product of 490 g L⁻¹. The per cent over run is _______(round off to 1 decimal place).

Answer: (77.4 to 77.6)

8. Impeller in a fruit juice mixing tank is rotating at 200 rpm with a Reynolds number >104. Density of juice is 1045 kg m⁻³. If diameter of the impeller is doubled and other conditions remained constant, the power requirement of mixing will increase by a factor of ______.

Answer: (32 to 32)

9. Paddy consisting of 20% husk has been milled to remove 6% bran during polishing. Assuming no other losses, yield (per cent) of polished rice from the paddy is _____ (round off to 1 decimal place).

Answer: (74.8 to 75.6)

10. Match the following laws in Column I with corresponding phenomenon in Column II.

(A) P-2, Q-3, R-4, S-1

(B) P-3, Q-2, R-4, S-1

(D) P-4, Q-3, R-2, S-1

Answer: (A)

11. Match the mold in Column I with its asexual/sexual spore shown in Column II.

(A) P-3, Q-1, R-4, S-2

(B) P-1, Q-4, R-3, S-2

(D) P-4, Q-1, R-2, S-3

Answer: (A)

12. Match the foods given in Column I with their specific usage given in Column II.

(A) P-2, Q-4, R-1, S-3

(B) P-4, Q-1, R-2, S-3

(D) P-1, Q-4, R-1, S-3

Answer: (A)

13. Match the bioactive compounds in Column I with their botanical source given in Column II.

(A) P-2, Q-4, R-1, S-3

(B) P-3, Q-4, R-1, S-2

(D) P-4, Q-3, R-2, S-1

Answer: (B)

14. Match the following microbial species in Column I with related disease caused by them as listed in Column II.

(A) P-1, Q-3, R-4, S-2

(B) P-2, Q-3, R-4, S-1

(D) P-3, Q-4, R-1, S-2

Answer: (D)

15. Buffalo milk having density of 1030 kg m⁻³ is homogenized with a pressure of 30 MPa. Given, acceleration due to gravity as 9.81 m s⁻² and assuming no pressure loss, the velocity (m s⁻¹) of the milk flowing through the homogenizer valve will be _____ (round off to 2 decimal places).

Answer: (240.00 to 242.00)

16. Potato slices have been dehydrated from an initial solid content of 12% to a final solid content of 94%. If the peeling and other losses are to the tune of 10%, final yield (per cent) of the dried chips per ton of fresh potato taken is ______ (round off to 2 decimal places).

Answer: (11.45 to 11.55)

17. A mixed fruit beverage with 12 °Brix having specific heat of 4298 J kg⁻¹ K⁻¹ is being heated from 30 °C to 95 °C for pasteurization at a flow rate of 1000 L h⁻¹ in a tubular heat exchanger. Steam at 100 °C is used as heating medium which is converted into condensate at 100 °C. If the density of beverage is 1075 kg m⁻³ and the latent heat of steam at the given temperature is 2257 kJ kg⁻¹, the mass flow rate of steam (kg min⁻¹) is ______(round off to 2 decimal places).

Answer: (2.16 to 2.25)

18. Fruit juice was cooled in a tubular heat exchanger from 50 °C to 7 °C using water at 2 °C, which gets heated to 5 °C. Assume, Pr = 0.72, Re = 20000 and thermal conductivity = 0.6W m-1 °C⁻¹ and no viscous effect. If pipe diameter was 10 cm, the convective heat transfer coefficient (W m-2 °C⁻¹) is _____ (round off to 1 decimal place).

Answer: (339.1 to 342.9)

19. Room air is at 40 °C with 60% relative humidity. Saturated vapour pressure of water at 40 °C is 7.375 kPa. Volume of humid air (m3 per kg of dry air) is ______ (round off to 3 decimal places).

Answer: (0.924 to 0.930)

20. A shallow-bed horizontal belt type solvent extractor is operating on 0.3 mm thick soybean flakes with 0.5 m bed depth and a forward speed of 0.8 m min⁻¹ with miscella flux rate of 0.25 m min⁻¹. If porosity of the flakes is 60%, the distance between washing nozzle and miscella collecting receptacle (cm) is _____ (round off to 1 decimal place).

Answer: (95.0 to 100.0)

21. An extruded snack food is packed in a barrier film having water vapour transmission rate of 0.02 mL m⁻² day⁻¹. Pack surface area is 0.0012 m2 per gram of dry food solids, EMC of the food is 6% (d.b.), initial moisture content is 2% (d.b.), critical moisture content is 5% (d.b.) and slope of moisture sorption isotherm is 3.4% (d.b.) per unit water activity (aw). Sealed pack is stored at 30 °C. Assume that the vapor pressure of pure water at 30 °C is 31.7 torr. Time required for the food to reach the critical moisture content (days) is______ (round off to 1 decimal place).

Answer: (58.1 to 62.9)

22. Freezing of 100 mm spherical meat ball with 60% moisture at 35 °C is being done in an air blast freezer maintained at −45 °C. Given, latent heat of fusion for water is 333.2 kJ kg⁻¹, thermal conductivity of meat is 1.5 W m⁻¹ °C⁻¹, convective heat transfer coefficient is 40 W m-2 °C⁻¹, density of frozen meat is 980 kg m^-3 and initial freezing temperature of meat ball is −10 °C. Using Plank’s equation, freezing time (h) is ______ (round off to 2 decimal places).

Answer: (1.06 to 1.09)

XE-H: Atmospheric and Oceanic Sciences

XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each. XE (B to H): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each. XL-P: Q. 1 – Q. 5 carry one mark each & Q. 6 – Q. 15 carry two marks each XL (Q to U):Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. In the equatorial belt, the Madden-Julian Oscillation (MJO) propagates

(A) northward

(B) southward

(D) westward

Answer: (C)

2. Potential temperature increases with height in an atmosphere, Upon adiabatic vertical displacement, a parcel of dry air is

(A) stable

(B) absolutely unstable

(D) conditionally unstable

Answer: (A)

3. Oxygen minimum zones in the ocean are formed in the layers where

(A) Photosynthesis is dominant

(B) Sunlight is maximum

(D) Iron availability is maximum

Answer: (C)

4. Water level in an estuary rises and falls in response to tidal forces. Assume that the only tidal period in an estuary is 12 hours. The speed of the ebb current in that estuary would be maximum

(A) At high tide

(B) At low tide

(D) About 6 hours after low tide

Answer: (C)

5. The most abundant ions in seawater are

(A) Sodium and chloride ions

(B) Magnesium and chloride ions

(D) Magnesium and sulphide ions

Answer: (A)

6. Which among the following statements is true with respect to the axis of the Indian monsoon trough

(A) Relative vorticity is cyclonic at 850 hPa

(B) Relative vorticity is anticyclonic at 850 hPa

(D) It moves to the head Bay of Bengal when a monsoon depression is present over the Indian subcontinent

Answer: (A)

7. A student considered the following possibilities regarding trade wind inversion:

(P) Zonal component of wind is westerly

(Q) Zonal component of wind is easterly

(R) Meridional component of wind is poleward

(S) Meridional component of wind is equatorward

The only combination of correct statements is

(A) P,S

(B) Q,S

(D) P,R

Answer: (B)

8. Which of the following statements about thermal wind is NOT correct:

(A) Flow is in geostrophic balance

(B) Horizontal temperature gradient is non-zero

(D) Flow is quasi-geostrophic

Answer: (D)

9. A numerical weather forecasting model follows sigma (σ) coordinate system in the vertical. ions A and B, the surface pressure is 1000 hPa and 500 hPa respectively. The values to pressure at A and B (in that order) for σ = 0.5 are:

(A) 2000 hPa, 1000 hPa

(B) 500 hPa, 250 hPa

(D) 500 hPa, 0 hPa

Answer: (B)

10. At a given temperature and pressure, equilibrium vapor pressure over the surface of a rain droplet compared to that over a flat surface of pure water is

(A) Always less

(B) Always more

(D) Can be less, equal to or more depending on the size and chemical composition of the cloud condensation nuclei, and droplet radius

Answer: (D)

11. Velocity field in a geophysical flow is given by u = -5x, v = 4y, w = 0 where u, v, w are zonal, meridional and vertical components of velocity, and x and y refer to eastward and northward distance. Which among the following statements is NOT true for the flow at 45oN:

(A) Flow is incompressible

(B) Relative vorticity is zero

(D) Flow is compressible

Answer: (A)

12. The distance between Mars and Earth is 0.52 times the distance between Sun and Earth. If the solar constant on Earth is 1370 W m⁻², then the solar constant on Mars is _____ W m⁻². (Round off to one decimal place.)

Answer: (592.8 to 593.2)

13. Ideal gas equation for dry air is expressed as p = ρ_d R_d T, where p is pressure, ρ_d is density, T is temperature and Rd is gas constant. If CO₂ concentration in Earth’s atmosphere quadruples due to fossil fuel burning, then the new gas constant is _______J kg⁻¹ K⁻¹. (Round off to two decimal places.)

Take the universal gas constant (R*) = 8.314 J K⁻¹ mole⁻¹, molecular weight of CO₂ = 44, and present value of Rd = 287 J kg⁻¹ K⁻¹, present concentration of CO₂ = 500 mg kg⁻¹.

Answer: (286.40 to 287.30)

14. On a calm evening under a clear sky, the lowest 20 m of the atmosphere is continuously losing energy at a rate of 10 W m⁻² due to radiative cooling. Sensible and latent heat flux exchange with the ground is zero. If air temperature and dew point depression at 6 p.m. are 25oC and 8oC, respectively, the probability of fog formation at midnight is ____%. (Round off to the nearest integer.)

Take C_p = 1005 J kg⁻¹ K⁻¹, density of air = 1.15 kg m⁻³

Answer: (99 to 100)

15. The dynamical core of a general circulation model uses 256 spherical harmonic waves to cover the globe in east-west direction. If two grids of the model exactly resolve the shortest of those waves, then the grid spacing at the equator is _____km. (Round off to one decimal place.)

Take radius of the earth (R_E) = 6400 km.

Answer: (78.4 to 78.6)

16. It rains 10 cm in a day over an ocean with a mixed layer depth of 5 m and initial salinity 30 g kg⁻¹. The rain water uniformly mixes with the existing mixed layer water. The finalsalinity after the rain is _____ g kg⁻¹. (Round off to one decimal place.)

Answer: (29.3 to 29.5)

17. A moist air parcel is lifted adiabatically to 800 hPa level. Initial temperature and pressure of the parcel are 300 K and 1010 hPa, and the partial pressure of water vapor is 10 hPa. The partial pressure of the water vapor at the new location is _____ hPa. (Round off to one decimal place.)

Take saturation vapor pressure of water at temperature T as

𝑒_s(𝑇) = 𝐴𝑒⁻^𝐵^/T

where A = 2.53 × 10⁹ hPa, B = 5420 K, gas constant (R) = 287 J kg⁻¹ K⁻¹, and Cp = 1005 J kg⁻¹ K⁻¹.

Answer: (7.8 to 8.1)

18. In steady state, global mean precipitation P is equal to global mean evaporation E from the surface of the earth. If P is 2.8 mm day-1, then global mean surface latent heat flux is ____ W m⁻². (Round off to the nearest integer).

Take latent heat of evaporation of water as 2.5 × 10⁶ J kg⁻¹.

Answer: (75 to 85)

19. A column of seawater from surface to 1000 m depth is initially at rest at the equator. The column is moved to 30oN with no change in column depth. In the absence of friction, the vertical component of relative vorticity of the water in the column at 30oN is _______ ×10⁻⁵ s⁻¹. (Round off to one decimal place.)

Answer: (-7.6 to -7.0)

20. Consider two north-south (i.e. meridional) sections A and B in the ocean, separated by 100 km; section B is to the east of section A (as shown in figure below). The steady northward wind stress at A and B are 0.1 N/m² and 0.2 N/m², respectively; zonal wind stress is zero everywhere. Density of seawater is 1000 kg m⁻³. At 30°N, the vertical velocity at the base of the Ekman layer is _______ meters per day. (Round off to one decimal place.)

Answer: (1.1 to 1.3)

21. A tsunami is a long gravity wave, i.e. its wavelength is much larger than the depth of the ocean. A tsunami moves from point A to point B (see figure below); water depth at A is 2000 m, and water depth at B is 500 m. Assume no frictional losses. By energy conservation, C_g <E> is constant, where C_g is group speed and <E> is the total (potential plus kinetic) energy density of the wave field. If the amplitude of the tsunami at point A is 1 m, its amplitude at B is ________m. (Round off to two decimal places.)

Answer: (1.30 to 1.50)

22. At mid-latitudes, long Rossby waves obey the dispersion relation σ = −βk / L⁻², where σ is frequency, k is zonal wavenumber, β is rate of change of Coriolis parameter with northward distance (units m⁻¹ s⁻¹), and L is Rossby radius. If L = 100 km, the speed of the long Rossby wave at 45oN is ________ m s⁻¹. (Round off to two decimal places.)

Take radius of the earth as 6400 km.

Answer: (0.13 to 0.19)

GATE Exam 2019 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

June 7, 2023December 15, 2019 by suresh84

General Aptitude Set-4

Q.1 – Q. 5 carry one mark each.

1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.

Which one of the following choices CANNOT fill the given blank?

(A) will be

(B) were to be

(D) might be

Answer: (B)

2. A final examination is the _______ of a series of evaluations that a student has to go through.

(A) culmination

(B) consultation

(D) insinuation

Answer: (A)

3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .

(A) JDE

(B) JED

(D) JCD

Answer: (B)

4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

(A) 6

(B) 7

(D) 9.5

Answer: (Marks to All)

5. Are there enough seats here? There are _______people here than I expected.

(A) many

(B) most

(D) more

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.

(A) 37.50

(B) 35.70

(D) 10.00

Answer: (A)

(A) 13.50

(B) 14.5

(D) 16.50

Answer: (B)

The writer of this passage is surprised by the creative writing assignments of his students, because ______ .

(A) Some of the students had written stories set in foreign places

(B) None of the students had written stories set in India

(D) Some of the students had written about ice cubes and cowboys

Answer: (B)

(A) 16.24

(B) 23.97

(D) 38.74

Answer: (B)

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

(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television

(B) Non-members prefer to watch cable television

(D) The X is cancelling accounts of non-members

Answer: (A)

Textile Engineering and Fibre Science

Q.1 – Q. 25 carry one mark each.

1. The value of is

(A) – 1/2

(B) 0

(D) 1

Answer: (C)

2. For 𝑥 in [0, 𝜋], the maximum value of (sin 𝑥 + cos 𝑥) is

(A) 1/√2

(B) 1

(D) 2

Answer: (C)

3. The eigenvalues of the matrix are

(A) −1, 1, 3

(B) −3, 2, −2

(D) 3, 2, 1

Answer: (A)

4. Acrylic fibre is made from at least 85% by weight of

(A) Acrylic acid

(B) Acrylonitrile

(D) Methyl methacrylate

Answer: (B)

5. The pair of natural fibres, belonging to the category of seed fibre, is

(A) Cotton and Sisal

(B) Kenaf and Kapok

(D) Cotton and Kapok

Answer: (D)

6. The term ‘half-lap’ is associated with

(A) Card

(B) Drawframe

(D) Roving frame

Answer: (C)

7. In a modern card, the highest angular velocity (rpm) is found in

(A) Feed roller

(B) Taker-in

(D) Doffer

Answer: (B)

8. For multifilament yarns, optimum add-on (%) of size is in the range

(A) 0-0.5

(B) 4-8

(D) 30-35

Answer: (B)

9. The movements of guide bars in warp knitting are

(A) Swinging and shaking

(B) Shaking and shogging

(D) Swinging and shogging

Answer: (D)

10. Among the following options, the thickest Classimat fault is

(A) B3

(B) D1

(D) H2

Answer: (A)

11. Work factor of a perfectly elastic yarn is

(A) 0

(B) 0.5

(D) 2

Answer: (B)

12. Barium Activity Number (BAN) of a cotton fabric was found to be 150. The fabric must have undergone

(A) Desizing only

(B) Desizing and scouring only

(D) Desizing, scouring and mercerization

Answer: (D)

13. The gum present in the raw mulberry silk fibre is

(A) Sericin

(B) Fibroin

(D) Casein

Answer: (A)

14. The value of 𝑘 for which the matrix does not have an inverse is______.

Answer: ()

[/bg_collapse6 to 6]

15. If a continuous random variable has the following probability density function then the value of 𝑘 is ______.

Answer: (4 to 4)

16. A blend of nylon 6 and polyester fibres when dissolved in formic acid at room temperature leaves a bone dry residue of 40% by weight. The weight fraction of polyester in the blend (rounded off to 1 decimal place) is _______.

Answer: (0.4 to 0.4)

17. Molecular weight of the repeat unit of poly (ethylene terephthalate) is _______.

Answer: (192.0 to 192.5)

18. Six carded slivers of 4 ktex each are drawn to produce a sliver of 5 ktex. The draft required (rounded off to 1 decimal place) is ________.

Answer: (4.7 to 4.9)

19. The ratio of yarn tensile modulus to fibre tensile modulus, where the surface fibres are inclined at a twist angle of 25°, (rounded off to 2 decimal places) is ______.

Answer: (0.81 to 0.83)

20. If the linear density (tex) of a yarn is doubled, then percentage increase in tightness factorof single jersey knitted fabric (rounded off to 1 decimal place) is ______.

Answer: (40.0 to 43.0)

21. A square plain jammed fabric has yarns with circular cross-section. If the yarn diameter is0.02 cm, then number of ends per cm (rounded off to 1 decimal place) is _______.

Answer: (24.0 to 34.0)

22. If the moisture content of a fibre is 10%, its moisture regain (%) (rounded off to 2 decimalplaces) is _______.

Answer: (11.00 to 11.20)

23. The 2.5% span length and uniformity ratio of a particular variety of cotton fibre are 30 mm and 45%, respectively. The 50% span length (mm) of the fibre (rounded off to 1 decimal place) is ______.

Answer: (13.0 to 14.0)

24. A wool fabric is to be dyed with an acid dye to a shade of 4% on the weight of fabric (owf).The material to liquor ratio is 1:40 and the exhaustion is 100%. The concentration (gpl) of the dye in the initial dye bath is ________.

Answer: (1 to 1)

25. A cellulosic fabric has been treated with boric acid to impart flame retardancy. The wet expression is 100%. The molecular weight of boric acid is 62 and the atomic mass of boron is 11. Assume that no chemical reaction takes place between boric acid and the fibre. If 2.2 % boron has been added on the weight of fabric (owf), then the add-on of boric acid on fabric (% owf) (rounded off to 1 decimal place) is __________.

Answer: (12.2 to 12.6)

Q.26 – Q. 55 carry two marks each.

26. One of the points which lies on the solution curve of the following differential equation

2𝑥𝑦 𝑑𝑥 + (𝑥² + 𝑦²) 𝑑𝑦 = 0

with the initial condition 𝑦(1) = 1 is

(A) (−1, 1)

(B) (0, 0)

(D) (2, 1)

Answer: (A)

27. Let 𝑋 be a binomial random variable with mean 1 and variance 3/4. The probability that 𝑋 takes the value 3 is

(A) 3/64

(B) 3/16

(D) ¾

Answer: (A)

28. Match the process steps in viscose fibre manufacture listed in Group I with the corresponding chemicals given in Group II. The correct option is

(A) P-4, Q-3, R-2, S-1

(B) P-4, Q-3, R-1, S-2

(D) P-2, Q-3, R-1, S-4

Answer: (B)

29. The correct combination of techniques to determine the crystallinity in fibres is

(A) TGA and DSC

(B) Birefringence and DSC

(D) Birefringence and X-ray diffraction

Answer: (C)

30. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Kevlar fibre has high strength and high modulus.

[r] : It has high orientation and low crystallinity.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(D) [a] is true but [r] is false

Answer: (D)

31. An opening roller in blowroom with 100 cm length, 38 cm diameter and 2 teeth per cm2 is rotating at an angular velocity of 400 rpm to deliver fibre tufts at a production rate of 500 kg/h. The intensity of opening (fibre mass in mg per tooth) of the opening roller approximately is

(A) 0.44

(B) 0.87

(D) 2.74

Answer: (B)

32. A drawframe with a 3 over 3 drafting arrangement, having an eccentric bottom middle roller of 28 mm diameter, is used to produce a sliver. The back zone and front zone drafts are 1.7 and 3.5, respectively. The sliver is further given a draft of 200 to produce a yarn. The wavelength (m) of the periodic fault in the yarn approximately is

(A) 17.6

(B) 29.9

(D) 104.7

Answer: (C)

33. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]

[a] : The short term mass irregularity of rotor yarn is less than that of ring yarn.

[r] : Rotor yarn has belt or wrapper fibres, but ring yarn does not.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(D) [a] is true but [r] is false

Answer: (B)

34. Match the looms listed in Group I with the corresponding components given in Group II. The correct option is

(A) P-1, Q-3, R-4, S-2

(B) P-3, Q-2, R-1, S-4

(D) P-1, Q-2, R-3, S-4

Answer: (C)

35. The punch density of a needle-punched nonwoven fabric is 50 punches/cm². If the stroke frequency of needle bed is doubled and the fabric delivery speed is halved, then the punch density (punches/cm²) would be

(A) 25

(B) 50

(D) 200

Answer: (D)

36. In air-jet weaving, the correct combination of parameters, on which drag force on weft yarn depends, is

(P) Weave pattern

(Q) Density of air

(R) Weft yarn diameter

(S) Picks per cm

(A) P and Q

(B) Q and R

(D) P and S

Answer: (B)

37. The correct combination of reasons, which leads to decrease in tear strength of a woven fabric, is

(P) Increase in yarn to yarn friction

(Q) Decrease in yarn to yarn friction

(R) Increase in fabric sett

(S) Decrease in fabric sett

(A) P and R

(B) P and S

(D) Q and S

Answer: (A)

38. Match the instruments listed in Group I with the corresponding operating principles given in Group II. The correct option is

(A) P-4, Q-3, R-1, S-2

(B) P-4, Q-2, R-3, S-1

(D) P-4, Q-3, R-2, S-1

Answer: (D)

39. The set containing oxidative bleaching agents only is

(P) Sodium hydrosulphite

(Q) Thiourea dioxide

(R) Sodium hypochlorite

(S) Hydrogen peroxide

(A) P and Q

(B) Q and R

(D) P and S

Answer: (C)

40. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a] : Synthetic thickeners used in pigment printing are neutralized before printing.

[r] : Without neutralization, the viscosity required for printing would not be achieved.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(D) [a] is true but [r] is false

Answer: (A)

41. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a] : The equilibrium dye uptake by a fibre decreases with increasing dyeing temperature.

[r] : Dyeing is an endothermic process.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(D) [a] is true but [r] is false

Answer: (D)

42. The value of the integral obtained using Simpson’s 1/3 rule (rounded off to 2 decimal places) is_________.

Answer: (0.24 to 0.28)

43. Let The value of λ for which the vector is ______.

Answer: (3 to 3)

44. In melt spinning, the diameter of monofilament at the spinneret exit is 0.3 mm and at thetake-up point is 0.15 mm. Assuming that there is no change in density of filament, the spin- draw ratio is ________.

Answer: (4 to4)

45. The experimentally determined density of a fibre is 1.31 g/cc. If the density of the void free fibre is 1.35 g/cc, then the void volume fraction (%) of the fibre sample (rounded off to 2 decimal places) is ________.

Answer: (2.60 to 3.00)

46. The spindle speed of a ring frame, producing a yarn of 25 tex, is 25000 rpm and the rate of delivery is 25 m/min. The twist multiplier (m⁻¹∙ tex^0.5) of the yarn is _______.

Answer: (5000 to 5000)

47. If the value of twist retraction of a yarn is 0.2, then the value of twist contraction (rounded off to 2 decimal places) is ________.

Answer: (1.24 to 1.26)

48. A yarn is passing through an additive type tensioner. The mass of dead weight on disc is 50 g and the coefficient of friction between yarn and disc is 0.3. If the input tension is 50 gf, then the output tension (gf) is __________.

Answer: (79 to 81)

49. In a shuttle loom, if the loom speed (picks per minute) is increased by 20%, then the percentage increase in picking power required per meter of fabric is _______.

Answer: (41 to 45)

50. A sample of 150 cotton fibres is tested for maturity. The number of normal and thin-walled fibres are 105 and 30, respectively. The rest are dead fibres. The maturity ratio is _______.

Answer: (1 to 1)

51. In a vibroscope, the fundamental resonant frequency of fibre X is twice that of fibre Y. Keeping the test length and tensioning weight the same, if the linear density of fibre Y is 10 denier, then the linear density (denier) of fibre X (rounded off to 1 decimal place) is______.

Answer: (2.5 to 2.5)

52. The 95% confidence limits of mean yarn tenacity (cN/tex) based on 100 test samples is 30 ± 1.5. The number of test samples required to obtain 95% confidence limits of 30 ± 0.5 is ________.

Answer: (900 to 900)

53. A 180 denier polyester multifilament yarn, a 60 Ne cotton yarn and a 50 Nm (metric count) polyester/wool yarn are twisted together. The resultant linear density (tex) of the 3-ply yarn, neglecting twist contraction, (rounded off to 2 decimal places) is______.

Answer: (49.50 to 50.00)

54. A polyester fabric is dyed with a disperse dye till equilibrium is reached. If the concentration of the dye in the spent dyebath is 0.05 gpl and the partition coefficient is 1000 ml/g, then amount of dye in the fibre (g/100 g) is ________.

Answer: (5 to 5)

55. A wet polyester fabric has areal density of 160 g/m². The initial temperature of the wet fabric is 20°C. After it is completely dried on a cylinder dryer, its areal density drops to 100 g/m².

Consider,

•Specific heat of polyester as 2.0 J/g °C

•Specific heat of water as 4.2 J/g °C

•Latent heat of evaporation of water as 2260 kJ/kg

Assuming that there is no heat loss, the energy (kJ) required to dry 1 m2 of the fabric (rounded off to 2 decimal places) is _______.

Answer: (170.00 to 173.00)

GATE Exam 2019 Stastics (ST) Question Paper With Answer Key

June 7, 2023December 13, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

6. Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit interest rates.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

7. In a country of 1400 million population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country?

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

8. The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education the term gharana became acceptable. Gharana originally referred to hereditary musicians from a particular lineage, including disciples and grand disciples.

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

9. Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is AM.

(A) 9

(B) 10

(D) 11.30

Answer: (B)

10. “I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community.”

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Statistics

Q.1 – Q.25 carry one mark each.

1. is equal to

(A) e/3

(B) 5/6

(D) π/4

Answer: (D)

2. Let The line integral where C is the triangle with vertices (0,0,0), (5,0,0) and (5,5,0) traversed in that order is

(A) -25

(B) 25

(D) 5

Answer: (B)

3. Let {1,2,3,4} represent the outcomes of a random experiment, and 𝑃({1}) = 𝑃({2}) = 𝑃({3}) = 𝑃({4}) = 1/4. Suppose that 𝐴₁ = {1,2}, 𝐴₂ = {2,3}, 𝐴₃ = {3,4}, and 𝐴₄ = {1,2,3}. Then which of the following statements is true?

(A) 𝐴₁ and 𝐴₂ are not independent.

(B) 𝐴₃ and 𝐴₄ are independent.

(D) 𝐴2 and 𝐴₄ are independent.

Answer: (C)

4. A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes is

(A) 4

(B) 4.5

(D) 5.5

Answer: (B)

5. The dimension of the vector space of 7 × 7 real symmetric matrices with trace zero and the sum of the off-diagonal elements zero is

(A) 47

(B) 28

(D) 26

Answer: (D)

6. Let 𝐴 be a 6 × 6 complex matrix with 𝐴³ ≠ 𝟎 and 𝐴4 = 𝟎. Then the number of Jordan blocks of 𝐴 is

(A) 1 or 6

(B) 2 or 3

(D) 5

Answer: (B)

7. Let 𝑋₁, … , 𝑋_𝑛 be a random sample from uniform distribution defined over (0, 𝜃), where 𝜃 > 0 and 𝑛 ≥ 2. Let 𝑋₍₁₎ = min{𝑋₁, … , 𝑋_𝑛} and 𝑋(𝑛) = max{𝑋₁, … , 𝑋_𝑛}. Then the covariance between 𝑋₍_𝑛) and 𝑋₍₁₎/ 𝑋₍_𝑛) is

(A) 0

(B) 𝑛(𝑛 + 1)𝜃

(D) 𝑛2(𝑛 + 1)𝜃

Answer: (A)

8. Let 𝑋₁, … , 𝑋_𝑛 be a random sample drawn from a population with probability density function 𝑓(𝑥; 𝜃) = 𝜃𝑥^𝜃⁻¹, 0 ≤ 𝑥 ≤ 1, 𝜃 > 0. Then the maximum likelihood estimator of 𝜃 is

Answer: (A)

9. Let 𝑌𝑖 = 𝛽₀ + 𝛽₁_𝑥1_𝑖 + 𝛽₂_𝑥2_𝑖 + 𝜖_𝑖, for 𝑖 = 1, … ,10, where 𝑥₁_𝑖′s and 𝑥₂_𝑖′s are fixed covariates, and 𝜖𝑖′s are uncorrelated random variables with mean 0 and unknown variance 𝜎². Here 𝛽₀, 𝛽₁ and 𝛽₂ are unknown parameters. Further, define is the unbiased least squares estimator of (𝛽₀, 𝛽₁, 𝛽₂). Then an unbiased estimator of 𝜎² is

Answer: (B)

10. For 𝑖 = 1,2,3, let 𝑌𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜖𝑖, where 𝑥_𝑖′s are fixed covariates, and 𝜖_𝑖′s are independent and identically distributed standard normal random variables. Here, 𝛼 and 𝛽 are unknown parameters. Given the following observations,

the best linear unbiased estimate of 𝛼 + 𝛽 is equal to

(A) 1.5

(B) 1

(D) 2.1

Answer: (A)

11. Consider a discrete time Markov chain on the state space {1,2,3} with one-step transition probability matrix Which of the following statements is true?

(A) States 1, 3 are recurrent and state 2 is transient.

(B) State 3 is recurrent and states 1, 2 are transient.

(D) States 1, 2 are recurrent and state 3 is transient.

Answer: (B)

12. The minimal polynomial of the matrix is

(A) (𝑥 − 1)(𝑥 − 2)

(B) (𝑥 − 1)²(𝑥 − 2)

(D) (𝑥 − 1)²(𝑥 − 2)²

Answer: (B)

13. Let (𝑋₁, 𝑋₂, 𝑋₃) be a trivariate normal random vector with mean vector (−3, 1,4) and variance-covariance matrix Which of the following statements are true?

(i) 𝑋₂ and 𝑋₃ are independent.

(ii) 𝑋₁ + 𝑋₃ and 𝑋₂ are independent.

(iii) (𝑋₂ , 𝑋₃) and 𝑋1 are independent.

(iv) 1/2 (𝑋2 + 𝑋3) and 𝑋1 are independent.2

(A) (i) and (iii)

(B) (ii) and (iii)

(D) (iii) and (iv)

Answer: (D)

14. A 2³ factorial experiment with factors 𝐴, 𝐵 and 𝐶 is arranged in two blocks of four plots each as follows: (Below (1) denotes the treatment in which 𝐴, 𝐵 and 𝐶 are at the lower level, ac denotes the treatment in which 𝐴 and 𝐶 are at the higher level and 𝐵 is at the lower level and so on.)

The treatment contrast that is confounded with the blocks is

(A) 𝐵𝐶

(B) 𝐴𝐶

(D) 𝐴𝐵𝐶

Answer: (D)

15. Consider a fixed effects two-way analysis of variance model 𝑌_𝑖𝑗𝑘 = 𝜇 + 𝛼_𝑖 + 𝛽_𝑗 + 𝛾_𝑖𝑗 + 𝜖_𝑖𝑗𝑘, where 𝑖 = 1, … , 𝑎; 𝑗 = 1, … , 𝑏 ; 𝑘 = 1, … , 𝑟, and 𝜖_𝑖𝑗𝑘′s are independent and identically distributed normal random variables with zero mean and constant variance. Then the degrees of freedom available to estimate the error variance is zero when

(A) 𝑎 = 1

(B) 𝑏 = 1

(D) None of the above.

Answer: (C)

16. For 𝑘 = 1,2, … ,10, let the probability density function of the random variable 𝑋_𝑘 be

Then is equal to …….

Answer: (385 to 385)

17. The probability density function of the random vector (𝑋, 𝑌) is given by

Then the value of 𝑐 is equal to………

Answer: (2 to 2)

18. Let { 𝑋_𝑛}_𝑛≥1 be a sequence of independent and identically distributed normal random variables with mean 4 and variance 1. Then is equal to ……

Answer: (0 to 0)

19. Let (𝑋₁, 𝑋₂) be a random vector following bivariate normal distribution with mean vector (0, 0), Variance(𝑋₁) = Variance(𝑋₂) = 1 and correlation coefficient 𝜌, where |𝜌| < 1. Then 𝑃(𝑋₁ + 𝑋₂ > 0) is equal to …………

Answer: (0.5 to 0.5)

20. Let 𝑋₁, … , 𝑋_𝑛 be a random sample from normal distribution with mean 𝜇 and variance 1. Let ϕ be the cumulative distribution function of the standard normal distribution. Given ϕ(1.96) = 0.975, the minimum sample size required such that the length of the 95% confidence interval for 𝜇 does NOT exceed 2 is …………..

Answer: (4 to 4)

21. Let 𝑋 be a random variable with probability density function 𝑓(𝑥; 𝜃) = 𝜃𝑒⁻^𝜃𝑥, where 𝑥 ≥ 0 and 𝜃 > 0. To test 𝐻₀: 𝜃 = 1 against 𝐻₁: 𝜃 > 1, the following test is used:

Reject 𝐻₀ if and only if 𝑋 > log_𝑒20.

Then the size of the test is ……….

Answer: (0.05 to 0.05)

22. Let {𝑋𝑛}_𝑛≥0 be a discrete time Markov chain on the state space {1,2,3} with one-step transition probability matrix

and initial distribution 𝑃(𝑋0 = 1) = 0.5, 𝑃(𝑋₀ = 2) = 0.2, 𝑃(𝑋₀ = 3) = 0.3 . Then 𝑃(𝑋₁ = 2, 𝑋₂ = 3, 𝑋₃ = 1) (rounded off to three decimal places) is equal to …..

Answer: (0.018 to 0.020)

23. Let 𝑓 be a continuous and positive real valued function on [0, 1]. Then is equal to …..

Answer: (0 to 0)

24. A random sample of size 100 is classified into 10 class intervals covering all the data points. To test whether the data comes from a normal population with unknown mean and unknown variance, the chi-squared goodness of fit test is used. The degrees of freedom of the test statistic is equal to ………

Answer: (7 to 7)

25. For 𝑖 = 1,2,3,4, let 𝑌_𝑖 = 𝛼 + 𝛽_𝑥𝑖 + 𝜖_𝑖 where 𝑥_𝑖′s are fixed covariates and 𝜖_𝑖′s are uncorrelated random variables with mean 0 and variance 3. Here, 𝛼 and 𝛽 are unknown parameters. Given the following observations,

the variance of the least squares estimator of 𝛽 is equal to …….

Answer: (0.1 to 0.1)

Q.26 – Q. 55 carry two marks each.

26. Let Then, for |𝑥| < 1, the series converges to

Answer: (C)

27. Let {𝑋_𝑘}_𝑘≥1 be a sequence of independent and identically distributed Bernoulli random variables with success probability 𝑝 ∈ (0,1). Then, as 𝑛 → ∞,

converges almost surely to

(A) p

(B) 1/1 – p

(D) 1

Answer: (A)

28. Let 𝑋 and 𝑌 be two independent random variables with 𝜒²_m and 𝜒²_n distributions, respectively, where 𝑚 and 𝑛 are positive integers. Then which of the following statements is true?

(A) For 𝑚 < 𝑛, 𝑃(𝑋 > 𝑎) ≥ 𝑃(𝑌 > 𝑎) for all 𝑎 ∈ ℝ.

(B) For 𝑚 > 𝑛, 𝑃(𝑋 > 𝑎) ≥ 𝑃(𝑌 > 𝑎) for all 𝑎 ∈ ℝ.

(D) None of the above.

Answer: (B)

29. The matrix is diagonalizable when (𝑥, 𝑦, 𝑧) equals

(A) (0,0,1)

(B) (1,1,0)

(D) (√2, √2, √2)

Answer: (C)

30. Suppose that 𝑃₁ and 𝑃₂ are two populations with equal prior probabilities having bivariate normal distributions with mean vectors (2, 3) and (1, 1), respectively. The variance- covariance matrix of both the distributions is the identity matrix. Let 𝑧₁ = (2.5, 2) and 𝑧₂ = (2, 1.5) be two new observations. According to Fisher’s linear discriminant rule,

(A) 𝑧₁ is assigned to 𝑃₁, and 𝑧₂ is assigned to 𝑃₂.

(B) 𝑧₁ is assigned to 𝑃₂, and 𝑧₂ is assigned to 𝑃₁.

(D) 𝑧₁ is assigned to 𝑃₂, and 𝑧₂ is assigned to 𝑃₂.

Answer: (A)

31. Let 𝑋₁, … , 𝑋_𝑛 be a random sample from a population having probability density function Then the method of moments estimator of 𝜃 is

Answer: (A)

32. Let 𝑋 be a normal random variable having mean 𝜃 and variance 1, where 1 ≤ 𝜃 ≤ 10. Then 𝑋 is

(A) sufficient but not complete.

(B) the maximum likelihood estimator of 𝜃.

(D) complete and ancillary.

Answer: (C)

33. Let {𝑋_𝑛}_𝑛≥1 be a sequence of independent and identically distributed random variables with mean 𝜃 and variance 𝜃, where 𝜃 > 0. Then is a consistent estimator of

(A) 1/1+θ

(B) 1+ θ/θ

(D) θ/1+θ

Answer: (A)

34. Let 𝑋₁, … , 𝑋₁₀ be a random sample from a population with probability density function

Then the maximum likelihood estimator of 𝜃

(A) does not exist.

(B) is not unique.

(D) is the smallest observation.

Answer: (B)

35. Consider the model 𝑌𝑖 = 𝛽 + 𝜖_𝑖, where 𝜖_𝑖′s are independent normal random variables with zero mean and known variance 𝜎ⁱ₂ > 0, for 𝑖 = 1, … , 𝑛. Then the best linear unbiased estimator of the unknown parameter 𝛽 is

Answer: (A)

36. Let (𝑋, 𝑌) be a bivariate random vector with probability density function

Then the regression of 𝑌 on 𝑋 is given by

(A) 𝑋 + 1

(B) 𝑋/2

(D) 𝑌 + 1

Answer: (A)

37. Consider a discrete time Markov chain on the state space {1, 2} with one-step transition probability matrix

38. Let (𝑋₁, 𝑋₂) be a random vector with variance-covariance matrix The two principal components are

(A) 𝑋₁ and 𝑋₂

(B) −𝑋₁ and 𝑋₂

(D) 𝑋₁ + 𝑋₂ and 𝑋₂

Answer: (A)

39. Consider the objects {1,2,3,4} with the distance matrix

Applying the single-linkage hierarchical procedure twice, the two clusters that result are

(A) {2,3} and {1,4}

(B) {1,2,3} and {4}

(D) {2,3,4} and {1}

Answer: (B)

40. The maximum likelihood estimates of the mean vector and the variance-covariance matrix of a bivariate normal distribution based on the realization of a random sample of size 3, are given by

41. Consider a fixed effects one-way analysis of variance model 𝑌_𝑖𝑗 = 𝜇 + 𝜏_𝑖 + 𝜖_𝑖𝑗, for 𝑖 = 1, … , 𝑎, 𝑗 = 1, … , 𝑟, and 𝜖_𝑖𝑗′s are independent and identically distributed normal random variables with mean zero and variance 𝜎². Here, 𝑟 and 𝑎 are positive integers.

Let is the least squares estimator for

(A) μ + τ_i/2

(B) τ_i

(D) μ

Answer: (C)

42. Let 𝐴 be a 𝑛 × 𝑛 positive semi-definite matrix with eigenvalues 𝜆₁ ≥ ⋯ ≥ 𝜆_𝑛, and with 𝛼 as the maximum diagonal entry. We can find a vector 𝑥 such that 𝑥𝑡𝑥 = 1, where 𝑡 denotes the transpose, and

(A) 𝑥^𝑡𝐴 𝑥 > 𝜆₁

(B) 𝑥^𝑡𝐴_𝑥 < 𝜆_𝑛

(D) 𝑥^𝑡𝐴 𝑥 > 𝑛 𝛼

Answer: (C)

43. Let 𝑋 be a random variable with uniform distribution on the interval (−1,1) and 𝑌 = (𝑋 + 1)2. Then the probability density function 𝑓(𝑦) of 𝑌, over the interval (0,4), is

(A) 3√𝑦/16

(B) 1/4 √𝑦

(D) 1/√𝑦

Answer: (B)

44. Let 𝑆 be the solid whose base is the region in the 𝑥𝑦-plane bounded by the curves 𝑦 = 𝑥² and 𝑦 = 8 − 𝑥², and whose cross-sections perpendicular to the 𝑥-axis are squares. Then the volume of 𝑆 (rounded off to two decimal places) is ………….

Answer: (136.51 to 135.55)

45. Consider the trinomial distribution with the probability mass function 𝑥 + 𝑦 ≤ 7.

Then 𝐸(𝑌|𝑋 = 3) is equal to ……

Answer: (2 to 2)

46. Let 𝑌_𝑖 = 𝛼 + 𝛽𝑥_𝑖 + 𝜖_𝑖, where 𝑖 = 1, 2, 3, 4, 𝑥_𝑖′s are fixed covariates and 𝜖𝑖′s are independent and identically distributed standard normal random variables. Here, 𝛼 and 𝛽 are unknown parameters. Let Φ be the cumulative distribution function of the standard normal distribution and Φ(1.96) = 0.975. Given the following observations,

the length (rounded off to two decimal places) of the shortest 95% confidence interval for 𝛽 based on its least squares estimator is equal to ……….

Answer: (0.91 to 0.93)

47. Consider a discrete time Markov chain on the state space {1,2,3} with one-step transition probability matrix Then the period of the Markov chain is …………

Answer: (1 to 1)

48. Suppose customers arrive at an ATM facility according to a Poisson process with rate 5 customers per hour. The probability (rounded off to two decimal places) that no customer arrives at the ATM facility from 1:00 pm to 1:18 pm is ……….

Answer: (0.21 to 0.23)

49. Let 𝑋 be a random variable with characteristic function 𝜙_𝑋(⋅) such that 𝜙_𝑋(2 𝜋) = 1. Let ℤ denote the set of integers. Then 𝑃(𝑋 ∈ ℤ) is equal to ……..

Answer: (1 to 1)

50. Let 𝑋₁ be a random sample of size 1 from uniform distribution over (𝜃, 𝜃²), where 𝜃 > 1. To test 𝐻0: 𝜃 = 2 against 𝐻₁: 𝜃 = 3, reject 𝐻0 if and only if 𝑋₁ > 3.5 . Let 𝛼 and 𝛽 be the size and the power, respectively, of this test. Then 𝛼 + 𝛽 (rounded off to two decimal places) is equal to ………

Answer: (1.15 to 1.18)

51. Let 𝑌_𝑖 = 𝛽₀ + 𝛽₁𝑥_𝑖 + 𝜖_𝑖, 𝑖 = 1, … , 𝑛, where 𝑥𝑖′s are fixed covariates, and 𝜖𝑖′s are uncorrelated random variables with mean zero and constant variance. Suppose that are the least squares estimators of the unknown parameters respectively. If then the correlation between is equal to ……..

Answer: (0 to 0)

52. Let 𝑓: ℝ → ℝ be defined by 𝑓(𝑥) = (3𝑥² + 4) cos 𝑥. Then is equal to ……

Answer: (2 to 2)

53. The maximum value of (𝑥 − 1)² + (𝑦 − 2)² subject to the constraint 𝑥² + 𝑦² ≤ 45 is equal to……

Answer: (80 to 80)

54. Let 𝑋₁, ……… , 𝑋₁₀ be independent and identically distributed normal random variables with mean 0 and variance 2. Then is equal to ………..

Answer: (0.1 to 0.1)

55. Let 𝐼 be the 4 × 4 identity matrix and 𝑣 = (1, 2, 3, 4)^𝑡, where 𝑡 denotes the transpose. Then the determinant of 𝐼 + 𝑣𝑣^𝑡 is equal to ………..

Answer: (31 to 31)

GATE Exam 2019 Production and Industrial Engineering (PI) Question Paper With Answer Key

June 7, 2023December 13, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Production and Industrial Engineering

Q.1 – Q. 25 carry one mark each.

1. For any real, square and non-singular matrix B , the det B1 is

(A) zero

(B) (det B)⁻¹

(D) det B

Answer: (B)

2. For a complex number z = 1 – 4i with

(A) 0

(B) 1/√2

(D)√2

Answer: (D)

3. The vector that is normal to the surface 2xz² − 3xy – 4x = 7 at the point (1, –1, 2) is

(A) 2i – 3j + 8k

(B) 2i + 3j + 4k

(D) 7i – 5j + 8k

Answer: (C)

4. If roots of the auxiliary equation of are real and equal, the general solution of the differential equation is

(A) y = c₁e^−ax/2 + c₂e^ax/2

(B) y = (c₁ + c₂x)^−ax/2

(D) y = (c₁ cos x + c₂ sin x)e^−ax/2

Answer: (B)

5. The solution of is

(A) ln(ab)

(B) ln(a / b)

(D) ln(a) ln(b)

Answer: (D)

6. Match the crystal structure in Column A with the corresponding packing fractions in Column B of the table

(A) 1-P, 2-R, 3-Q, 4-Q

(B) 1-R, 2-P, 3-R, 4-Q

(D) 1-P, 2-R, 3-P, 4-Q

Answer: (C)

7. The link lengths of a planar four bar mechanism are AB = 100 mm, BC = 25 mm, CD = 75 mm and DA = 90 mm. For achieving the full rotation of both the input (crank) as well as the output (follower) links, the link that needs to be fixed is

(A) AB

(B) BC

(D) DA

Answer: (B)

8. The process used for producing continuous insulation coating on an electrical wire is

(A) Extrusion

(B) Injection molding

(D) Deep drawing

Answer: (A)

9. The correct statement pertaining to the friction welding process is

(A) Heat affected zone is not formed

(B) Flashes are not produced

(D) Melting of the base material(s) is not involved

Answer: (D)

10. The end product obtained using spinning process is shown in the figure. The initial blank thickness is 2.5 mm. The blank diameter (in mm) is

(A) 75

(B) 105

(D) 210

Answer: (D)

11. For a classical (Wilson) model of determining economic order quantity (EOQ), the carrying and ordering costs are Cr and Co, respectively. For an annual demand D, the minimum yearly total inventory cost is

Answer: (C)

12. A company has purchased an asset by investing Rs.30,000. The useful life of the asset is 5 years and it has no salvage value at the end of its useful life. The depreciation cost (in Rs.) for the 2nd year using sum-of-years-digit (SYD) method is

(A) 10,000

(B) 8,000

(D) 4,000

Answer: (B)

13. In a NC milling operation, the tool path is generated using absolute programing for the trajectory shown in the figure

The corresponding block of the NC program is

(A) G02 X 120.0 Y 60.0 R 60.0;

(B) G02 X 60.0 Y 120.0 R 60.0;

(D) G03 X 120.0 Y 60.0 R 60.0;

Answer: (A)

14. The SQC chart based on Binomial distribution is

(A) p chart

(B) c chart

(D) R chart

Answer: (A)

15.The capacity of a passenger airline is expressed in terms of

(A) available seats

(B) available miles

(D) available seat miles

Answer: (D)

16. REL chart is used in

(A) Quality management

(B) Inventory management

(D) Human resource management

Answer: (C)

17. A metallic rod of diameter d₀ is subjected to the tensile test. The engineering stress and the true stress at fracture are 800 MPa and 900 MPa, respectively. The ratio of the rod diameter at fracture d_f to the initial diameter d₀ is _______ (round off to 2 decimal places)

Answer: (0.93 to 0.95)

18. A heat pump is to supply heat at the rate of 10 kW to a building to be maintained at 22°C. The outside temperature is 2 ˚C. The minimum power (in kW) required to run the heat pump is ______(round off to 2 decimal places)

Answer: (0.67 to 0.69)

19. One kilogram of air is compressed at constant temperature of 150°C until its volume is halved. Considering gas constant R = 0.287 kJ/kg-K for air, magnitude of heat rejected (in kJ) in the compression process is ________ (round off to 2 decimal places)

Answer: (84.00 to 84.30)

20. For the abrasive jet machining process, the ratio of abrasive volume to carrier gas volume is 0.25. Further, the ratio of abrasive density to carrier gas density is 25. The mass ratio of abrasive to the mixture of abrasive and carrier gas is_______ (round off to 2 decimal places)

Answer: (0.85 to 0.90)

21. In a typical turning tool life test, the following data are generated for tools A and B:

Assuming the same tool life exponent for the tools, the value of constant in the Taylor’s tool life equation (with cutting speed in m/min and tool life in min) is (round off to 2 decimal places)

Answer: (445.00 to 455.00)

22. The average proportion non-conforming of 20 samples each of size 100 items is 0.12. The upper control limit for the relevant chart is ______(round off to 2 decimal places)

Answer: (0.21 to 0.23)

23. For a process which is in a state of statistical control (within±3σ ), estimated process standard deviation (σ) is 3 mm. The specification limits for the corresponding product are 100 ± 7 mm. The capability ratio Cr is ______ (round off to 3 decimal places)

Answer: (1.200 to 1.400)

24. In a work study experiment, normal time was recorded as 140 s with a rating of 100%. Considering 2% allowance, the standard time (in s) is ________ (round off to 1 decimal place)

Answer: (141.0 to 145.0)

25. A warehouse has 1 loading dock and 3 persons for loading operations. The arrival rate of trucks follows Poisson distribution with a mean of 4 trucks/hour. The average loading time (by three persons together) per truck is exponentially distributed with a mean of 10 minutes. The charge of the trucks per hour and loading charges per person per hour are Rs.20 and Rs.6, respectively. The total cost (in Rs./hour) is ______

Answer: (57 to 59)

Q.26 – Q. 55 carry two marks each.

26. If the Laplace transform of , the Laplace transform of t cosh t is

Answer: (A)

27. General solution of the Cauchy-Euler equation is

(A) y = c₁x² +c² x⁴

(B) y = c₁x² +c₂x⁻⁴

(D) y = c₁x⁴ +c2 x⁻⁴ ln x

Answer: (C)

28. A uniform cantilever beam ABC of length L is subjected to a point load P at point B and a concentrated moment M at point C (as shown in figure). Let E be the Young’s modulus of the beam material and I be the area moment of inertia of the beam’s cross-section. Assuming the validity of the Euler-Bernoulli theory of slender beams, the downward deflection at point C is

Answer: (D)

29. Three Carnot engines 𝔼₁, 𝔼₂, 𝔼₃ operate as shown in the figure (T₁ > T₂ > T₃).

The efficiency of the engine 𝔼₃ in terms of the efficiencies η₁ and η₂ of the engines 𝔼₁ and 𝔼₂ respectively, is

(A) η₁+ η₂

(B) η₁ + η₂ – η₁η₂

(D) 1 – η₁η₂

Answer: (B)

30. True centrifugal casting process in horizontal configuration is to be used for casting a metallic cylinder with outside diameter 0.275 m and inside diameter 0.250 m. If G-factor (ratio of centrifugal force experienced by the rotating cast metal to its weight) is 65 and acceleration due to gravity is 9.8 m/s², the minimum rotational speed (in rpm) required is closest to

(A) 325

(B) 650

(D) 1300

Answer: (B)

31. In a sine bar, let h denote height of slip gauge and l be the distance between the rollers. The relationship between error in angular measurement ( dθ) and errors in the slip gauge combination ( dh ) and in the spacing of the rollers ( dl ) is

Answer: (C)

32. A 100 mm long cylindrical workpiece of diameter 50 mm is reduced to 25 mm diameter using extrusion process. The flow curve for the metal has strength coefficient as K = 750 MPa and the strain hardening co-efficient is 0.15. Assuming no friction and no redundant work, the required ram pressure (in MPa) is closest to

(A) 164

(B) 364

(D) 950

Answer: (D)

33. An LPP is defined as

Minimize z = 15x₁ + 12x₂

subject to,

x₁ + 2x₂ ≤ 3

2x₁ – 4x₂ ≤ 5

x₁, x₂ ≥ 0

The objective function of the dual of this LPP is

(A) Maximize w = y₁ + y₂

(B) Maximize w = y₁ + 2y₂

(D) Maximize w = 3y₁ + 5y₂

Answer: (D)

34. A 20 mm HSS drill with a point angle of 118° is used for drilling a through hole on a metallic plate of thickness 100 mm with a cutting speed of 333.33 mm/s and feed of 0.22 mm/rev. Assuming that the drill is touching the surface of the plate at the start, the drilling time (in s) is closest to

(A) 85

(B) 90

(D) 100

Answer: (B)

35. An acceptance sampling plan is selected with sample size n = 80, acceptance number c = 2 for a lot size of 10,000 units. The probability of accepting the lot is based on Poisson distribution. Assuming rectification inspection, if incoming lot quality p is 0.03 and mean (λ) is 2.4, the average outgoing quality (AOQ) is closest to

(A) 0.0011

(B) 0.0087

(D) 0.0338

Answer: (C)

36. The mean time to repair (MTTR) for a repairable system is 30 minutes. When maintenance time changes from 20 minutes to 40 minutes, the net increase in maintainability is closest to

(A) 0.15

(B) 0.25

(D) 0.60

Answer: (B)

37. A company invests Rs.50 thousand in assets. The initial investment is Rs.30 thousand with two subsequent investments of Rs.10 thousand each at the end of 1st year and 2nd year. The useful life of the assets is 10 years with no salvage value at the end. If the interest rate is 10% and the minimum attractive rate of return (MARR) is 12%, the annual capital recovery and return (CRR) in thousands of Rs. is

(A) 8.38

(B) 7.06

(D) 3.10

Answer: (A)

38. The man-hours required ( Tn ) to manufacture the nth unit in a plant is given by T_n = T₁n^b, where b = − 0.322 at the 80% learning rate. If the manufacturing time for the first unit ( T₁ ) is 80 man-hours, the total time (in man-hours) required to manufacture the first 4 units, at 80% learning rate, is

(A) 322.11

(B) 251.35

(D) 51.19

Answer: (B)

39. A firm, with a production target of 50,000 units/year, has the following data for the selection of a new location for its plant

The most economical location for the firm is

(A)P

(B) Q

(D) S

Answer: (A)

40. Considering included angle θ of the thread to be 60° using the Best-Wire method, the difference between the effective diameter (E ) and the dimension under the wire (T ) for M10 × 1.0 mm is closest to

(A) 0.289

(B) 0.578

(D) 0.982

Answer: (A)

41. If z is a complex variable with i = √−i, the length of the minor axis of an ellipse defined by |z – (1 + i) | + |z – (9 + i)| = 0 is _____

Answer: (5.9 to 6.1)

42. The numerical value of the definite integral using trapezoidal rule with function evaluations at points x = 0, 0.5 and 1 is ______ (round off to 3 decimal places)

Answer: (0.640 to 0.650)

43. A thin walled cylindrical pressure vessel with an inside diameter of 300 mm and wall thickness of 3 mm is subjected to an internal gauge pressure of 1.5 MPa. The maximum shear stress (in MPa) at a point located on the inner surface of the pressure vessel is ______

Answer: (37 to 40)

44. A cam is designed to achieve a simple harmonic motion of a flat-faced follower. Starting from the rest, the follower rises to the maximum height of 50 mm at 180˚ of cam rotation as shown in the figure.

If the cam rotates at a uniform angular speed of 100 rpm, the speed of the follower (in mm/s) at the instance when the cam rotates 45° from the initial position is _______

Answer: (180 to 190)

45. An open tank of 2 m × 2 m × 2 m is filled with layers of two fluids. Depth of each layer is one meter. The top layer is that of an oil of specific gravity 0.8. The bottom layer is of water. Consider the density of water ρ_w = 1000 kg/m and acceleration due to gravity g = 9.8 m/s².

Neglecting the effect of atmospheric pressure, the force (in N) exerted by the fluids on one of the side walls of the tank is ______

Answer: (33000 to 34000)

46. During a storm, the wind speed is 90 km/hr. In a high-rise building, there is a window of size 1.2 m × 1.8 m facing the storm on an upper floor. Neglecting the ground effects on wind speed and considering the density of air ρ_air = 1.2 kg/m , the force (in N) acting on the window due to the storm is______

Answer: (800 to 820 OR 1600 to 1640)

47. The heat transfer efficiency in arc welding of a plate using a current of 250 A at 20 V is 90%. The heat required to melt the material is 10 J/mm³. If the cross-sectional area of the weld joint is 30 mm² and the travel speed is 5 mm/s, the melting efficiency (in %) is ____ (round off to 2 decimal places)

Answer: (32.00 to 34.00)

48. A sand casting process has a mold constant of 2 s/mm² and solidification exponent of 2. If the solidification time is to be doubled for a given unit volume of material, the corresponding reduction in the cast surface area (in %) is ______

Answer: (28 to 31)

49. During a turning operation of a specific work material having shear strength of 220 MPa under orthogonal cutting condition, the process parameters are

Given chip thickness ratio as 0.5, friction angle as 49.2˚ and shear angle as 25.4˚, the feed force (in N) is_______

Answer: (450 to 470)

50. A CO₂ laser in continuous mode is used for drilling a plate. The process parameters and their values are

The drilled depth (in mm) after 2 seconds is _____

Answer: (6 to 6)

51. A process which is in a state of statistical control (within ±3σ) has an estimate of standard deviation (σ)² mm. The specification limits for the corresponding product are 120 ± 8 mm. When process mean shifts from 118 mm to 122 mm with no change in process standard deviation, the difference in process capability index C_pk is ______

Answer: (0 to 0)

52. A monitoring system has seven components. The reliability of each component is shown in the figure. The system reliability is _____ (round off to 2 decimal places)

Answer: (0.16 to 0.18)

53. A PERT project network consists of 5 activities A to E. The time estimates of these activities follow Beta-distribution. The predecessor–successor (P-S) relationships between the nodes and time estimates of activities are given in table.

The variance (in days) of the critical path is ______ (round off to 2 decimal places)

Answer: (4.00 to 4.40)

54. The sales data of a product for 5 years are

Assume the forecast for the year 2014 as 260 units. Using an exponential smoothing method with smoothing constant α = 0.5, the sales forecast (units) for the year 2019, is ______

Answer: (276 to 278)

55. The layout for an AGV system is shown in figure. The loading time is 0.5 minutes and the unloading time is also 0.5 minutes. All distances are in meters.

Considering a vehicle velocity of 50 m/min, availability of 0.95 and traffic factor of 0.9, the number of vehicles required to satisfy a demand of 50 delivery/hour is ______

Answer: (4 to 5)

GATE Exam 2019 Physics (PH) Question Paper With Answer Key

June 7, 2023December 11, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Physics

Q.1 – Q. 25 carry one mark each.

1. The relative magnetic permeability of a type-I superconductor is

(A) 0

(B) −1

(D) 1/4π

Answer: (A)

2. Considering baryon number and lepton number conservation laws, which of the following processes is/are allowed?

(i) 𝑝 → 𝜋⁰ + 𝑒‑ + 𝜈_𝑒

(ii) 𝑒⁺ + 𝜈_𝑒 → 𝜇⁺ + 𝜈_𝜇

(A) both (i) and (ii)

(B) only (i)

(D) neither (i) nor (ii)

Answer: (C)

3. For the following circuit, what is the magnitude of V_out if V_in = 1.5 V?

(A) 0.015 V

(B) 0.15 V

(D)150 V

Answer: (C)

4. For the differential equation where 𝑛 is a constant, the product of its two independent solutions is

(A) 1/x

(B) x

(D)1/xⁿ⁺¹

Answer: (B)

5. Consider a one-dimensional gas of 𝑁 non-interacting particles of mass 𝑚 with the Hamiltonian for a single particle given by,

The high temperature specific heat in units of 𝑅 = 𝑁𝑘_𝐵 (𝑘_𝐵 is the Boltzmann constant) is

(A) 1

(B) 1.5

(D) 2.5

Answer: (A)

6. An electric field is applied to a Hydrogen atom in 𝑛 = 2 excited state. Ignoring spin, the 𝑛 = 2 state is fourfold degenerate, which in the |𝑙, 𝑚⟩ basis are given by |0,0〉, |1,1⟩, |1,0⟩ and |1, −1⟩. If 𝐻′ is the interaction Hamiltonian corresponding to the applied electric field, which of the following matrix elements is nonzero?

(A) ⟨0,0|𝐻′|0,0⟩

(B) ⟨0,0|𝐻′|1,1⟩

(D) ⟨0,0|𝐻′|1, −1⟩

Answer: (C)

7. A large number 𝑁 of ideal bosons, each of mass m, are trapped in a three-dimensional potential The bosonic system is kept at temperature 𝑇 which is much lower than the Bose-Einstein condensation temperature 𝑇_𝑐. The chemical potential (𝜇) satisfies

Answer: (A)

8. During a rotation, vectors along the axis of rotation remain unchanged. For the rotation matrix the unit vector along the axis of rotation is

Answer: (B)

9. For a spin denote its spin up and spin down states, respectively. If are composite states of two such particles, which of the following statements is true for their total spin S ?

Answer: (D)

10. Consider a transformation from one set of generalized coordinate and momentum (𝑞, 𝑝) to another set (𝑄, 𝑃) denoted by,

𝑄 = 𝑝𝑞^𝑠; 𝑃 = 𝑞^𝑟

where 𝑠 and 𝑟 are constants. The transformation is canonical if

(A) 𝑠 = 0 and 𝑟 = 1

(B) 𝑠 = 2 and 𝑟 = −1

(D) 𝑠 = 2 and 𝑟 = 1

Answer: (B)

11. In order to estimate the specific heat of phonons, the appropriate method to apply would be

(A) Einstein model for acoustic phonons and Debye model for optical phonons

(B) Einstein model for optical phonons and Debye model for acoustic phonons

(D) Debye model for both optical and acoustic phonons

Answer: (B)

12. The pole of the function f(z) = cot z at z = 0 is

(A) a removable singularity

(B) an essential singularity

(D) a second order pole

Answer: (C)

13. A massive particle X in free space decays spontaneously into two photons. Which of the following statements is true for X?

(A) X is charged

(B) Spin of X must be greater than or equal to 2

(D) X must be a baryon

Answer: (C)

14. The electric field of an electromagnetic wave is given by The wave is

(A) linearly polarized at an angle tan⁻¹ (4/3) from the x-axis

(B) linearly polarized at an angle tan⁻¹ (3/4) from the x-axis

(D) elliptically polarized in counter-clockwise direction when seen travelling towards the observer

Answer: (D)

15. The nuclear spin and parity of in its ground state is

(A) 0⁺

(B) 0⁻

(D) 1⁻

Answer: (A)

16. An infinitely long thin cylindrical shell has its axis coinciding with the z-axis. It carries a surface charge density 𝜎₀cos𝜙, where 𝜙 is the polar angle and 𝜎₀ is a constant. The magnitude of the electric field inside the cylinder is

(A) 0

(B) 𝜎₀/2𝜖₀

(D) 𝜎₀/4𝜖₀

Answer: (B)

17. Consider a three-dimensional crystal of 𝑁 inert gas atoms. The total energy is given by where 𝑝 = 12.13, 𝑞 = 14.45, and 𝑅 is the nearest neighbour distance between two atoms. The two constants, 𝜖 and 𝑅, have the dimensions of energy and length, respectively. The equilibrium separation between two nearest neighbour atoms in units of 𝜎 (rounded off to two decimal places) is ______

Answer: (1.07 to 1.11)

18. The energy-wavevector (𝐸-𝑘) dispersion relation for a particle in two dimensions is 𝐸 = 𝐶𝑘, where 𝐶 is a constant. If its density of states 𝐷(𝐸) is proportional to 𝐸𝑝 then the value of 𝑝 is________

Answer: (1 to 1)

19. A circular loop made of a thin wire has radius 2 cm and resistance 2 Ω. It is placed perpendicular to a uniform magnetic field of magnitude Tesla. At time 𝑡 = 0 the field starts decaying as The total charge that passes through a cross section of the wire during the decay is Q. The value of Q in 𝜇𝐶 (rounded off to two decimal places) is _______

Answer: (6.26 to 6.30)

20. The electric field of an electromagnetic wave in vacuum is given by

The wave is reflected from the 𝑧 = 0 surface. If the pressure exerted on the surface is 𝛼𝜖₀𝐸²₀, the value of 𝛼 (rounded off to one decimal place) is ______

Answer: (0.8 to 0.8)

21. The Hamiltonian for a quantum harmonic oscillator of mass 𝑚 in three dimensions is

where 𝜔 is the angular frequency. The expectation value of r² in the first excited state of the oscillator in units of h/mω (rounded off to one decimal place) is_______

Answer: (2.5 to 2.5)

22. The Hamiltonian for a particle of mass m is where 𝑞 and 𝑝 are the generalized coordinate and momentum, respectively, 𝑡 is time and 𝑘 is a constant. For the initial condition, 𝑞 = 0 and 𝑝 = 0 at 𝑡 = 0, 𝑞(𝑡) ∝ 𝑡^α. The value of α is_______

Answer: (3 to 3)

23. At temperature T Kelvin (K), the value of the Fermi function at an energy 0.5 eV above the Fermi energy is 0.01. Then T, to the nearest integer, is ________

(𝑘_B = 8.62 × 10⁻⁵ eV/K)

Answer: (1260 to 1266)

24. Let represent two possible states of a two-level quantum system. The state obtained by the incoherent superposition of |𝜓₁〉 and |𝜓₂〉 is given by a density matrix that is defined as 𝜌 ≡ 𝑐₁|𝜓₁〉〈𝜓₁| + 𝑐₂|𝜓₂〉〈𝜓₂|. If 𝑐₁ = 0.4 and 𝑐₂ = 0.6, the matrix element 𝜌₂₂ (rounded off to one decimal place) is _________

Answer: (0.6 to 0.6)

25. A conventional type-I superconductor has a critical temperature of 4.7 K at zero magnetic field and a critical magnetic field of 0.3 Tesla at 0 K. The critical field in Tesla at 2 K (rounded off to three decimal places) is ______

Answer: (0.244 to 0.248)

Q.26 – Q. 55 carry two marks each.

26. Consider the following Boolean expression:

It can be represented by a single three-input logic gate. Identify the gate.

(A) AND

(B) OR

(D) NAND

Answer: (D)

27. The value of the integral where 𝑘 > 0 and 𝑎 > 0, is

Answer: (A)

28. The wave function 𝜓(𝑥) of a particle is as shown below

Here 𝐾 is a constant, and 𝑎 > 𝑑. The position uncertainty 〈Δ𝑥〉 of the particle is

Answer: (B)

29. A solid cylinder of radius 𝑅 has total charge 𝑄 distributed uniformly over its volume. It is rotating about its axis with angular speed 𝜔. The magnitude of the total magnetic moment of the cylinder is

Answer: (C)

30. Consider the motion of a particle along the x-axis in a potential 𝑉(𝑥) = 𝐹|𝑥|. Its ground state energy 𝐸₀ is estimated using the uncertainty principle. Then 𝐸0 is proportional to

(A) F^1/3

(B) F^1/2

(D) F^2/3

Answer: (D)

31. A 3-bit analog-to-digital converter is designed to digitize analog signals ranging from 0 V to 10 V. For this converter, the binary output corresponding to an input of 6 V is

(A) 011

(B) 101

(D) 010

Answer: (C)

32. The Hamiltonian operator for a two-level quantum system is If the state of the system at t = 0 is given by at a later time 𝑡 is

Answer: (C)

33. A particle of mass m moves in a lattice along the x-axis in a periodic potential 𝑉(𝑥) = 𝑉(𝑥 + 𝑑) with periodicity d. The corresponding Brillouin zone extends from −𝑘0 to 𝑘0 with these two k-points being equivalent. If a weak force F in the x-direction is applied to the particle, it starts a periodic motion with time period T. Using the equation of motion for a particle moving in a band, where p_crystal is the crystal momentum of the particle, the period T is found to be (h is the Planck constant)

Answer: (D)

34. Consider a potential barrier 𝑉(𝑥) of the form:

where 𝑉₀ is a constant. For particles of energy 𝐸 < 𝑉0 incident on this barrier from the left, which of the following schematic diagrams best represents the probability density |𝜓 (𝑥)|² as a function of 𝑥.

Answer: (A)

35. The spin-orbit interaction term of an electron moving in a central field is written as where r is the radial distance of the electron from the origin. If an electron moves inside a uniformly charged sphere, then

(A) 𝑓(𝑟) = constant

(B) 𝑓(𝑟) ∝ 𝑟⁻¹

(D) 𝑓(𝑟) ∝ 𝑟⁻³

Answer: (A)

36. For the following circuit, the correct logic values for the entries X₂ and Y₂ in the truth table are

(A) 1 and 0

(B) 0 and 0

(D) 1 and 1

Answer: (A)

37. In a set of 𝑁 successive polarizers, the 𝑚th polarizer makes an angle (𝑚𝜋/2N) with the vertical. A vertically polarized light beam of intensity 𝐼₀ is incident on two such sets with 𝑁 = 𝑁₁ and 𝑁 = 𝑁₂, where 𝑁₂ > 𝑁₁. Let the intensity of light beams coming out be 𝐼(𝑁1) and 𝐼(𝑁2) , respectively. Which of the following statements is correct about the two outgoing beams?

(A) 𝐼(𝑁₂) > 𝐼(𝑁₁) ; the polarization in each case is vertical

(B) 𝐼(𝑁₂) < 𝐼(𝑁₁) ; the polarization in each case is vertical

(D) 𝐼(𝑁₂) < 𝐼(𝑁₁) ; the polarization in each case is horizontal

Answer: (C)

38. A ball bouncing off a rigid floor is described by the potential energy function

V(x) = mgx for x > 0

= ∞ for x ≤ 0

Which of the following schematic diagrams best represents the phase space plot of the ball?

Answer: (B)

39. An infinitely long wire parallel to the x-axis is kept at 𝑧 = 𝑑 and carries a current I in the positive x direction above a superconductor filling the region 𝑧 ≤ 0 (see figure). The magnetic field inside the superconductor is zero so that the field just outside the superconductor is parallel to its surface. The magnetic field due to this configuration at a point (𝑥, 𝑦, 𝑧 > 0) is

Answer: (B)

40. The vector potential inside a long solenoid, with n turns per unit length and carrying current 𝐼, written in cylindrical coordinates If the term where α≠ 0, β ≠ 0, is added to the magnetic field remains the same if

(A) 𝛼 = 𝛽

(B) 𝛼 = −𝛽

(D) 𝛼 = 𝛽/2

Answer: (D)

41. Low energy collision (s-wave scattering) of pion (π+) with deuteron (d) results in the production of two protons (𝜋+ + 𝑑 → 𝑝 + 𝑝). The relative orbital angular momentum (in units of ℏ) of the resulting two-proton system for this reaction is

(A) 0

(B) 1

(D) 3

Answer: (B)

42. Consider the Hamiltonian where 𝛼 and 𝛽 are parameters with appropriate dimensions, and 𝑞 and 𝑝 are the generalized coordinate and momentum, respectively. The corresponding Lagrangian 𝐿(𝑞, 𝑞̇) is

Answer: (A)

43. For a given load resistance RL = 4.7 ohm, the power transfer efficiencies of a dc voltage source and a dc current source with internal resistances R1 and R2, respectively, are equal. The product R1R2 in units of ohm2 (rounded off to one decimal place) is _______

Answer: (22.0 to 22.2)

44. The ground state electronic configuration of the rare-earth ion (Nd³⁺) is [Pd] 4f³5s²5p⁶. Assuming LS coupling, the Land𝑒́ 𝑔-factor of this ion is 8/11 . The effective magnetic moment in units of Bohr magneton 𝜇_B (rounded off to two decimal places) is__________

Answer: (3.61 to 3.63)

45. A projectile of mass 1 kg is launched at an angle of 30° from the horizontal direction at 𝑡 = 0 and takes time 𝑇 before hitting the ground. If its initial speed is 10 ms−1 , the value of the action integral for the entire flight in the units of kg m2s⁻¹ (rounded off to one decimal place) is________

[Take 𝑔 = 10 ms⁻²]

Answer: (33.2 to 33.4)

46. Let 𝜃 be a variable in the range − 𝜋 ≤ 𝜃 < 𝜋. Now consider a function

𝜓(𝜃) = 1 for − 𝜋/2 ≤ 𝜃 < 𝜋/2

= 0 otherwise.

If its Fourier-series is written as then the value of|𝐶₃|² (rounded off to three decimal places) is ____

Answer: (0.010 to 0.013)

47. Two spaceships A and B, each of the same rest length 𝐿, are moving in the same direction with speeds 4𝑐/5 and 3𝑐/5, respectively, where 𝑐 is the speed of light. As measured by B, the time taken by A to completely overtake B [see figure below] in units of 𝐿/𝑐 (to the nearest integer) is _________

Answer: (5 to 5)

48. A radioactive element X has a half-life of 30 hours. It decays via alpha, beta and gamma emissions with the branching ratio for beta decay being 0.75. The partial half-life for beta decay in unit of hours is_______

Answer: (40 to 40)

49. In a thermally insulated container, 0.01 kg of ice at 273 K is mixed with 0.1 kg of water at 300 K. Neglecting the specific heat of the container, the change in the entropy of the system in J/K on attaining thermal equilibrium (rounded off to two decimal places) is ________

(Specific heat of water is 4.2 kJ/kg-K and the latent heat of ice is 335 kJ/kg).

Answer: (1.02 to 1.04)

50. Consider a system of three charges as shown in the figure below:

For 𝑟 = 10 m; 𝜃 = 60 degrees; 𝑞 = 10⁻⁶ Coulomb, and 𝑑 = 10⁻³ m, the electric dipole potential in volts (rounded off to three decimal places) at a point (𝑟, 𝜃) is ________

Answer: (0.044 to 0.046)

51. Consider two systems A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0, 1, 2 and 3 units with equal probability. The total energy of the combined system is 5 units. Assuming that the system A has energy 3 units and the system B has energy 2 units, the entropy of the combined system is 𝑘B ln 𝜆. The value of 𝜆 is _________

Answer: (12 to 12)

52. Electrons with spin in the 𝑧-direction are passed through a Stern-Gerlach (SG) set up with the magnetic field at 𝜃 = 60o from . The fraction of electrons that will emerge with their spin parallel to the magnetic field in the SG set up (rounded off to two decimal places) is _________

Answer: (0.75 to 0.75)

53. The Hamiltonian of a system is with 𝜀 ≪ 1. The fourth order contribution to the ground state energy of 𝐻 is 𝛾𝜀⁴. The value of 𝛾 (rounded off to three decimal places) is _________

Answer: (0.125 to 0.125)

54. Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth’s frame. The time difference between the two events as seen by an observer in a spaceship moving with velocity 0.5c in the earth’s frame along the line joining the earth to the Sun is Δ𝑡, where c is the speed of light. Given that light travels from the Sun to the earth in 8.3 minutes in the earth’s frame, the value of |Δ𝑡| in minutes (rounded off to two decimal places) is__________

(Take the earth’s frame to be inertial and neglect the relative motion between the earth and the sun)

Answer: (4.77 to 4.81)

55. In a certain two-dimensional lattice, the energy dispersion of the electrons is

where denotes the wave vector, 𝑎 is the lattice constant and 𝑡 is a constant in units of eV. In this lattice the effective mass tensor 𝑚𝑖𝑗 of electrons calculated at the center of the Brillouin zone has the form The value of 𝛼 (rounded off to three decimal places) is _________

Answer: (0.333 to 0.333)

GATE Exam 2019 Petroleum Engineering (PE) Question Paper With Answer Key

June 7, 2023December 11, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Petroleum Engineering

Q.1 – Q. 25 carry one mark each.

1. Let 𝑟 and 𝜃 be the modulus and argument of the complex number 𝑧 = 1 + 𝑖, respectively. Then (𝑟, 𝜃) equals

(A) (√2, 𝜋/4)

(B) (2, 𝜋/2)

(D) (√2, 𝜋)

Answer: (A)

2. Let 𝜆₁ and 𝜆₂ be the two eigenvalues of the matrix Then, 𝜆₁ + 𝜆₂ and 𝜆₁𝜆₂, are respectively

(A) 1 and 1

(B) 1 and −1

(D) −1 and −1

Answer: (A)

3. The Laplace transform of the function 𝑓(𝑡) = 𝑒−𝑡 is given by

Answer: (C)

4. The relative decline rate of oil is given by where q is the oil production rate, a (> 0) is the decline rate and b is a constant. The equation gives harmonic decline curve when b is

(A) 1.5

(B) 1

(D) 0

Answer: (B)

5. Which one of the following provides a vertical stab for the flow lines and annulus access lines from multiple wells in offshore subsea completion?

(A) Moon pool deck

(B) Spider beams

(D) Manifold

Answer: (D)

6. In a faulted reservoir, the principle of superposition for the pressure drop using diffusivity equation is applicable. This is due to

(A) high Reynolds number flow in the well.

(B) constant permeability.

(D) linearity of the diffusivity equation.

Answer: (D)

7. Which one of the following parameters is measured using routine core analysis (RCA)?

(A) Porosity

(B) Relative permeability

(D) Wettability

Answer: (A)

8. Match the following:

(A) P-II, Q-IV, R-III, S-I

(B) P-III, Q-I, R-IV, S-II

(D) P-III, Q-IV, R-I, S-II

Answer: (D)

9. Which one of the following rocks and reservoir fluids are arranged in the decreasing order of their electrical resistivity? Assume that rocks have equal porosity and are filled with brine.

(A) Shale > Brine > Sandstone > Limestone > Gas

(B) Gas > Shale > Sandstone > Limestone > Brine

(D) Shale > Brine > Limestone > Sandstone > Gas

Answer: (C)

10. Which one of the following is the correct sequence of events for hydrocarbon generation in the subsurface?

(A) Catagenesis → Metagenesis → Diagenesis

(B) Catagenesis → Diagenesis → Metagenesis

(D) Diagenesis → Metagenesis → Catagenesis

Answer: (C)

11. Match the following:

(A) P-II, Q-I, R-III

(B) P-I, Q-III, R-II

(D) P-III, Q-I, R-II

Answer: (D)

12 Match the following for drill pipe failure :

(A) P-III, Q-IV, R-I, S-II

(B) P-II, Q-I, R-IV, S-III

(D) P-IV, Q-III, R-II, S-I

Answer: (B)

13. Which one of the following flow regimes is more favorable for gas lift operation?

(A) Bubbly flow

(B) Annular flow

(D) Stratified flow

Answer: (A)

14. H₂S gas is

(A) acidic.

(B) non-corrosive.

(D) non-flammable.

Answer: (A)

15. Which one of the following offshore platforms DOES NOT use buoyant columns or pontoons?

(A) Tension leg platforms

(B) Jack up platforms

(D) Semi-submersible platforms

Answer: (B)

16. In which one of the following offshore platforms, the condition of the sea floor is a vital consideration?

(A) Drill ship platforms

(B) Tension leg platforms

(D) Floating, production, storage and offloading (FPSO) platforms

Answer: (C)

17. The ‘Klinkenberg effect’ is related to

(A) viscous fingering during water flooding in oil reservoirs.

(B) hysteresis effect in relative permeability during drainage and imbibition process.

(D) slippage of gas phase at the sand grain surface.

Answer: (D)

18. Favourable conditions for formation of gas hydrates are

(A) high temperature and high pressure.

(B) high temperature and low pressure.

(D) low temperature and low pressure.

Answer: (C)

19. Match the following quantities with their dimensions:

(A) P-III, Q-II, R-IV, S-I

(B) P-II, Q-I, R-IV, S-III

(D) P-I, Q-II, R-III, S-IV

Answer: (A)

20. The plot of dissolved gas oil ratio (R_S), defined as the “ratio of STP volume of gas dissolved in the oil at pressure P, to the volume of the oil at STP” is given below.

For the same oil, the plot of produced gas oil ratio (RP) defined as the “ratio of STP volume of the gas liberated from the oil at pressure P, to the volume of the oil at STP” is

Answer: (B)

21. Which one of the following denotes a regular four-spot flood pattern?

∆ represents injection well

O represents production well

(A)

(B)

(C)

(D)

Answer: (A)

22. The value of is____(round off to 2 decimal places).

Answer: (0.49 to 0.51)

23. Let If AX = Y, then a + b equals ______.

Answer: (2 to 2)

24. Let where i, j and k are cartesian unit vectors. If is perpendicular to v, then a equals _________.

Answer: (2 to 2)

25. If the neutron log porosity (ϕ_N) is 0.09 and density log porosity (ϕ_D) is 0.24 in the cross-over region, then the average porosity of the gas bearing region is ____ (round off to 2 decimal places).

Answer: (0.17 to 0.20)

Q.26 – Q. 55 carry two marks each.

26. The general solution of the differential equation is (here C₁ and C₂₁ are arbitrary constants)

(A) y = C₁e^x + C₂e^−x

(B) y = C₁xe^x + C₂xe^2x

(D) y = C₁e^x + C₂xe^x

Answer: (D)

27. Consider the following system of linear equations (where 𝑝 and 𝑞 are constants)

x₁ + x₂ + x₃ = 1

x₁ – x₂ + 2x₃ = p

3x₁ – x₂ + 5x₃ = q

This system has at least one solution for any p and q satisfying

(A) 2𝑝 − 𝑞 + 1 = 0.

(B) 2𝑞 + 𝑝 + 1 = 0.

(D) 2𝑞 + 𝑝 − 1 = 0.

Answer: (A)

28. Three reservoirs P, Q and R have identical geometry and rock properties. The plot of the height of the transition zone (h) above the free water level (FWL) against the water saturation (S_w) is given in the figure. Assume 𝜎 cos 𝜃 for all the three fluid combinations remains the same. Which one of the following is the correct match of the reservoir fluids with the reservoir (𝜎 is the interfacial tension between the respective fluid phases and 𝜃 is the contact angle).

(A) P: low density oil – water, Q: gas – water, R: high density oil – water

(B) P: gas – water , Q: low density oil – water, R: high density oil – water

(D) P: gas – water, Q: high density oil – water, R: low density oil – water

Answer: (C)

29. The fractional flow (f_w) versus water saturation (S_w) curve for an imbibition process (neglecting the capillary forces) in a given core for three different inclinations is shown in the figure.

Which one of the following is the correct representation of the fractional flow curves?

(A) P: Down-dip, Q: No-dip, R: Up-dip

(B) P: Down-dip, Q: Up-dip, R: No-dip

(D) P:Up-dip, Q: No-dip, R: Down-dip

Answer: (A)

30. Match the following:

(A) P-IV, Q-II, R-I, S-III

(B) P-III, Q-I, R-IV, S-II

(D) P-II, Q-IV, R-III, S-I

Answer: (C)

31. Match the following:

(A) P-I, Q-IV, R-III, S-II

(B) P-I, Q-II, R-IV, S-III

(D) P-IV, Q-I, R-II, S-III

Answer: (C)

32. An exploratory well encountered three reservoir formations S1 (perfectly cemented), S2 (poorly cemented) and S3 (fractured). The Formation Factor (F) is governed by the equation 𝐹 = 𝑎𝜙⁻^𝑚, where ‘𝜙’ is the porosity and ‘m’ is the cementation factor. The constant ‘a’, linked to tortuosity is assumed to be 1 for all the formations. The log-log plot between Formation Factor (F) and porosity (𝜙) is shown.

Which one of the following represents the correct match of the formations with their respective plots?

(A) S1-P, S2-Q, S3-R

(B) S1-R, S2-P, S3-Q

(D) S1-R, S2-Q, S3-P

Answer: (D)

33. Typical parameters obtained in the pyrolysis experiment of the source rock materials are shown in the Figure. Which one of the following is NOT true about pyrolysis in source rock analysis?

(A) Peak S1 represents volatilization of existing hydrocarbons.

(B) Peak S2 represents breakdown of kerogen and generation of hydrocarbons.

(D) S1/(S1+S2) represents the production index.

Answer: (C)

34. A single well encounters multiple clean sands of exactly the same thickness, porosity and permeability. R_w is the formation fluid resistivity and R_mf is the mud filtrate resistivity.

Which one of the following match the relation between R_w and R_mf to that of Self Potential (SP) log deflection?

(A) P-I, Q-III, R-II

(B) P-III, Q-I, R-II

(D) P-I, Q-II, R-III

Answer: (B)

35. Which one of the following options is NOT a part of the mudlogs prepared by the drill-site geologist?

(A) Rate of Penetration (ROP)

(B) Chromatograph showing presence of C1 to C5 concentration

(D) Reservoir unit delineation based on volume of shale (Vsh)

Answer: (D)

36. Match the following:

(A) P-II, Q-I, R-IV, S-III

(B) P-IV, Q-II, R-III, S-I

(D) P-IV, Q-III, R-II, S-I

Answer: (A)

37. A box contains 2 red and 3 black balls. Three balls are randomly chosen from the box and are placed in a bag. Then the probability that there are 1 red and 2 black balls in the bag, is _______.

Answer: (0.59 to 0.61)

38. The values of a function 𝑓(𝑥) over the interval [0,4] are given in the table below:

Then, according to the trapezoidal rule, the value of the integral is _______(round off to 2 decimal places).

Answer: (1.32 to 1.34)

39. Oil is produced at a constant rate from a well in a bounded reservoir. The variation of the bottom-hole pressure with time is shown in the given Table. The magnitude of the slope of the pressure vs time curve that you would use to find the drainage area is ____ psi/day (round off to 1 decimal place).

Answer: (29.0 to 31.0)

40. In a core flood experiment of immiscible and incompressible displacement of oil (𝜇_𝑜 = 1 cP) with water (𝜇_𝑤 = 1 cP), only axial flow is observed. The relative permeability of water is given by 𝑘_𝑟𝑤 = 𝑆²_w , where 𝑆 is water saturation. The relative permeability of oil is given by 𝑘𝑟𝑜 = (1 − 𝑆_𝑤)². The gravity and capillary pressure are neglected. From the fractional flow and water saturation relationship, the saturation of water at the flood front is______ % (round off to 1 decimal place).

Answer: (69.0 to 72.0)

41. In an oil well, the pressure at the gas oil contact (GOC) at a depth of 2000 m is 205 bar (gauge), as shown in the figure.

The static oil pressure gradient is 0.08 bar/m in the pay zone. If a constant hydrostatic pressure gradient of 0.1 bar/m prevails throughout the subsurface, then the thickness of the oil column is _____ m (round off to 1 decimal place).

Answer: (240.0 to 260.0)

42. Oil is produced at a constant rate of10 m³/day from a reservoir for 500 days. The producing gas oil ratio (GOR) is constant at for the first 100 days. Then, the producing gas oil ratio increases linearly and on the 500th day the measured GOR is The cumulative produced gas oil ratio after 500 days of production is______ (round off to 1 decimal place). Assume that all volumes are measured at

Answer: (25.5 to 26.5)

43. A pressure build-up test was conducted in a well after 1000 days of producing oil at a constant rate of 0.01 reservoir-m³/s. The two shut-in bottom-hole pressure readings taken at 0.5 day and 1 day after shut-in are 150 × 10⁵ Pa and 151 × 10⁵ Pa, respectively. These pressure points correspond to the linear region of the Horner’s plot. The reservoir thickness is 100 m and oil viscosity is 0.001 Pa.s. The permeability of the reservoir is ______ mD (round off to 1 decimal place). [1 mD = 10⁻¹⁵ m²].

Answer: (52.0 to 58.0)

44. In an oil reservoir, the residual oil saturation in the volume flooded with polymer solution is 20%. The initial water saturation is 20%. The volumetric sweep efficiency is 50%. The maximum possible recovery factor for the reservoir is _______ % (round off to 1 decimal place).

Answer: (36.0 to 39.0)

45. An electrical submersible pump (ESP) delivers well fluid with 100% watercut. In the ESP, the impeller diameter is 0.1 m and speed is 3600 rpm. The total head developed by the ESP is 300 m (water column height). If the stage efficiency of the ESP is 60%, then the minimum number of stages required is ______ (round off to nearest integer). [g = 9.81 m/s²]

Answer: (27 to 29)

46. In a counter flow heat exchanger, hot fluid enters at 100°C and leaves at 50°C. Cold fluidenters at 30°C and leaves at 40°C. If heat losses are ignored, then the logarithmic mean temperature difference (LMTD) is _______°C (round off to 1 decimal place).

Answer: (35.0 to 38.0)

47. A model porous block of cross sectional area (A) and length (L) is made up of N independent capillaries of equal radii (r) and length (L). The porosity of the block is 10%, and the permeability for a laminar, incompressible and steady state flow is 0.02 mD. If the flow is only through the capillaries, then the value of r is _______ x 10⁻⁶ cm (round off to 1 decimal place). [1 mD = 10⁻¹⁵ m² ].

Answer: (3.0 to 5.0)

48. A model porous medium of 5 cylindrical capillaries of radii varying from 60 to 100 micrometers (refer Table) is subjected to Mercury Injection Capillary Pressure (MICP) treatment. The capillaries are being filled in an increasing order of their entry pressure. The magnitude of ,where 𝜎 is the interfacial tension and 𝜃 is the contact angle. The minimum applied mercury pressure to achieve 50% mercury saturation in the sample is _______ × 10³ dyne/cm² (round off to 1 decimal place).

Answer: (80.0 to 83.0)

49. The sonic log parameters from an exploratory well in a reservoir are as follows: Measured P-wave transit time (∆𝑡_𝑙𝑜𝑔) = 85 µs/ft

True resistivity (R_t) = 10 ohm-m Matrix transit time (∆𝑡𝑚𝑎) = 45 µs/ft

Fluid transit time (∆𝑡_𝑓𝑙) = 205 µs/ft

Formation water resistivity at reservoir temperature (R_w) = 0.1 ohm-m

The hydrocarbon saturation (in percentage) in the reservoir is ______(round off to 1 decimal place).

[Hint: Wyllie time average equation is ∆𝑡𝑙𝑜𝑔 = (1 − 𝜑)∆𝑡_𝑚𝑎 + 𝜑∆𝑡_𝑓𝑙 and formation water resistivity has the correlation , where S_w is water saturation, 𝜑 is porosity]

Answer: (59.0 to 61.0)

50. A vertical well of 8000 ft is producing below bubble point pressure. Oil and water each is produced at the rate of 500 bbl/day. The indicated bottom hole pressure is 3000 psi. If the same gas to liquid ratio (GLR) is maintained, using the given figure, the new bottom hole pressure at 5000 ft is ______psi.

Answer: (1600 to 1900)

51. In a drilling rig, the crown block and the traveling block have three and two sheaves, respectively. A single wireline connects the hoisting drum to the deadline anchor as shown in the figure. Neglect the weight of the pulleys and the wireline, and friction between the sheaves and wireline. The ratio of the deadline load to static crown load is ______(round off to 2 decimal places).

Answer: (0.16 to 0.18)

52. Cement weighing 100 kg is mixed with 50 liters of water. The specific gravity of cement is 3.14 and the density of water is 1000 kg/m³. Neglecting volume changes, the resulting density of the slurry is __________ kg/m³ (round off to 1 decimal place).

Answer: (1820.0 to 1880.0)

53. In an active water drive during a certain period, the rate of production and reservoir pressure remain constant. The water influx into the reservoir from the aquifer is 6000 bbl/day. The surface oil and water production rates are 3000 STB/day and 1500 STB/day, respectively. The current production gas to oil ratio is 825 SCF/STB, and the formation volume factors at the current pressure for oil, water and gas are 1.375 bbl/STB, 1.04 bbl/STB and 0.007 bbl/STB, respectively. The solution gas to oil ratio at the current pressure is _______SCF/STB (round off to 1 decimal place).

Answer: (739.0 to 815.0)

54. In a water flooding experiment, the pressure gradients in the displacing and displaced phases are 400 psi/ft and 350 psi/ft, respectively. Assume that the displacement front is stable in the absence of capillary and gravity forces. Consider that only water flows upstream and only oil flows downstream of the displacement front. Then the mobility ratio for this immiscible displacement process is ______ (round off to 2 decimal places).

Answer: (0.85 to 0.90)

55. In a pressure draw-down testing, the well bore flowing pressure (𝑃_𝑤𝑓) is given by

The following data is given in the oil field units,

Initial reservoir pressure (𝑃_𝑖) = 5000 psia

Pressure after 1 hr of production (P_1hr) = 4000 psia

Oil flow rate (q) = 500 STB/day

Porosity (∅) = 0.25

Viscosity of oil (𝜇) = 2 cP

Formation volume factor of oil (B) = 1.2 bbl/STB

Formation thickness (h) = 20 ft

Total compressibility (𝑐) = 30 × 10⁻⁶ psi^-1

Well bore radius (𝑟_𝑤) = 0.3 ft

The slope of 𝑃_𝑤𝑓 versus log t is −100 psi/cycle. Then, the skin factor (S) for this well is ________ (round off to 1 decimal place).

Answer: (5.0 to 7.0)

GATE Exam 2019 Metallurgical Engineering (MT) Question Paper With Answer Key

June 7, 2023December 10, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Metallurgical Engineering

Q.1 – Q. 25 carry one mark each.

1. One of the eigenvalues for the following matrix is _______.

(A) a – 4

(B) −a – 4

(D) −4

Answer: (A)

2. The curl of vector fields shown below is not zero for _______.

(A)

(B)

(C)

(D)

Answer: (D)

3. The smallest period of function is ________.

(A) 2π

(B) k/n

(D) 2πn/k

Answer: (C)

4. The directional derivative of ϕ = x² + y along the unit vector at (1, 1) is ______.

(A) 3

(B) 2

(D) 0

Answer: (B)

5. Liquid steel is kept in a graphite crucible for sufficiently long time such that equilibrium is established. Activity of carbon (with respect to graphite as the standard state) in the liquid is_______.

(A) 0.0

(B) 0.5

(D) 2.0

Answer: (C)

6. The variation of standard free energies for two oxides AO and BO with temperature are shown below.

The correct statement with reference to the above figure is .

(A) AO is a gas

(B) BO is a gas

(D) B will reduce AO below temperature T1

Answer: (B)

7. Terminal rise velocity of a spherical shaped solid in a liquid obeys the following functional relationship:

U = f (d,W , μ, ρ)

Where, U is the terminal rise velocity, d is the diameter of the solid, W is the apparent weight of the solid, µ is the viscosity of liquid and ρ is the density of liquid.

According to Buckingham Π theorem, the number of independent dimensionless variables needed to describe the phenomenon is _______.

(A) 1

(B) 2

(D) 5

Answer: (B)

8. Consider electrodeposition of copper on a copper electrode from an aqueous solution containing 0.5 × 10⁻³ mol.cm⁻³ CuSO₄.

Given: Faraday constant, F = 96500 Coulomb per gram equivalent.

Assume transport of reactant is rate limiting, and mass transfer coefficient is 10⁻⁴ cm. 𝑠⁻¹. The limiting current density (in mA. cm⁻²) is __________.

(A) 4.83

(B) 9.65

(D) 38.60

Answer: (B)

9. The correct sequence of steelmaking operations is ______.

[BOF: Basic Oxygen Furnace; LF: Ladle Furnace; VD: Vacuum Degassing; CC: Continuous Casting].

(A) BOF → LF → VD → CC

(B) CC → BOF → LF→ VD

(D) LF → BOF → VD → CC

Answer: (A)

10. The common ore of titanium is ________.

(A) Bauxite

(B) Chalcopyrite

(D) Ilmenite

Answer: (D)

11. Coarse suspended particles are to be separated from a flowing gas in a dust catcher. All factors remaining same, maximum gas-solid separation is expected from the dust catcher_______shown below.

Answer: (A)

12. The Boudouard (or, carbon gasification) reaction is ______.

Answer: (C)

13. The fastest diffusing element in iron at 1100°C is ______.

(A) Ni

(B) Co

(D) C

Answer: (D)

14. Hydrogen bonds are stronger than _____.

(A) Ionic bonds

(B) Metallic bonds

(D) Covalent bonds

Answer: (C)

15. The carbide that is primarily responsible for intergranular corrosion in austenitic stainless steel is ___________ .

(A) Cr₂₃C₆

(B) Fe₃C

(D) Mn₃C

Answer: (A)

16. During low strain rate (≤ 0.1 per second) deformation of a metal at room temperature, the one that deforms by twinning mode is _______.

(A) Fe

(B) Mg

(D) Ni

Answer: (B)

17. In a tensile creep test of a metal, Nabarro-Herring mechanism is favored over Coble mechanism for ________.

(A) larger grain size and lower temperature

(B) smaller grain size and higher temperature

(D) smaller grain size and lower temperature

Answer: (C)

18. Beach marks are commonly observed on the fractured surfaces of metals after a .

(A) Creep test

(B) Fatigue test

(D) Compression test

Answer: (B)

19. The length of internal cracks in two samples of the same glass is measured to be c₁ = 0.5 mm and c₂ = 2 mm. The ratio (𝜎₁/σ₂) of the fracture strength of the two samples

(A) 0.5

(B) 1.0

(D) 4.0

Answer: (C)

20. Two blocks of the same metal are to be welded. The configuration that will undergo the least distortion after welding is __________.

Answer: (D)

21. The most suitable non-destructive testing method for detecting small internal flaws in a dense bulk aterial is ________.

(A) Dye penetrant method

(B) Ultrasonic inspection

(D) Magnetic particle inspection

Answer: (B)

22. Alligotoring is a detect commonly observed in _______.

(A) Extrusion

(B) Deep drawing

(D) Rolling

Answer: (D)

23. The standard deviation (rounded off to one decimal place) of the following set of five numbers is _______.

6, 8, 8, 9, 9

Answer: (1.0 to 1.4)

24. A FCC crystal with a lattice parameter of 0.3615 nm is used to measure the wavelength of monochromatic X-rays. The Bragg angle (θ) for the reflection from (111) planes is 21.68°. The wavelength of X-rays (in nm, rounded off to three decimal places) is _________.

Answer: (0.153 to 1.55)

25. A plate of width 100 cm and thickness 5 cm is rolled to a thickness of 3 𝑐𝑚. If the entry velocity is 10 cm. s⁻¹, the exit velocity of the plate (in cm. s⁻¹, rounded off to one decimal place) is ________.

Assume no change in the width of the plate.

Answer: (16.0 to 17.4)

Q.26 – Q. 55 carry two marks each.

26. Match the reactors / refining sites in Column I with the corresponding refining processes in Column II.

(A) P-4, Q-1, R-2, S-3

(B) P-4, Q-2, R-3, S-1

(D) P-1, Q-3, R-2, S-4

Answer: (A)

27. Match the injection metallurgy techniques in Column I with the corresponding objectives in Column II.

(A) P-2, Q-1, R-3, S-4

(B) P-4, Q-3, R-2, S-1

(D) P-4, Q-1, R-2, S-3

Answer: (D)

28. The table (see options below) providing correct information about crystal structure, co- ordination number and packing fraction is_______.

[Note: FCC: Face centered cubic; BCC: Body centered cubic; DC: Diamond cubic.

CN: Coordination number; PF: Packing fraction]

Answer: (A)

29. Match the phase transformation in Column I with the corresponding reaction in Column II.

[Note: α, β, γ are solid phases; L, L₁, L₂ are liquid phases.]

(A) P-4, Q-3, R-1, S-2

(B) P-3, Q-4, R-2, S-1

(D) P-4, Q-2, R-3, S-1

Answer: (A)

30. In a typical scanning electron microscope (SEM) image, information about topography and atomic contrast are obtained from _________.

(A) secondary electron and auger electron, respectively.

(B) primary electron and secondary electron, respectively.

(D) back-scatter electron and auger electron, respectively.

Answer: (C)

31. Match the ceramics in Column I with corresponding application in Column II.

(A) P-2, Q-3, R-1, S-4

(B) P-4, Q-1, R-2, S-3

(D) P-2, Q-4, R-1, S-3

Answer: (D)

32. An aluminium single crystal is loaded in tension along axis. Among the following slip systems, the one that will be activated first is______.

Answer: (A)

33. The correct Mohr’s circle construction for the stress state given below is ______.

Answer: (B)

34. Match the automobile components in Column I with the corresponding manufacturing processes in Column II.

(A) P-1, Q-2, R-3, S-4

(B) P-3, Q-4, R-1, S-2

(D) P-4, Q-1, R-3, S-2

Answer: (B)

35. The equilibrium constant for the following reaction at 300 K is _______.

C(graphite) + 2H₂(g) → CH₄(g)

Given: At 300 K, ∆H° = −74,900 J.mol⁻¹; ∆S° = −80 J.mol⁻¹;

R = 8.314 J.mol⁻¹

(A) 5.6 × 10⁶

(B) 3.6 × 10⁷

(D) 7.3 × 10⁸

Answer: (D)

36. A 50 cm long rod is placed against a vertical wall such that the bottom of the rod is 30 cm away from the wall. If the bottom of the rod is pulled horizontally away from the wall at 4 𝑐𝑚. 𝑠⁻¹, the top of the rod starts sliding down the wall with an instantaneous velocity (in 𝑐𝑚. 𝑠⁻¹, rounded off to two decimal places) of magnitude __________.

Answer: (2.90 to 3.10)

37. The probability of solving a problem by Student A is (1/3), and the probability of solving the same problem by Student B is (2/5). The probability (rounded off to two decimal places) that at least one of the students solves the problem is _________.

Answer: (0.59 to 0.61)

38. Numerical value of work done (rounded off to the nearest integer) by a position- dependent force along the path, from (0,0) to (2,2) in the xy plane is _______.

https://entranceindia.com/wp-content/uploads/2019/12/38-3-1.png

Answer: (17 to 19)

39. The estimated value of the cube root of 37 (rounded off to two decimal places) obtained from the Newton-Raphson method after two iterations (x₂) is _________. [Start with an initial guess value of x₀ = 1].

Answer: (8.50 to 9.00)

40. The partial pressure of zinc (in torr, rounded off to two decimal places) in equilibrium with liquid lead containing 0.03 mole % zinc at 900 K is _______.

Given: Vapour pressure of pure zinc (p_Zn° ) at 900 K is 0.027 atm. Henry’s law coefficient (γ_Zn° ) for zinc at infinite dilute solution in lead on Raoultian scale is 8.55.

1 torr = 1.316 × 10⁻³ atm.

Answer: (0.04 to 0.06)

41. Steady state radial heat conduction through a hollow, infinitely long zirconia cylinder is governed by the following ordinary differential equation:

Where, T is the temperature and r is the radial distance. The inner surface of the hollow cylinder is maintained at 1473 K and the outer surface at 973 K. The rate of heat loss per unit length through the outer surface of the hollow cylinder (in W. m⁻¹, rounded off to the nearest integer) is _______.

Given: Inner radius of cylinder = 0.05 m; outer radius of cylinder = 0.07 m and thermal conductivity of zirconia (k) = 2 W. m⁻¹. K⁻¹.

Answer: (18660 to 18690)

42. A 50 mm (diameter) sphere of solid nickel is oxidized in a gas mixture containing 60% argon and 40% oxygen by volume. The rate of oxidation of nickel is controlled by the rate of transport of oxygen through the concentration boundary layer. The rate of oxidation (in moles of nickel per minute (mol/min), rounded off to two decimal places) is _______.

Given: Total pressure = 1atm.; Temperature = 1173 K; Concentration of oxygen at the surface of the solid = 0; Boundary layer mass transfer coefficient = 0.03 𝑚. 𝑠−1; Universal gas constant, R = 8.205 × 10⁻⁵ m³. atm. K⁻¹. mol⁻¹ . Assume ideal gas behavior.

Answer: (0.11 to 0.13)

43. Equilibrium concentration of dissolved nitrogen (in wt.%, rounded off to three decimal places) in pure liquid iron, exposed to atmospheric air at 1873 K, is _______.

Given: Sieverts’ law constant as a function of temperature (T; in Kelvin) is where K_{[N ]} has the dimension of atm^−(1/2).

Assume [h_N ] =[wt.% N] , where [h_N ] is the activity of nitrogen with respect to 1 wt.% Henrian standard state.

Answer: (0.039 to 0.042)

44. Pressure drop in the granular zone of a blast furnace is 300 mm of water per meter of the bed height. The bed permeability is 0.8 m⁴. N⁻¹. s⁻¹. The volumetric flow rate of gas per unit area through the bed [in (m³. s⁻¹). m⁻², rounded off to the nearest integer] is ______.

Assume Darcy’s law is applicable and g = 9.8 m. s⁻². Density of water = 1000 kg. m⁻³.

Answer: (2347 to 2357)

45. A blast furnace charged with hematite containing 90 wt.% Fe2O3 produces liquid iron with 3.6 wt.% carbon. Coke containing 90 wt.% carbon is charged at a rate of 500 kg per Metric ton of liquid iron produced. The blast furnace top gas contains (by volume), 22% CO, 18% CO₂, and balance nitrogen. The volume of the blast furnace top gas [in m³ (NTP), rounded off to the nearest integer] is .

Given: Assume ideal gas behavior, and molar volume of the gas at NTP is 22.4 liter.

Answer: (1927 to 1937)

46. 100 Metric tons of copper concentrate containing 21 wt.% Cu is to be processed in 6 months with 25 working days per month and 8 working hours per day. The concentrate is leached by sulphuric acid and lectrolyzed in 10 cells arranged in series. The minimum current rating (Ampere per month per cell, rounded off to the nearest integer) is ______.

Given: Faraday constant = 96500 coulomb per gram equivalent.

Atomic weight of copper is 63.

Answer: (1485 to 1495)

47. Cold working of iron leads to increase in dislocation density from 10¹⁰ to 10¹⁵ m⁻². The associated stored energy (in MJ. m⁻³, rounded off to one decimal place) is ______.

Given: Shear modulus of iron = 82 GPa, Burger’s vector,

a₀ = 0.2856 nm.

Answer: (0.4 to 5.1)

48. The critical radius (in nm, rounded off to one decimal place) of nickel nucleus during solidification at 1673 K is _________.

Given: Enthalpy of fusion of nickel = 2.65 × 10⁹ J. m⁻³;

Liquid-solid interfacial energy = 0.5 J. m⁻², and

Equilibrium melting temperature of nickel = 1728 K.

Answer: (11.0 to 12.5)

49. A material, made up of alternating layers of metals A and B, is loaded as shown below. If the volume % of B is 25%, the elastic modulus (in GPa, rounded off to one decimal place) of the material is ________.

Given: Elastic moduli of A and B are 200 GPa and 100 GPa, respectively.

Answer: (155.0 to 165.0)

50. The S-N curve for a steel is shown below. If the stress ratio, (𝜎_min/𝜎_max) = −0.8, the maximum stress (in MPa, rounded off to the nearest integer) that the steel can withstand for infinite fatigue life is ______.

Answer: (330 to 335)

51. True stress – true strain behavior of a metal is given by the flow curve equation σ = 1750ε^0.37 , where σ is in MPa. The true stress at necking (in MPa, rounded off to the nearest integer) is ______.

Answer: (1160 to 1260)

52. In sand-mold casting of a metal, it takes 180 seconds for complete solidification of a 27 cm3 cube-shaped casting. All other parameters remaining constant, the total solidification time (in seconds, rounded off to one decimal place) for a cylinder-shaped [radius = 1 cm and height = 6 cm] casting of the same metal, is _______.

Answer: (130.0 to 134.0)

53. If the solid-solid interfacial energy (γ_SS) is 0.87 𝐽. m⁻² and solid-liquid interfacial energy (γ_SL) is 0.5 J. m⁻², the dihedral angle (ϕ, in degree, rounded off to one decimal place) during sintering is _______.

Answer: (58.0 to 60.2)

54. The maximum possible reduction (in 𝑚𝑚, rounded off to one decimal place) of a 100 mm thick slab during rolling is ________.

Answer: (3.6 to 4.2)

Given: The coefficient of friction between roll and the slab is 0.2, and the roll diameter is 200 mm.

55. An arc welding is performed at 400 Amperes, 20 V at a traverse speed of 5 mm. s⁻¹. If the heat transfer efficiency is 0.6, the energy input per unit length (in J.mm⁻¹, rounded off to the nearest integer) during the process is ________.

Answer: (955 to 965)

GATE Exam 2019 Mining Engineering (MN) Question Paper With Answer Key

June 7, 2023December 10, 2019 by suresh84

General Aptitude Set-2

Q.1 – Q. 5 carry one mark each.

1. John Thomas, an writer, passed away in 2018.

(A) imminent

(B) prominent

(D) dominant

Answer: (C)

2. _________I permitted him to leave, I wouldn’t have had any problem with him being absent, _________I?

(A) Had, wouldn’t

(B) Have, would

(D) Have, wouldn’t

Answer: (C)

3. A work her staer noticed that the hour hand on the factory clock had moved by 225 degrees during y at the factory. For how long did she stay in the factory?

(A) 3.7 5 hours

(B) 4 hours and 15 mins

(D) 7.5 hours

Answer: (D)

4. The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is _______.

(A) 2

(B) 3

(D) 6

Answer: (C)

5. The minister avoided any mention of the issue of women’s reservation in the private sector. He was accused of_______the issue.

(A) collaring

(B) skirting

(D) belting

Answer: (B)

Q.6 – Q. 10 carry two marks each.

6. Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then they are shot. One prisoner made a statement and the judge had no option but to set him free. Which one of the following could be that statement?

(A) I did not commit the crime

(B) I committed the crime

(D) You committed the crime

Answer: (C)

7. A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are interchanged with these investments he would have got Rs.120 less. Find the ratio between his investments in the two schemes.

(A) 9 : 16

(B) 11 : 14

(D) 47 : 53

Answer: (D)

8. Congo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces. However, the name Zaire was a Portuguese alteration of Nzadi o Nzere, a local African term meaning ‘River that swallows Rivers’. Zaire was the Portuguese name for the Congo river in the 16th and 17th centuries.

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

(A) Mobuto was not entirely successful in Africanising the name of his country

(B) The term Nzadi o Nzere was of Portuguese origin

(D) As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire

Answer: (A)

9. A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown. There were a total of 600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total employment at skill levels P, Q and R remained unchanged during this period. If the employment at skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in 2016?

(A) 30

(B) 35

(D) 72

Answer: (C)

10. M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily FALSE?

(A) M is the grandmother of Y

(B) R is the father of Y

(D) W is the wife of P

Answer: (D)

Mining Engineering

Q.1 – Q. 25 carry one mark each.

1. Shear strength of rock joint is NOT dependent on

(A) applied normal stress

(B) applied shear stress

(D) cohesion of the joint plane

Answer: (B)

2. If f (x) is a polynomial function that passes through origin, and g(x) = f‘(x) , then

Answer: (C)

3. A flat longwall panel is mined out at an area having subsidence factor a. The measured maximum subsidence on the surface is S for a mining height of m. The subsidence is subcritical if

(A) S = am

(B) S = m/a

(D) S = am

Answer: (D)

4. The PV diagram of four explosives is given below. The preferred explosive for adequate fragmentation in hard and brittle rock is

(A) Explosive A

(B) Explosive B

(D) Explosive D

Answer: (A)

5. As per classification of mineral resources “reserve” means

(A) Identified resources

(B) Identified and techno-economically viable resources

(D) Inferred resources

Answer: (B)

6. If the sample statistic is an unbiased estimator of the parameter μ, then

Answer: (A)

7. The vector sum of all the external forces acting on a rigid body is expressed as ∑F and the vector sum of moments of the external forces about a point is given as ∑M. The rigid body is in equilibrium if

(A) ∑F − ∑M = 0

(B) ∑F + ∑M = 0

(D) ∑F ≠ 0 and ∑M ≠ 0

Answer: (C)

8. For a regionalized variable Z (x) , at a lag distance h, the empirical semi-variogram γ (h) is given by

Answer: (B)

9. The coefficient of variation of a dataset is defined as

Answer: (D)

10. In project planning, the activity durations are calculated by PERT and CPM techniques assuming

(A) PERT: probabilistic, CPM: deterministic

(B) PERT: probabilistic, CPM: probabilistic

(D) PERT: deterministic, CPM: deterministic

Answer: (A)

11. Respirable dust in an underground coal mine contains 4.5% free silica. As per the CMR 2017, the maximum allowable respirable dust concentration, in mg/m³, in the mine air is

(A) 1.5

(B) 2.0

(D) 3.0

Answer: (B)

12. The purpose of rotating a whirling hygrometer in hygrometric survey is to

(A) wet the cotton wick with water thoroughly

(B) maintain constant temperature of water in the container

(D) prevent the heat produced by the cap lamp of the observer from affecting the readings

Answer: (C)

13. Stone dust barriers in underground coal mines are used to arrest

(A) black damp explosions

(B) air blast

(D) coal dust explosions

Answer: (D)

14. The correct sequence of attachments between the winding rope and the cage in a drum winding system is

(A) Triangular plate → Rope capel → Bull chain → Detaching hook → Cage chain

(B) Rope capel → Bull chain → Triangular plate → Detaching hook → Cage chain

(D) Rope capel → Detaching hook → Bull chain → Triangular plate → Cage chain

Answer: (D)

15. The functions of automatic contrivances in a winding system are to prevent

(A) over-speeding and over-winding

(B) slow banking and load balancing

(D) over-speeding and load balancing

Answer: (A)

16. A low-grade deep-seated ore body dipping at 70° has a strike length of 2 km, and width of 100 m. The ore body and wall rocks are weak and fractured. The preferred method of mining is

(A) shrinkage stoping

(B) cut-and-fill stoping

(D) room and pillar stoping

Answer: (C)

17. If the figures A and B represent contour plots in a terrain, then the correct statement is

(A) Fig. A shows ridge and Fig. B shows valley

(B) Fig. A shows anticline and Fig. B shows syncline

(D) Fig. A shows valley and Fig. B shows ridge.

Answer: (A)

18. The availability of water in the root zone for plant use is maximum in the case of

(A) sand

(B) loam

(D) gravel

Answer: (B)

19. If the time to failure of a machine component is exponentially distributed, the reliability of the same at Mean Time To Failure (MTTF), (rounded off to three decimal places), is_________.

Answer: (0.350 to 0.375)

20. The major and minor principal stresses at a point are 25 MPa and -5 MPa respectively. The maximum shear stress, in MPa at that point is________.

Answer: (15 to 15)

21. For a function f (x) , f (1) = 5 and f’(1) = −5 . Ignoring all higher order terms in Taylor series, the value of the function at x = 1.01 (rounded off to two decimal places) is ________.

Answer: (4.94 to 4.96)

22. Proximate analysis of a coal sample gives 2.46% moisture, 25.73% volatile matter, and 42.89% ash. The volatile matter of the coal sample, in percentage, on dry ash free (daf) basis (rounded off to two decimal places) is _________.

Answer: (46.00 to 48.00)

23. A coarse sand aquifer has porosity 20% and hydraulic conductivity 3.5 × 10⁻³ m/s. If the hydraulic gradient is 0.00423 (m/m), then the average linear velocity of the groundwater in mm/s, (rounded off to three decimal places) is _______.

Answer: (0.070 to 0.080)

24. In a slake durability test, mass of the drum with samples before the test and mass of the drum with oven-dried samples after the test are 1.52 kg and 1.48 kg respectively. If the mass of the drum is 1.05 kg, slake durability index in percentage (rounded off to two decimal places) is _______.

Answer: (91.00 to 92.00)

25. The ionic concentration of a mine water sample with pH close to 7.0 is given below. The alkalinity of the water expressed as equivalent CaCO₃, in mg/l, (rounded off to two decimal places) is _____.

Answer: (131.10 to 131.20)

Q.26 – Q. 55 carry two marks each.

26. From an elevated point A, when a stone is thrown vertically, it attains an upward velocity of v at a height of h from the point A. While falling, its downward velocity becomes 2v at a distance h below the point A. The maximum height attained by the stone from point A is

(A) 5h/3

(B) 4h/3

(D) 2h

Answer: (A)

27. Water is pumped through a steel pipe of diameter 200 mm at a flow rate of 30 l/s. If the dynamic viscosity of water is 10⁻³ Pa.s, the Reynolds number of the flow is

(A) 2.83 × 10³

(B) 2.83 × 10⁴

(D) 1.91 × 10⁶

Answer: (C)

28. Matrix is orthogonal. The value of α, β and γ respectively are

Answer: (D)

29. Match the following based on the equipment usage in a comminution circuit:

(A) P-1, Q-4, R-2, S-3

(B) P-1, Q-2, R-3, S-4

(D) P-3, Q-1, R-4, S-2

Answer: (C)

30. Match the following for coal mining operation:

(A) P-C-1, Q-D-3, R-A-2, S-B-4

(B) P-C-1, Q-A-3, R-B-4, S-D-2

(D) P-B-3, Q-C-2, R-A-1, S-D-4

Answer: (B)

31. In the context of mine planning, match the following:

(A) P-4, Q-3, R-2, S-1

(B) P-1, Q-2, R-3, S-4

(D) P-3, Q-2, R-4, S-1

Answer: (C)

32. The figures shown represent the analysis of gas samples collected from a sealed off area in a coal mine over a period of time. The best representation of the progressive change of gaseous environment inside the sealed-off area is

(A) Figure P

(B) Figure Q

(D) Figure S

Answer: (A)

33. The net annual cash flows for two small scale mining projects A and B are given below. The correct decision assuming 10% discount rate as per NPV criterion is

(A) Project A is accepted but project B is rejected

(B) Projects A and B both are rejected

(D) Projects A and B are both accepted but project A is better than project B

Answer: (D)

34. Match the following features with the mining methods:

(A) P-2, Q-4, R-3, S-1

(B) P-4, Q-3, R-2, S-1

(D) P-4, Q-3, R-1, S-2

Answer: (C)

35. If area S, in the x-y plane, is bounded by a triangle with vertices (0, 0), (10, 1) and (1, 1), the value of

Answer: (6 to 6)

36. A double ended ranging drum shearer operates in a longwall retreating panel. The following data are provided:

Face length : 200 m Average cutting speed : 1.5 m/min

Web depth : 0.6 m Average flitting speed : 4.0 m/min

Cutting height : 2.5 m Number of shifts/day 3

Density of coal : 1.4 tonne/m³

Method of cutting is unidirectional and each shift requires a non-operational time of 2.0 hours. The production per day in tonne (rounded off to one decimal place) is ________.

Answer: (2450.1 to 2550.5)

37. In the linear programming problem,

Maximize Z = 48X₁ + 36X₂

Subject to:

The value of Z is ______.

Answer: (408 to 408)

38. A shovel operates 300 days in a year, 2 shifts in a day, and 4 hours in a shift to achieve the target production of 30 Million tonne per annum. The following parameters relate to the loading operations:

Bucket capacity of shovel : 15 m³

Shovel cycle time : 44 s

Bucket fill factor : 0.85

Bulk density of the muck : 3.00 tonne/m³

The minimum number of shovels required to achieve the production is _________.

Answer: (4 to 4)

39. A set of tubs is pulled by a 15 tonne diesel locomotive at a gradient of 1 in 100 with an acceleration of 0.05 m/s2. The coefficient of adhesion between the wheel and the track is 0.2 and the frictional resistance coefficient is 0.01. The maximum mass, in tonne, the locomotive can pull (rounded off to one decimal place) is _______.

Answer: (102.5 to 107.5)

40. The characteristic curves of two mine fans installed in series in a fan drift are P = 2000 – 6Q − 0.2Q² and P = 3000 – 8Q − 0.2Q² where P is pressure in Pa and Q is quantity in m³/s. If the mine quantity is 70 m³/s, the mine resistance, in Ns²m⁻⁸, (rounded off to two decimal places) is ________.

Answer: (0.40 to 0.45)

41. Three equipment A, B, and C located side by side and operating simultaneously produce a sound power level of 77.5 dB. The sound power levels of A and B are 68 dB and 70 dB respectively. The sound power level of C (rounded off to one decimal place) in dB, is _______.

Answer: (75.5 to 76.5)

42. The main surface fan of a mine as shown in the figure, has characteristic curve approximated by P = 1700 – 10Q, where P is pressure in Pa and Q is quantity in m³/s. A booster fan is installed in section A such that there is no air flow in section B. The operating pressure of the main surface fan, in Pa, (rounded off to two decimal places) is _______.

Answer: (858.25 to 865.25)

43. Two points A and B are located 150 m apart in the East-West orientation on the bank of a river as shown in the figure. Considering a station C on the north bank the bearings of AC and BC are observed to be 42° and 335° respectively. The width of the river, in m, (rounded off to two decimal places) is________.

Answer: (108.00 to 111.00)

44. If x = 3^1/3 + 3⁻^1/3 , the value of 3x³ − 9x −10 is _________.

Answer: (0 to 0)

45. A pump delivers 3000 liter of water in 2.0 minutes through a pipe of length 1000 m laid on a gradient of 1 in 10. The combined efficiency of pump and motor is 70%. If friction and shock losses are negligible, the input power to the motor in kW (rounded off to one decimal place) is _________.

Answer: (33.0 to 37.0)

46. A sand water slurry of specific gravity 1.45 contains sand of grain density 2.6 g/cc. The weight percent of sand in the slurry (rounded off to two decimal places) is ________.

Answer: (50.00 to 52.00)

47. For a mining company the unit transportation cost from a mine to a washery, and supply and demand are shown below:

The total cost of transportation using the Vogel’s approximation method is _______.

Answer: (37200 to 37200)

48. In a bord and pillar panel, 6 square pillars are developed as shown in the figure below. The depth of the seam is 300 m and the average unit weight of overburden rock is 25 kN/m³. If the pillar strength is 15 MPa, the safety factor of the shaded pillar zone (round off to two decimal places) is _______.

Answer: (1.38 to 1.40)

49. Water enters a sump having the shape of an inverted frustum at a rate of 500 m³/h. The sump is initially filled up to 2.0 m height. The time taken in days to fill the remaining part of the sump (rounded off to one decimal places) is ________.

Answer: (7.1 to 7.5)

50. The uniaxial stress-strain behavior of a rock sample is shown in the figure. The elastic modulus E is 20,000 MPa. If ε_p is the plastic strain, the value of the damage parameter D (rounded off to two decimal place) is ________.

Answer: (0.72 to 0.77)

51. The insitu stress field around a circular tunnel is shown in the figure. Points A and B are located at the boundary of the tunnel. If the tangential stress at Point A is 3 times of that at Point B, the value of insitu stress ratio, k is ________.

Answer: (2 to 2)

52. Data related to explosive and blasthole are given below. Assuming 1 kcal to be 4.2 kJ, the power of explosive in GW in the blasthole (round off to one decimal place) is ________.

Diameter of the borehole : 200 mm

Charge length : 8 m

Density of ANFO : 0.8 g/cc

Heat of explosion : 912 cal/g

VOD : 4500 m/s

Initiation : Bottom

Answer: (430.0 to 437.0)

53. A rock block of mass 100 kg is to be lifted by a horizontal force P as shown in the figure below. Smooth rollers are placed between the wedges. The coefficient of static friction between wedge A and surface C and between wedge B and surface D is 0.3. Ignoring the weight of the wedges and the friction between the roller and the wedges, the minimum force P in kg required to lift the block (round off to one decimal place) is ________.

Answer: (50.0 to 51.0)

54. A joint plane dipping at 30° intersects the slope edge and the crest as shown in the figure below. The unit weight of rock is 25 kN/m³, and cohesion and friction angle of the joint surface are 40 kPa and 25°respectively. The safety factor of the shaded block (round off to two decimal places) is ________.

Answer: (2.12 to 2.22)

55. The random variable X has probability density function as given by

The value E(X²) (rounded off to one decimal place) is __________.

Answer: (0.5 to 0.7)

GATE Exam 2019 Mechanical Engineering (ME-2) Question Paper With Answer Key

June 7, 2023December 10, 2019 by suresh84

General Aptitude Set-4

Q.1 – Q. 5 carry one mark each.

1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.

Which one of the following choices CANNOT fill the given blank?

(A) will be

(B) were to be

(D) might be

Answer: (B)

2. A final examination is the _______ of a series of evaluations that a student has to go through.

(A) culmination

(B) consultation

(D) insinuation

Answer: (A)

3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .

(A) JDE

(B) JED

(D) JCD

Answer: (B)

4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

(A) 6

(B) 7

(D) 9.5

Answer: (Marks to All)

5. Are there enough seats here? There are _______people here than I expected.

(A) many

(B) most

(D) more

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.

(A) 37.50

(B) 35.70

(D) 10.00

Answer: (A)

(A) 13.50

(B) 14.5

(D) 16.50

Answer: (B)

The writer of this passage is surprised by the creative writing assignments of his students, because ______ .

(A) Some of the students had written stories set in foreign places

(B) None of the students had written stories set in India

(D) Some of the students had written about ice cubes and cowboys

Answer: (B)

(A) 16.24

(B) 23.97

(D) 38.74

Answer: (B)

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

(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television

(B) Non-members prefer to watch cable television

(D) The X is cancelling accounts of non-members

Answer: (A)

Mechanical Engineering

1. In matrix equation [A] {X} = {R},

One of the eigenvalues of matrix [A] is

(A) 4

(B) 8

(D) 16

Answer: (D)

2. The directional derivative of the function f (x, y) = x² + y² along a line directed from (0,0) to (1,1), evaluated at the point x = 1, y = 1 is

(A) √2

(B) 2

(D) 4√2

Answer: (C)

3. The differential equation is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The solution of the differential equation is

(A)y = e^−4x + 5

(B) y = e^−4x + 1.25

(D) y = e^4x + 1.25

Answer: (B)

4. An analytic function f(z) of complex variable z = x + iy may be written as f(z) = u(x, y) + iv(x, y). Then, u(x, y) and v(x, y) must satisfy

Answer: (B)

5. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of points P and R are VP and VR , in the x and y directions, respectively. The magnitude of the angular velocity of the body is

(A) 2V_R

(B) 2V_P

(D) V_P/√3

Answer: (A)

6. Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio ν = 0.3 are given. The principal strains in the plane of the sheet are

(A) (0.35, −0.15)

(B) (0.5, 0.0)

(D) (0.5, −0.5)

Answer: (C)

7. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is

(A) πD/T

(B) T/D

(D) 2πD/T

Answer: (A)

8. Endurance limit of a beam subjected to pure bending decreases with

(A) decrease in the surface roughness and decrease in the size of the beam

(B) increase in the surface roughness and decrease in the size of the beam

(D) decrease in the surface roughness and increase in the size of the beam

Answer: (C)

9. A two-dimensional incompressible frictionless flow field is given by If ρ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

Answer: (B)

10. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor F₁₂ is

(A) 0.0625

(B) 0.25

(D) 1.0

Answer: (D)

11. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is

(A) Linear

(B) Quadratic

(D) Exponential

Answer: (C)

12. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell’s relations, is equal to

Answer: (D)

13. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?

(A) Increasing the boiler pressure.

(B) Decreasing the boiler pressure.

(D) Decreasing the condenser pressure.

Answer: (C)

14. Hardenability of steel is a measure of

(A) the ability to harden when it is cold worked

(B) the maximum hardness that can be obtained when it is austenitized and then quenched

(D) the ability to retain its hardness when it is heated to elevated temperatures

Answer: (C)

15. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in

(A) viscosity

(B) surface tension

(D) degree of superheat

Answer: (D)

16. The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface with a regular pattern is

(A) Roll forming

(B) Strip rolling

(D) Chamfering

Answer: (C)

17. The most common limit gage used of inspecting the hole diameter is

(A) Snap gage

(B) Ring gage

(D) Master gage

Answer: (C)

18. The transformation matrix for mirroring a point in x – y plane about the line y = x is given by

Answer: (C)

19. If x is the mean of data 3, x, 2 and 4, then the mode is_______.

Answer: (3 to 3)

20. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is _______ N.

Answer: (0 to 0)

21. The state of stress at a point in a component is represented by a Mohr’s circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is _______ MPa.

Answer: (79 to 81)

22. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ________ MPa.

Answer: (49 to 51)

23. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number Re_D = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is _________.

Answer: (500 to 500)

24. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is given as Nu = K Ra^1/4 , where K is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h₁ and that for the second plate is h₂, the value of the ratio h₁/h₂ is______.

Answer: (2 to 2)

25. In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is 200 V and the capacitance of the RC circuit is 50 µF. The energy (in J) released per spark across the IEG is _________

Answer: (1 to 1)

Q.26 – Q. 55 carry two marks each.

26. Given a vector and as the unit normal vector to the surface of the hemisphere (x² + y² + z² = 1; z ≥ 0), the value of integral evaluated on the curved surface of the hemisphere S is

(A) –π/2

(B) π/3

(D) π

Answer: (C)

27. A differential equation is given as

The solution of the differential equation in terms of arbitrary constants C₁ and C₂ is

Answer: (A)

28. The derivative of f(x) = cos(x) can be estimated using the approximation

The percentage error is calculated as

The percentage error in the derivative of f(x) at x = π/6 radian, choosing h = 0.1 radian, is

(A)< 0.1 %

(B) > 0.1 % and < 1 %

(D)> 5 %

Answer: (B)

29. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value(s) of m is/are

(A) 1 kg only

(B) 6 kg only

(D) 1 kg, 9 kg

Answer: (D)

30. Consider two concentric circular cylinders of different materials M and N in contact with each other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder system is subjected to internal pressure 𝑃. Let denote the radial and tangential displacement and stress components, respectively, in material M. Similarly, denote the radial and tangential displacement and stress components, respectively, in material N. The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:

Answer: (A)

31. A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is

Answer: (B)

32. A slender uniform rigid bar of mass 𝑚 is hinged at O and supported by two springs, with stiffnesses 3𝑘 and 𝑘, and a damper with damping coefficient 𝑐, as shown in the figure. For the system to be critically damped, the ratio 𝑐/√𝑘𝑚 should be

(A) 2

(B) 4

(D) 4√7

Answer: (D)

33. The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q₂) rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (W) of the heat engine. If temperatures, T₁ > T₃ >T₂ , then the relation between the efficiency (η) of the heat engine and the coefficient of performance (COP) of the heat pump is

(A) COP = η

(B) COP = 1 + η

(D) COP = η⁻¹ – 1

Answer: (C)

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at 1250°C, respectively, will be

(A) 77.8% and 22.2%

(B) 22.2% and 77.8%

(D) 32.0% and 68.0%

Answer: (B)

35. The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship “X < Y, Z” means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ______ weeks.

(A) 17

(B) 21

(D) 25

Answer: (C)

36. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

(A) − ω²r

(B) 2ω²r

(D) −2ω²r

Answer: (C)

37. A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity EI = 200 N ∙ m² is subjected to an applied moment MA = 1.0 N ∙ m at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is ______ mm (round off to one decimal place).

Answer: (2.4 to 2.6)

38. Two masses A and B having mass m_a and m_b, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses ma and m_b are r_a and r_b, respectively. The angle between lines OA and OB is 90°. If ma = 10 kg, mb = 20 kg, ______ r_a = 200 mm and r_b = 400 mm, then the balance mass to be placed at a radius of 200 mm is _______ kg (round off to two decimal places).

Answer: (41.00 to 42.00)

39. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed ω₂ . Length of different links are:

O₂O₄ = O₂A = L,

AB = O₄B = √2L.

The magnitude of the angular speed of the output link 4 is ω₄ at the instant when link 2makes an angle of 90° with O₂O₄ as shown. The ratio ω₄/ω₂ is_________(round off to two decimal places).

Answer: (0.78 to 0.80)

40. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _________ (round off to two decimal places).

Answer: (0.16 to 0.18)

41. A uniform disc with radius 𝑟 and a mass of m kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular speed ω, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical axis at ω_p = ω ⁄ 10 in the clockwise direction when viewed from above. Let RP and R_Q (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming ω² r = 300 m/s² and g = 10 m/s², the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is _______

Answer: (-3 to -3)

42. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______ N ∙ m (round off to two decimal places).

Answer: (19.00 to 21.00)

43. Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates Q_B /Q_A is _______(round off to two decimal places).

Answer: (0.48 to 0.52)

44. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ______ km/h (The density of air and the frontal area may be assumed to be constant).

Answer: (21.90 to 22.20)

45. Three sets of parallel plates LM, NR and PQ are given in figures 1, 2 and 3. The view factor F_U is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of F_LM and F_NR are 0.8 and 0.4, respectively. The value of F_PQ (round off to one decimal place is _______.

Answer: (0.6 to 0.6)

46. Hot and cold fluids enter a parallel flow double tube heat exchanger at 100°C and 15°C, respectively. The heat capacity rates of hot and cold fluids are C_h = 2000 W/K and C_c = 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45 °C, the log mean temperature difference (LMTD) of the heat exchanger is______K (round off to two decimal places).

Answer: (57.00 to 58.00)

47. Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entropy increases by 0.007 kJ/kg∙K. The power input to the electric heater is 2.50 kW. There is no other work or heat interaction between the system and the surroundings. Assuming an ambient temperature of 300 K, the irreversibility rate of the system is ______ kW (round off to two decimal places).

Answer: (2.05 to 2.15)

48. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is______ kg/s (round off to two decimal places).

Answer: (8.00 to 8.20)

49. An air standard Otto cycle has thermal efficiency of 0.5 and the mean effective pressure of the cycle is 1000 kPa. For air, assume specific heat ratio γ = 1.4 and specific gas constant R = 0.287 kJ/kg∙K. If the pressure and temperature at the beginning of the compression stroke are 100 kPa and 300 K, respectively, then the specific net work output of the cycle is ______ kJ/kg (round off to two decimal places).

Answer: (705.00 to 715.00)

50. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81 m/s². The time (in s, round off to two decimal places) to fill up the mold cavity (of size 40 cm × 30 cm × 15 cm) is _________

Answer: (28.80 to 29.00)

51. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of 20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input per unit length of the weld will be ________ kJ/mm (round off to one decimal place).

Answer: (0.7 to 0.7)

52. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ____ mm (round off to two decimal places).

Answer: (1.24 to 1.26)

53. A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specific energy required for cutting this material is 0.7 N∙m/mm³, the power required for drilling is______ W (round off to two decimal places).

Answer: (274.00 to 276.00)

54. In an orthogonal machining with a single point cutting tool of rake angle 10°, the uncut chip thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant’s first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool interface is _______ (round off to two decimal places).

Answer: (0.72 to 0.76)

55. The annual demand of valves per year in a company is 10,000 units. The current order quantity is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs. 400 per order. If the current order quantity is changed to Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. _______(round off to two decimal places).

Answer: (941.00 to 946.00)

GATE Exam 2019 Mechanical Engineering (ME-1) Question Paper With Answer Key

June 7, 2023December 9, 2019 by suresh84

General Aptitude Set-2

Q.1 – Q. 5 carry one mark each.

1. John Thomas, an writer, passed away in 2018.

(A) imminent

(B) prominent

(D) dominant

Answer: (C)

2. _________I permitted him to leave, I wouldn’t have had any problem with him being absent, _________I?

(A) Had, wouldn’t

(B) Have, would

(D) Have, wouldn’t

Answer: (C)

3. A work her staer noticed that the hour hand on the factory clock had moved by 225 degrees during y at the factory. For how long did she stay in the factory?

(A) 3.7 5 hours

(B) 4 hours and 15 mins

(D) 7.5 hours

Answer: (D)

4. The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is _______.

(A) 2

(B) 3

(D) 6

Answer: (C)

5. The minister avoided any mention of the issue of women’s reservation in the private sector. He was accused of_______the issue.

(A) collaring

(B) skirting

(D) belting

Answer: (B)

Q.6 – Q. 10 carry two marks each.

(A) I did not commit the crime

(B) I committed the crime

(D) You committed the crime

Answer: (C)

(A) 9 : 16

(B) 11 : 14

(D) 47 : 53

Answer: (D)

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

(A) Mobuto was not entirely successful in Africanising the name of his country

(B) The term Nzadi o Nzere was of Portuguese origin

(D) As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire

Answer: (A)

(A) 30

(B) 35

(D) 72

Answer: (C)

(A) M is the grandmother of Y

(B) R is the father of Y

(D) W is the wife of P

Answer: (D)

Mechanical Engineering

Q.1 – Q. 25 carry one mark each.

1. Consider the matrix

The number of distinct eigenvalues of P is

(A) 0

(B) 1

(D) 3

Answer: (B)

2. A parabola x = y² with 0 ≤ x ≤ 1 is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360° around the x-axis is

(A) π/4

(B) π/2

(D) 2π

Answer: (B)

3. For the equation if y(0) = 3/7, then the value of y(1) is

4. The lengths of a large stock of titanium rods follow a normal distribution with a mean (𝜇) of 440 mm and a standard deviation (σ) of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?

(A) 81.85%

(B) 68.4%

(D) 86.64%

Answer: (A)

5. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity 𝜔. At time 𝑡 = 0, the vertical position of the follower is y(0) = 0, and the system is in the configuration shown below.

The vertical position of the follower face, 𝑦(𝑡) is given by

(A) 𝑒 sin 𝜔𝑡

(B) 𝑒(1 + cos 2𝜔𝑡)

(D) 𝑒 sin 2𝜔𝑡

Answer: (C)

6. The natural frequencies corresponding to the spring-mass systems I and II are 𝜔_𝐼 and 𝜔_𝐼𝐼, respectively. The ratio 𝜔_𝐼/𝜔_𝐼𝐼 is

(A) 1/4

(B) 1/2

(D) 4

Answer: (B)

7. A spur gear with 20° full depth teeth is transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is

(A) 0.36 kN

(B) 0.73 kN

(D) 2.78 kN

Answer: (B)

8. During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction (Q_1-2 = W_1-2) when the process is

(A) Isentropic

(B) Polytropic

(D) Adiabatic

Answer: (C)

9. For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux ( Nu_q ) and that at constant wall temperature ( Nu_T ) are related as

(A) Nu_q > Nu_T

(B) Nu_q < Nu_T

(D) Nu_q = (Nu_T)²

Answer: (A)

10. As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, are

(A) Kaplan, Francis, Pelton

(B) Pelton, Francis, Kaplan

(D) Pelton, Kaplan, Francis

Answer: (A)

11. A slender rod of length L, diameter d ( L > > d ) and thermal conductivity k1 is joined with another rod of identical dimensions, but of thermal conductivity k2 , to form a composite cylindrical rod of length 2L . The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod is

Answer: (D)

12. Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle?

(A) Coefficient of performance is higher than that of the original cycle.

(B) Coefficient of performance is lower than that of the original cycle.

(D) Refrigerating effect is lower than that of the original cycle.

Answer: (A)

13. In a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is called

(A) blister

(B) sprue

(D) pin hole

Answer: (B)

14. Which one of the following welding methods provides the highest heat flux (W/mm²)?

(A) Oxy-acetylene gas welding

(B) Tungsten inert gas welding

(D) Laser beam welding

Answer: (D)

15. The length, width and thickness of a steel sample are 400 mm, 40 mm and 20 mm, respectively. Its thickness needs to be uniformly reduced by 2 mm in a single pass by using horizontal slab milling. The milling cutter (diameter: 100 mm, width: 50 mm) has 20 teeth and rotates at 1200 rpm. The feed per tooth is 0.05 mm. The feed direction is along the length of the sample. If the over-travel distance is the same as approach distance, the approach distance, the approach distance and time taken to complete the required machining task re

(A) 14 mm, 18.4 s

(B) 21 mm, 28.9 s

(D) 14 mm, 21.4 s

Answer: (D)

16. The position vector of point P (20, 10) is rotated anti-clockwise in X-Y plane by an angle θ = 30° such that point P occupies position Q, as shown in the figure. The coordinates (x, y) of Q are

(A) (13.40, 22.32)

(B) (22.32, 8.26)

(D) (18.66, 12.32)

Answer: (C)

17. The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is

(A) 490

(B) 510

(D) 536.67

Answer: (B)

18. Evaluation of using a 2-equal-segment trapezoidal rule gives a value of _______

Answer: (63 to 63)

19. A block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is 9.81 m/s². The coefficient of static friction between the floor and the block is 0.2. A horizontal force of 10 N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is_____

Answer: (10 to 10)

20. A cylindrical rod of diameter 10 mm and length 1.0 m is fixed at one end. The other end is twisted by an angle of 10° by applying a torque. If the maximum shear strain in the rod is p × 10⁻³, then p is equal to _______ (round off to two decimal places).

Answer: (0.80 to 0.90)

21. A solid cube of side 1 m is kept at a room temperature of 32°C. The coefficient of linear thermal expansion of the cube material is 1 × 10⁻⁵/°C and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly to 42°C, then the magnitude of volumetric (mean) stress (in MPa) induced due to heating is_______

Answer: (59.5 to 60.5)

22. During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of +140 MPa, and a minimum stress of −70 MPa. The R-ratio (minimum stress to maximum stress) for this cyclic loading is_______ (round off to one decimal place)

Answer: (-0.2 to -0.2)

23. Water flows through a pipe with a velocity given by is the unit vector in the y direction, t (> 0) is in seconds, and x and y are in meters. The magnitude of total acceleration at the point (x, y) = (1, 1) at t = 2 s is _______ m/s².

Answer: (3 to 3)

24. Air of mass 1 kg, initially at 300 K and 10 bar, is allowed to expand isothermally till it reaches a pressure of 1 bar. Assuming air as an ideal gas with gas constant of 0.287 kJ/kg.K, the change in entropy of air (in kJ/kg.K, round off to two decimal places) is______

Answer: (0.64 to 0.68)

25. Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes through initial yield point at P, and then strain hardens to point Q, where the loading was stopped. From point Q, the specimen was unloaded to point R, where the stress is zero. If the same specimen is reloaded in tension from point R, the value of stress at which the material yields again is _________ MPa.

Answer: (210 to 210)

Q.26 – Q. 55 carry two marks each.

26. The set of equations

𝑥 + 𝑦 + 𝑧 = 1

𝑎𝑥 – 𝑎𝑦 + 3𝑧 = 5

5𝑥 − 3𝑦 + 𝑎𝑧 = 6

has infinite solutions, if a =

(A) −3

(B) 3

(D) −4

Answer: (C)

27. A harmonic function is analytic if it satisfies the Laplace equation. If 𝑢(𝑥, 𝑦) = 2𝑥² − 2𝑦² + 4𝑥𝑦 is a harmonic function, then its conjugate harmonic function 𝑣(𝑥, 𝑦) is

(A) 4𝑥𝑦 − 2𝑥² + 2𝑦² + constant

(B) 4𝑦² − 4𝑥𝑦 + constant

(D) −4𝑥𝑦 + 2𝑦² − 2𝑥² + constant

Answer: (A)

28. The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is

(A) 0

(B) 0.25

(D) 0.50

Answer: (B)

29. A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is l. The acceleration of the car is a, and acceleration due to gravity is g. The reactions on the front wheels (R_f) and rear wheels (R_r) are given by

Answer: (C)

30. In a four bar planar mechanism shown in the figure, AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of 10 rad/s. The magnitude of angular velocity (in rad/s) of bar DC at this instant is

(A) 0

(B) 10

(D) 25

Answer: (D)

31. The rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia 10 kg∙m² about the rotor axis. The rotor rotates at a constant speed of 1100 rad/s in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800 km per hour takes a turn with a radius of 1.5 km to the left. The gyroscopic moment exerted by the rotor on the aircraft structure and the direction of motion of the nose when the aircraft turns, are

(A) 1629.6 N∙m and the nose goes up

(B) 1629.6 N∙m and the nose goes down

(D) 162.9 N∙m and the nose goes down

Answer: (B)

32. The wall of a constant diameter pipe of length 1 m is heated uniformly with flux 𝑞” by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to 0 ºC at the inlet and 50 ºC at the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow thermally develops after some distance from the inlet. The following measurements are made:

Among the locations P, Q and R, the flow is thermally developed at

(A) P, Q and R

(B) P and Q only

(D) R only

Answer: (C)

33. A gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section of the duct at 100 kPa and 27°C with a volume flow rate of 15 m³/s. If heat is lost from the gas in the duct to the surroundings at a rate of 51 kW, the exit temperature of the gas is

(Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant specific heat; C_p = 1 kJ/kg∙K; R = 0.5 kJ/kg∙K.)

(A) 32°C

(B) 37°C

(D) 76°C

Answer: (A)

34. A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction zero. The yield strength (S_y) in uniaxial tension/compression of the material of the block is 300 MPa it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where σ_x = 40 MPa (compressive) and τ_xx = 0, the stress component, σ_y is

(A) 340 MPa (compressive)

(B) 340 MPa (tensile)

(D) 260 MPa (tensile)

Answer: (A)

35. In orthogonal turning of a cylindrical tube of wall thickness 5 mm, the axial and the tangential cutting forces were measured as 1259 N and 1601 N, respectively. The measured chip thickness after machining was found to be 0.3 mm. The rake angle was 10° and the axial feed was 100 mm/min. The rotational speed of the spindle was 1000 rpm. Assuming the material to be perfectly plastic and Merchant’s first solution, the shear strength of the material is closest to

(A) 722 MPa

(B) 920 MPa

(D) 875 MPa

Answer: (A)

36. A circular shaft having diameter is manufactured by turning process. A 50 µm thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is ± 5 µm. The minimum hole diameter (in mm) to just provide clearance fit is

(A) 65.01

(B) 65.12

(D) 65.10

Answer: (B)

37. Match the following sand mold casting defects with their respective causes.

(A) P-4, Q-3, R-1, S-2

(B) P-3, Q-4, R-2, S-1

(D) P-3, Q-4, R-1, S-2

Answer: (D)

38. A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is______

Answer: (4.98 to 5.02)

39. Consider an elastic straight beam of length 𝐿 = 10 𝜋 m, with square cross-section of side a = 5 mm, and Young’s modulus E = 200 GPa. This straight beam was bent in such a way that the two ends meet, to form a circle of mean radius R. Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is ______MPa.

Answer: (99 to 101)

40. Consider a prismatic straight beam of length 𝐿 = 𝜋 m, pinned at the two ends as shown in the figure. The beam has a square cross-section of side p = 6 mm. The Young’s modulus E = 200 GPa, and the coefficient of thermal expansion 𝛼 = 3 × 10⁻⁶ K⁻¹. The minimum temperature rise required to cause Euler buckling of the beam is ______ K.

Answer: (1 to 1)

41. In a UTM experiment, a sample of length 100 mm, was loaded in tension until failure. The failure load was 40 kN. The displacement, measured using the cross-head motion, at failure, was 15 mm. The compliance of the UTM is constant and is given by 5 × 10⁻⁸ m/N. The strain at failure in the sample is ______ %.

Answer: (12 to 14)

42. At a critical point in a component, the state of stress is given as σ_xx = 100 MPa , σ_yy = 220 MPa σ_xy = σ_yx = 80 MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is_____(round off to one decimal place).

Answer: (1.7 to 1.9)

43. A uniform thin disk of mass 1 kg and radius 0.1 m is kept on a surface as shown in the figure. A spring of stiffness 𝑘1 = 400 N/m is connected to the disk center A and another spring of stiffness 𝑘₂ = 100 N/m is connected at point B just above point A on the circumference of the disk. Initially, both the springs are unstretched. Assume pure rolling of the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is ______ rad/s (round off to one decimal place).

Answer: (23.0 to 24.0)

44. A single block brake with a short shoe and torque capacity of 250 N∙m is shown. The cylindrical brake drum rotates anticlockwise at 100 rpm and the coefficient of friction is 0.25. The value of a, in mm (round off to one decimal place), such that the maximum actuating force 𝑃 is 2000 N, is ______.

Answer: (212.0 to 213.0)

45. Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant velocity of 3 m/s. With the assumptions of Newtonian fluid, steady, and fully developed laminar flow with zero pressure gradient in all directions, the momentum equations simplify to

If the dynamic viscosity of the lower fluid, 𝜇₂, is twice that of the upper fluid, 𝜇₁, then the velocity at the interface (round off to two decimal places) is ______m/s.

Answer: (0.98 to 1.02)

46. A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m³. Liquid of density 1000 kg/m³ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is _________mm.

Answer: (80 to 80)

47. Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to 10000 Wm⁻³, while the left and right slabs have no internal heat generation. All slabs have thickness equal to 1 m and thermal conductivity of each slab is equal to 5 Wm⁻¹K⁻¹. The two extreme faces are exposed to fluid with heat transfer coefficient 100 Wm⁻² K⁻¹ and bulk temperature 30°C as shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties are constant. If the left extreme face temperature T₁ is measured to be 100 °C, the right extreme face temperature T₂ is ________°C.

Answer: (60 to 60)

48. If one mole of H2 gas occupies a rigid container with a capacity of 1000 litres and the temperature is raised from 27°C to 37°C, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is _______ Pa. (R=8.314 J/mol∙K)

Answer: (82.14 to 84.14)

49. A steam power cycle with regeneration as shown below on the T-s diagram employs a single open feedwater heater for efficiency improvement. The fluids mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater heater from the turbine is at state 2 as shown in the figure. Process 3-4 occurs in the condenser. The pump work is negligible. The input to the boiler is at state 5. The following information is available from the steam tables:

The mass flow rate of steam bled from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state 1 is_______

Answer: (19 tp 21)

50. A gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when operating at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5, while maintaining the same inlet conditions. Assume air as a perfect gas with specific heat ratio γ = 1.4 . If the specific work output remains the same for both the cases, the isentropic efficiency of the turbine at the pressure ratio of 5 is ________ (round off to two decimal places)

Answer: (0.50 to 0.52)

51. The value of the following definite integral is _______ (round off to three decimal places)

Answer: (2.090 to 2.104)

52. In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are 45° and 10°, respectively. The feed during cylindrical turning is 0.1 mm/rev. The center line average surface roughness (in µm, round off to one decimal place) of the generated surface is ___________

Answer: (3.5 to 3.9)

53. Taylor’s tool life equation is given by VTⁿ = C , where V is in m/min and T is in min. In a turning operation, two tools X and Y are used. For tool X, n = 0.3 and C = 60 and for tool Y, n = 0.6 and C = 90. Both the tools will have the same tool life for the cutting speed (in m/min, round off to one decimal place) of _______

Answer: (38.0 to 42.0)

54. Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. However, each job is assigned to a specific machine in such a way that the total processing time is minimum. The total processing time is ______ minutes.

Answer: (146 to 146)

55. A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:

If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of the activity S without delaying the completion of the project is_____.

Answer: (6 to 6)

GATE Exam 2019 Mathematics (MA) Question Paper With Answer Key

June 7, 2023December 7, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

MATHEMATICS

MATHEMATICS

Q.1 – Q.25 carry one mark each.

1. For a balanced transportation problem with three sources and three destinations where costs, availabilities and demands are all finite and positive, which one of the following statements is FALSE?

(A) The transportation problem does not have unbounded solution

(B) The number of non-basic variables of the transportation problem is 4

(D) The transportation problem has at most 5 basic feasible solutions

Answer: (D)

2. Let f : [a, b]→ ℝ (the set of all real numbers) be any function which is twice differentiable in (a, b) with only one root a in (a, b). Let f’(x) and f’’(x) denote the first and second order derivatives of f(x) with respect to x If a is a simple root and is computed by the Newton-Raphson method, then method converges if

Answer: (A)

3. Let f : ℂ → ℂ (the set of all complex numbers) be defined by

f(x + iy) =x³ + 3xy² + i(y³ + 3x²³y), i = √−i

Let f’(z) denote the derivative of f with respect to z.

Then which one of the following statements is TRUE?

(A) f’(1+ i) exists and |f’(1+i)| = 3√5

(B) f is analytic at the origin

(D)f is differentiable at 1

Answer: (D)

4. The partial differential equation

(A)parabolic in the region x² + y² > 2

(B) hyperbolic in the region x² + y² > 2

(D) hyperbolic in the region x < x² + y² < 2

Answer: (D)

5. If

then which one of the following statements is TRUE?

Answer: (C)

6. Let Γ = {(x, y, z) ∈ ℝ : −1 < x < 1, −1 < y < 1, −1 < z < 1} and ϕ : Γ →ℝ be a function whose all second order partial derivatives exist and are continuous. If ϕ satisfies the Laplace equation ∇²ϕ= 0 for all (x, y, z) ∈Γ, then which one of the following statements is TRUE in Γ?

(ℝ is the set of all real numbers, and ℝ³ = {(x, y, z) : x, y, z ∈ ℝ})

Answer: (C)

7. Let X = {(x₁, x₂ ….) : x₁ ∈ ℝ and only finitely many x_i’s are non-zero} and d : X ×X → ℝ be a metric on X defined by

(ℝ is the set of all real number and ℕ is the set of all natural numbers)

Consider the following statements:

P : (X, d) is a complete metric space.

Q : The set {x ∈ d(0, x) ≤ 1} is compact, where 0 is the zero element of X.

Which of the above statements is/are TRUE?

(A) Both P and Q

(B) P only

(D) Neither P nor Q

Answer: (D)

8. Consider the following statements:

(I) The set ℚ × ℤ is uncountable.

(II) The set {f : f is the function from ℕ to {0, 1}} is uncountable.

(III) The set {√p : p is a prime number} is uncountable.

(IV) For any infinite set, there exists a bijection from the set of one of its proper subsets.

(ℚ is the set of all rational numbers, ℤ is the set of all integers and ℕ is the set of all natural numbers)

Which of the above statements are TRUE?

(A) I and IV only

(B) II and IV only

(D) I, II and IV only

Answer: (B)

9. Let f : ℝ² → ℝ be defined by

f(x, y ) = x⁶ – 2x² – x⁴y + 2y².

(ℝ is the set of all real number and ℝ² = {(x, y) : x, y ∈ ℝ})

Which one of the following statements is TRUE?

(A) f has a local maximum at origin

(B) f has a local minimum at origin

(D) The origin is not a critical point of f

Answer: (C)

10. Let be any sequence of real numbers such that If the radius of convergence of then which one of the following statements is necessarily TRUE?

Answer: (A)

11. Let T₁ be the co-countable topology on ℝ(the set of real numbers) and T₂ be the co-finite topology on ℝ.

Consider the following statements:

(I) In (ℝ, T₁), the sequence converges to 0.

(II) In (ℝ, T₂) the sequence converges to 0.

(III) In (ℝ, T₁), there is no sequence of rational numbers which converges to √3.

(IV) In (ℝ, T₂), there is no sequence of rational numbers which converges to √3.

Which of the above statements are TRUE?

(A) I and II only

(B) II and III only

(D I and IV only

Answer: (B)

12. Let X and Y be normed linear spaces, and let T : X → Y be any bijective linear map with closed graph. Then which one of the following statements is TRUE?

(A) The graph of T is equal to X × Y

(B) T⁻¹ is continuous

(D) T is continuous

Answer: (C)

13. Let g : ℝ² → ℝ² be a function defined by g(x, y) = (e^x cosy, e^x siny) and (a, b) = g(1, π/3).

(ℝ is the set of all real numbers and ℝ²= ({(x, y): x, y ∈ ℝ})

Which one of the following statements is TRUE?

(A) g is injective

(B) If h is the continuous inverse of g, defined in some neighbourhood of (a, b) ∈ ℝ², such that h(a, b)= (1, π/3), then the Jacobian of h at (a, b) is e²

(C) If h is the continuous inverse of g, defined in some neighbourhood of (a, b) ∈ ℝ², such that h(a, b) = (1, π/3), then the Jacobian of h at (a, b) is e⁻²

(D) g is sujective

Answer: (C)

14. Let

(the set of all natural numbers).

Answer: (0 to 0)

15. If the differential equation

is solved using the Euler’s method with step-size h = 0.1, then y(1.2) is equal to______(round off to 2 places of decimal)

Answer: (2.40 to 2.50)

16. Let f be any polynomial function of degrees at most 2 over ℝ (the set of all real numbers). If the constants a and b are such that

then 4a + 3b is equal to _______(round off to 2 places of decimal).

Answer: (-7.5 to -7.5)

17. Let L denote the value of the line integral ∮_C (3x- 4x²y)dx + (4xy² + 2y)dy, where C, a circle of radius 2 with centre at origin of the xy-place, is traversed once in the anti-clockwise direction. Then L/π is equal to ______.

Answer: (31.90 to 32.10)

18. The temperature T : ℝ³\{(0, 0, 0)} → ℝ at any point P(x, y, z) is inversely proportional to the square of the distance of P from the origin. If the value of the temperature T at the point R(0, 0, 1) is √3, then the rate of change of T at the point Q(1, 1, 2) in the direction of is equal to ______(round off to 2 places of decimal).

(ℝ is the set of all real numbers, ℝ³ = {(x, y, z) : x, y, z ∈ ℝ} and ℝ³\{(0, 0, 0)} denotes ℝ³ excluding the origin)

Answer: (0.21 to 0.23)

19. Let f be a continuous function defined on [0, 2] such that f(x) ≥ 0 for all x ∈ [0, 2]. If the area bounded by y = f(x), x = 0, y = 0 and x = b is , where b ∈ (0, 2], then f(1) is equal to _____(round off to 1 place of decimal).

Answer: (0.5 to 0.5)

20. If the characteristic polynomial and minimal polynomial of a square matrix A are (λ – 1) (λ + 1)⁴ (λ −2)⁵ and (λ – 1) (λ + 1) (λ – 2), respectively, then the rank of the matrix A + I is ____, where I is the identity matrix of appropriate order.

Answer: (6 to 6)

21. Let ω be a primitive complex cube root of unity and i = √−1. Then the degree of the field extension ℚ(i, √3, ω) over ℚ (the field of rational numbers) is ______.

Answer: (4 to 4)

22. Let

Then the greatest integer has less than or equal to |α| is ______.

Answer: (2 to 2)

23. Consider the system:

3x₁ + x₂ + 2x₃ – x₄=0

x₁ + x₂ + x₃ – 2x₄ = 3,

x₁, x₂, x₃, x₄ ≥ 0.

If x₁ = 1, x₂ = b, x₃ = 0, x₄ = c is a basic feasible solution of the above system (where a, b and c are real constants), then a + b + c is equal to ______.

Answer: (7 to 7)

24. Let f : ℂ → ℂ be a function defined by f(z) = z⁶ – 5z⁴ + 10. Then the number of zeros of f in {z ∈ ℂ : |z| < 2} is _____.

(ℂ is the set of all complex numbers)

Answer: (4 to 4)

25. Let

be a normed linear space with the norm

Let g : ℓ² → ℂ be the bounded linear functional defined by

Then (sup{|g(x)| : ||x||₂ ≤ 1})² is equal to ______ (round off to 3 places of decimal).

(ℂ is the set of all complex numbers).

Answer: (0.125 to 0.125)

Q.26 – Q.55 Carry two marks each.

26. For the linear programming problem (LPP):

Maximize Z = 2x₁ + 4x₂

subject to – x₁ + 2x₂ ≤ 4,

3x₁ + βx₂ ≤ 6,

x₁, x₂ ≥ 0, β ∈ ℝ,

(ℝ is the set of all real numbers)

consider the following statements:

(I) The LPP always has a finite optimal value for any β ≥ 0.

(II) The dual of the LPP may be infeasible for some β ≥ 0.

(III) If for some β, the point (1, 2) is feasible to the dual of the LPP, then Z ≤ 16, for any feasible solution (x₁, x₂) of the LPP.

(IV) If for some β, x₁ and x₂ are the basic variables in the optimal table of the LPP with x₁ = ½, then the optimal value of dual of the LPP is 10.

Then which of the above statements are TRUE?

(A) I and III only

(B) I, III and IV only

(D) II and IV only

Answer: (B)

27. Let f : ℝ² → ℝ² be defined by

Consider the following statements:

(I) The partial derivatives ∂f/∂x, ∂f/∂y exist at (0, 0) but are unbounded in any neighbourhood of (0, 0).

(II) f is continuous but not differentiable at (0, 0).

(III) f is not continuous at (0, 0).

(IV) f is differentiable at (0, 0).

(ℝ is the set of all real numbers and ℝ² = {(x, y): x, y ∈ ℝ})

Which of the above statements is/are TRUE?

(A) I and II only

(B) I and IV only

(D) III only

Answer: (B)

28. Let be an infinite matrix cover ℂ (the set of all complex numbers) such that (i) for each i ∈ ℕ (the set of all natural numbers), the ith row( k_{i, 1}, k_{i, 2}…..) of K is in ℓ^∞ and (ii) for every is summable for all i ∈ ℕ, and (y₁, y₂ …) ∈ ℓ¹, where

Let the set of all rows of K be denoted by E. Consider the following statements:

P: E is bounded set in ℓ^∞

Q: E is dense set in ℓ^∞.

Which of the above statements is/are TRUE?

(A) Both P and Q

(B) P only

(D) Neither P nor Q

Answer: (B)

29. Consider the following heat conduction problem for a finite rod

with the boundary conditions u(0, t) = −t², u(π, t) = −πe^t – t², t > 0 and the initial condition u(x, 0) = sin x – sin³ x – x, 0 ≤ x ≤ π. If v(x, t) = u(x, t) + xe^t+ t², then which one of the following is CORRECT?

Answer: (A)

30. Let f : ℂ → ℂ be non-zero and analytic at all points in ℤ.

If F(z) = π f(z) cot(πz) for z ∈ℂ\ℤ, then the residue of F at n ∈ ℤ is ______.

(ℂ is the set of all complex numbers, ℤ is the set of all integers and ℂ\ℤ denotes the set of all complex numbers excluding integers)

(A) π f(n)

(B) f(n)

(D) (df/dz)_{z = N}

Answer: (B)

31. Let the general integral of the partial differential equation

be given by F(u v) = 0, where F: ℝ² → ℝ is the continuously differentiable function.

(ℝ is the set of all real numbers and ℝ² = {(x, y): x, y ∈ ℝ})

Then which one of the following is TRUE?

(A) u = x² + y² + z, v = xz + y

(B) u = x² + y² – z, v = xz – y

(D) u = x² + y² – z, v = yz – x

Answer: (A)

32. Consider the following statements:

(I) If ℚ denotes the additive group of rational numbers and f: ℚ → ℚ is a non-trivial homomorphism, then f is an isomorphism.

(II) Any quotient group of a cyclic group is cyclic.

(III) If every subgroup of a group G is a normal subgroup, then G is abelian.

(IV) Every group of order 33 is cyclic.

Which of the above statements are TRUE?

(A) II and IV only

(B) II and III only

(D) I, III and IV only

Answer: (C)

33. A solution of the Dirichlet problem

∇²u(r, θ) = 0, 0<r<1, −π≤θ≤π

u(1, θ) =|θ|, −π≤θ≤π,

is given by

Answer: (C)

34. Consider the subspace Y = {(x, x) : x ∈ ℂ} of the normed linear space (ℂ², || ||_∞).

If ϕ is a bounded linear functional on Y, defined by ϕ(x, x) = x, then which one of the following sets is equal to

{Ψ(1, 0): Ψ is a norm preserving extension of ϕ to(ℂ², || ||_∞)}.

(ℂ is the set of all complex numbers, ℂ² = {(x, y) : x, y ∈ ℂ} and ||(x₁, x₂)||_∞ = sup{|x₁|, |x₂|})

(A) {1}

(B) [1/2, 3/2]

(D)[0, 1]

Answer: (D)

35. Consider the following statements:

(I) The ring ℤ[√−1] is a unique factorization domain.

(II) The ring ℤ[√−5] is a principal ideal domain.

(III) In the polynomial ring ℤ₂[x], the ideal generated by x³ + x + 1 is a maximal ideal.

(IV) In the polynomial ring ℤ₃[x], the ideal generated by x⁶ + 1 is a prime ideal.

(ℤ denotes the set of all integers, ℤ_n denotes the set of all integers modulo, n, for any positive integer n)

Which of the above statements are TRUE?

(A) I, II and III only

(B) I and III only

(D) II and III only

Answer: (B)

36. Let M be a 3 × 3 real symmetric matrix with eigenvalues 0, 2 and a with the respective eigenvectors u = (4, b, c)^T, v =(−1, 2, 0)^T and w = (1, 1, 1)^T.

Consider the following statements.

(I) a + b – c = 10.

(II) The vector x = (0, 3/2, ½)^T satisfies Mx = v + w.

(III) For any d ∈ span{u, v, w}, Mx= d has a solution.

(IV) The trace of the matrix M² + 2M is 8.

(y^T denotes the transpose of the vector y)

Which of the above statements are TRUE?

(A) I, II and III only

(B) I and II only

(D) III and IV only

Answer: (B)

37. Consider the region

in the complex plane. The transformation x + iy → e^x+iy maps the region Ω onto the region S ⊂ ℂ (the set of all complex numbers). Then the area of the region S is equal to

(A) π/3(e⁴ − e⁻²)

(B) π/4(e⁴ + e⁻²)

(D) π/6(e⁴ − e⁻²)

Answer: (A)

38. Consider the sequence of functions, where is the derivative of g_n(x) with respect to x.

(ℝ is the set of all real numbers, ℕ is the set of all natural numbers.)

Answer: (D)

39. Consider the boundary value problem (BVP)

with the boundary conditions y(0) = 0, y(π) = k (k is a non-zero real number).

Then which one of the following statements is TRUE?

(A) For α = 1, the BVP has infinitely many solutions

(B) For α =1, the BVP has a unique solution

(D)For α = −1, k = 0, the BVP has a solution y(x) such that y(x) > 0 for all x ∈(0, π

Answer: (D)

40. Consider the ordered square I₀², the set [0, 1] × [0, 1] with the dictionary order topology. Let the general element of I₀² be denoted by x × y, where x, y ∈[0, 1]. Then the closure of the subset is

(A) S ⋃ ((a, b] ×{0}) ⋃([a, b) × {1})

(B) S ⋃ ([a, b] ×{0}) ⋃((a, ]) × {1})

(D) S ⋃ ((a, b] ×{0})

Answer: (A)

41. Let P₂ be the vector space of all polynomials of degree at most 2 over ℝ (the set of real numbers). Let a linear transformation T : P₂ → P₂ be defined by

T(a + bx + cx²) = (a + b) + (b – c)x + (a + c)x².

Consider the following statements:

(I) The null space of T is {α(−1 + x +x²) : α ∈ ℝ}.

(II) The range space of T is spanned by the set {1 + x², 1 + x}.

(III) T(T(1 + x) = 1 + x².

(IV) If M is the matrix representation of T with respect of the standard basis {1, x, x²} of P₂ then the trace of the matrix M is 3.

Which of the above statements are TRUE?

(A) I and II only

(B) I, III and IV only

(D) II and IV only

Answer: (C)

42. Let T₁ and T₂ be two topologies defined on ℕ (The set of all natural numbers), where T₁ is the topology generated byB = {{2n – 1, 2n} : n ∈ ℕ} and T₂ is the discrete topology on ℕ.

Consider the statements:

(I) In (ℕ, T₁), every infinite subset has a limit point.

(II) The function f : (ℕ, T₁) → (ℕ, T₂) define by

is a continuous function.

Which of the above statements is/are TRUE?

(A) Both I and II

(B) I only

(D) Neither I nor II

Answer: (A)

43. Let 1 ≤ p < q < ∞. Consider the following statements:

(I) ℓ^p ⊂ ℓ^q

(II) L^p[0, 1] ⊂ L^q[0,1],

(ℝ is the set of all real numbers

Which of the above statements is/are TRUE?

(A) Both I and II

(B) I only

(D) Neither I nor II

Answer: (B)

44. Consider the differential equation

If Y(s) is the Laplace transform of y(t), then the value of Y(1) s _____(round off to 2 places of decimal).

(Here, t he inverse trigonometric functions assume principal values only)

Answer: (0.76 to 0.83)

45. Let R be the region in the xy-place bounded by the curves y = x², y = 4x², xy = 1 and xy = 5.

Then the value of integral is equal to _______

Answer: (12 to 12)

46. Let V be the vector space of all 3 × 3 matrices with complex entries over the real field. If

then the dimension of W₁ + W₂ is equal to _____.

Answer: (17 to 17)

47. The number of elements of order 15 in the additive group ℤ₆₀ × ℤ₅₀ is ______

(ℤ_n denotes the group of integers modulo n, under the operation of addition modulo n, for any positive integer n)

Answer: (48 to 48)

48. Consider the following cost matrix of assigning four jobs to f our persons:

Then the minimum cost of the assignment problem subject to the constraint that job J₄ is assigned to person P₂, is _____.

Answer: (27 to 27)

49. Let y : [−1, 1] → ℝ with y(1) = 1 satisfy the Legendre differential equation

Then the value of is equal to _______(round off to 2 places of decimal).

Answer: (0.25 to 0.30)

50. Let ℤ₁₂₅ be the ring of integers modulo 125 under the operations of addition modulo 125 and multiplication modulo 125. If m is the number of maximal ideals of ℤ₁₂₅ and n is the number of non-units of ℤ₁₂₅, then m + n is equal to ______.

Answer: (26 to 26)

51. The maximum value of the error term of the composite Trapezoidal rule when it is used to evaluate the definite integral

with 12 sub-intervals of equal length, is equal to ______ (round off to 3 places of decimal).

Answer: (0.022 to 0.028)

52. By the Simplex method, the optimal table of the linear programming problem:

where α, β, γ are real, constants, is

Then the value of α + β + γ is ______

Answer: (14.0 to 16.0 OR 17.0 to 18.5)

53. Consider the inner product space P₂ of all polynomials of degree at most 2 over the field of real numbers with the inner product

Let {f₀, f₁, f₂) be an orthogonal set in P₂, where f₀ = 1, f₁ = t +c₁, f₂ = t² + c₂f₁ +c₃ and c₁, c₂, c₃ are real constants. Then the value of 2c₁ + c₂+ 3c₃ is equal to _____.

Answer: (-3 to -3)

54. Consider the system of linear differential equations

with the initial conditions x₁(0) = 0, x₂(0) = 1.

The log_e(x₂(2) – x₁(2)) is equal to

Answer: (1.95 to 2.05)

55. Consider the differential equation

The sum of the roots of the indicial equation of the Frobenius series solution for the above differential equation in a neighbourhood of x = 0 is equal to ____.

Answer: (10 to 10)

GATE Exam 2019 Instrumentation Engineering (IN) Question Paper With Answer Key

June 7, 2023December 5, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Instrumentation Engineering

Q.1 – Q. 25 carry one mark each.

1. are three orthogonal vectors. Given that the vector is parallel to

Answer: (C)

2. The vector function where u(x, y) is a scalar function. Then is

(A) -1

(B) 0

(D) ∞

Answer: (B)

3. A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is

(A) 4/15

(B) 7/16

(D) 8/15

Answer: (A)

4. In the Figures (a) and (b) shown below, the transformers are identical and ideal, except that the transformer in Figure (b) is centre-tapped. Assuming ideal diodes, the ratio of the root- mean-square (RMS) voltage across the resistor 𝑅 in Figure (a) to that in Figure (b) is

(A) √2:1

(B) 2:1

(D) 4:1

Answer: (B)

5. The y(t) of a system is related to its input x(t) as

where, x(t) = 0 and y(t) = 0 for t ≤ 0. The transfer function of the system is

Answer: (C)

6. The input 𝑥[𝑛] and output 𝑦[𝑛] of a discrete-time system are related as y[n] = αy[n − 1] + x[n]. The condition on 𝛼 for which the system is Bounded-Input Bounded-Output (BIBO) stable is

(A) |α| < 1

(B) |α| = 1

(D) |α| < 3/2

Answer: (A)

7. In a cascade control system, the closed loop transfer function of the inner loop may be assumed to have a single time-constant τ₁ . Similarly, the closed loop transfer function of the outer loop may be assumed to have a single time-constant 𝜏₂. The desired relationship between τ₁ and τ₂ in a well-designed control system is

(A) τ₁ is much less than τ₂

(B) τ₁ is equal to τ₂

(D) τ₁ is independent of τ₂

Answer: (A)

8. The loop-gain function L(s) of a control system with unity feedback is given to be where k > 0 . If the gain cross-over frequency of the loop-gain function is less than its phase cross-over frequency, the closed-loop system is

(A) unstable

(B) marginally stable

(D) stable

Answer: (D)

9. If each of the values of inductance, capacitance and resistance of a series LCR circuit are doubled, the Q-factor of the circuit would

(A) reduce by a factor √2

(B) reduce by a factor √2

(D) increase by a factor √2

Answer: (B)

10. In the circuit shown below, the input voltage V_in is positive. The current (I) – voltage (V) characteristics of the diode can be assumed to be I = I₀e^V^/^VT under the forward bias condition, where VT is the thermal voltage and I₀ is the reverse saturation current. Assuming an ideal op-amp, the output voltage V_out of the circuit is proportional to

Answer: (C)

11. The correct biasing conditions for typical operation of light emitting diodes, photodiodes, Zener diodes are, respectively

(A) forward bias, reverse bias, reverse bias

(B) reverse bias, reverse bias, forward bias

(D) reverse bias, forward bias, reverse bias

Answer: (A)

12. The circuit shown in the figure below uses ideal positive edge-triggered synchronous J-K flip flops with outputs X and Y. If the initial state of the output is X=0 and Y=0 just before the arrival of the first clock pulse, the state of the output just before the arrival of the second clock pulse is

(A) X=0, Y=0

(B) X=0, Y=1

(D) X=1, Y=1

Answer: (D)

13. Thermocouples measure temperature based on

(A) Photoelectric effect

(B) Seebeck effect

(D) Thermal expansion

Answer: (B)

14. Four strain gauges in a Wheatstone bridge configuration are connected to an instrumentation amplifier as shown in the figure. From the choices given below, the preferred value for the common mode rejection ratio (CMRR) of the amplifier, in dB, would be

(A) -20

(B) 0

(D) 100

Answer: (D)

15. In a single-mode optical fiber, the zero-dispersion wavelength refers to the wavelength at which the

(A) material dispersion is zero.

(B) waveguide dispersion is zero.

(D) material dispersion and waveguide dispersion are simultaneously zero.

Answer: (C)

16. A 3 × 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is ________.

Answer: (10 to 10)

17. In the circuit shown below, maximum power is transferred to the load resistance RL , when R_L = _________Ω.

Answer: (5 to 5)

18. Consider a circuit comprising only resistors with constant resistance and ideal independent DC voltage sources. If all the resistances are scaled down by a factor 10, and all source voltages are scaled up by a factor 10, the power dissipated in the circuit scales up by a factor of ________.

Answer: (1000 to 1000)

19. In the circuit shown below, initially the switch S1 is open, the capacitor C1 has a charge of 6 coulomb, and the capacitor C2 has 0 coulomb. After S1 is closed, the charge on C2 in steady state is ________coulomb.

Answer: (4 to 4)

20. An 8-bit weighted resistor digital-to-analog converter (DAC) has the smallest resistance of 500 Ω. The largest resistance has a value ________k Ω.

Answer: (64 to 64)

21. The total number of Boolean functions with distinct truth-tables that can be defined over 3 Boolean variables is_________.

Answer: (256 to 256)

22. The figure below shows the 𝑖𝑡ℎ full-adder block of a binary adder circuit. C_i is the input carry and C_i+1 is the output carry of the circuit. Assume that each logic gate has a delay of 2 nanosecond, with no additional time delay due to the interconnecting wires. If the inputs A_i , B_i are available and stable throughout the carry propagation, the maximum time taken for an input C_i to produce a steady-state output C_i+1 is _____ nanosecond.

Answer: (4 to 4)

23. The resistance of a resistor is measured using a voltmeter and an ammeter. The voltage measurements have a mean value of 1V and standard deviation of 0.12 V while current measurements have a mean value of 1 mA with standard deviation of 0.05 mA. Assuming that the errors in voltage and current measurements are independent, the standard deviation of the calculated resistance value is___________Ω.

Answer: (130 to 130)

24. A pitot-static tube is used to estimate the velocity of an incompressible fluid of density 1 kg/m³. If the pressure difference measured by the tube is 200 N/m², the velocity of the fluid, assuming the pitot-tube coefficient to be 1.0, is _______m/s.

Answer: (20 to 20)

25. A signal cos(2π f_mt) modulates a carrier cos(2π f_ct) using the double-sideband-with-carrier (DSBWC) scheme to yield a modulated signal cos(2 πf_ct) + 0.3cos(2π f_mt) cos(2π f_ct) . The modulation index is _________. (Answer should be rounded off to one decimal place)

Answer: (0.3 to 0.3)

Q.26 – Q. 55 carry two marks each.

26. The curve y = f(x) is such that the tangent to the curve at every point (𝑥, 𝑦) has a 𝑌-axis intercept 𝑐, given by C = −Y. Then, f (x) is proportional to

(A) x⁻¹

(B) x²

(D) x⁴

Answer: (B)

27. The function 𝑝(𝑥) is given by 𝑝(𝑥) = 𝐴/𝑥^𝜇 where 𝐴 and 𝜇 are constants with 𝜇 > 1 and 1 ≤ x < ∞ and 𝑝(𝑥) = 0 for −∞ < 𝑥 < 1. For 𝑝(𝑥) to be a probability density function, the value of 𝐴 should be equal to

(A) 𝜇− 1

(B) 𝜇 + 1

(D) 1/(𝜇 + 1)

Answer: (A)

28. The dynamics of the state of a system is governed by the differential equation

Given that the initial state is the steady state value of is

29. A complex function f(z) = u(x, y) + iv(x, y) and its complex conjugate f*(z) = u (x, y) – iv(x, y) are both analytic in the entire complex plane, where z = x + i y and i = √−1. The function f is then given by

(A) 𝑓(𝑧) = 𝑥 + 𝑖 𝑦

(B) 𝑓(𝑧) = 𝑥² − 𝑦² + 𝑖 2𝑥𝑦

(D) 𝑓(𝑧) = 𝑥² + 𝑦²

Answer: (D)

30. In a control system with unity gain feedback, the plant has the transfer function P(s)= 3/s . Assuming that a controller of the form C(s) = K/ (s + p) is used, where 𝐾 is a positive constant, the value of p for which the root-locus of the closed-loop system passes through the points −3 ±j3√3 where j=√−1 , is

(A) 3

(B) 3√3

(D) 9

Answer: (C)

31. The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d (t) is given by d(t) = 0.1sin(ωt) where ω = 5 rad s , the steady-state amplitude of the output y(t) is

(A) 1.00 × 10⁻³

(B) 2.50 × 10⁻³

(D) 10.00 × 10⁻³

Answer: (A)

32. In the control system shown in the figure below, a reference signal r(t) = t² is applied at time 𝑡 = 0. The control system employs a PID controller C(s) = K_P + K_I/s + K_Ds and the plant has a transfer function P(s) = 3/s. If K_P = 10, K_I = 1 and K_D = 2, the steady state value of e is

(A) 0

(B) 2/3

(D) ∞

Answer: (B)

33. A voltage amplifier is constructed using enhancement mode MOSFETs labeled M1, M2, M3 and M4 in the figure below. M1, M2 and M4 are n-channel MOSFETs and M3 is a p-channel MOSFET. All MOSFETs operate in saturation mode and channel length modulation can be ignored. The low frequency, small signal input and output voltages are 𝑣_𝑖𝑛 and 𝑣𝑜𝑢𝑡respectively and the dc power supply voltage is V_DD . All n-channel MOSFETs have identical transconductance 𝑔_𝑚𝑛 while the p-channel MOSFET has transconductance 𝑔_𝑚𝑝. The expressions for the low frequency small signal voltage gain 𝑣_𝑜𝑢𝑡/𝑣_𝑖𝑛 is

(A) − g_mn/g_mp

(B) –g_mn(g_mn + g_mp)⁻¹

(D) g_mn(g_mn + g_mp)⁻¹

Answer: (C)

34. In the circuit shown below, assume that the comparators are ideal and all components have zero propagation delay. In one period of the input signal 𝑉_𝑖𝑛 = 6 sin(𝜔𝑡), the fraction of the time for which the output OUT is in logic state HIGH is

(A) 1/12

(B) 1/2

(D) 5/6

Answer: (D)

35. 𝑋 = 𝑋₁𝑋₀ and 𝑌 = 𝑌₁𝑌₀ are 2-bit binary numbers. The Boolean function 𝑆 that satisfies the condition “If 𝑋 > 𝑌, then 𝑆 = 1”, in its minimized form, is

Answer: (B)

36. In the circuit below, the light dependent resistor (LDR) receives light from the LED. The LDR has resistances of 5 kΩ and 500Ω under dark and illuminated conditions, respectively. The LED is OFF at time 𝑡 < 0. At time t = 0 s, the switch S₁ is closed for 1 ms and then kept open thereafter. Assuming zero propagation delay in the devices, the LED

(A) turns ON when S₁ is closed and remains ON after S₁ is opened

(B) turns ON when S₁ is closed and turns OFF after S₁ is opened

(D) remains OFF when S₁ is closed and continues to remain OFF after S1 is opened

Answer: (A)

37. A differential capacitive sensor with a distance between the extreme plates 100 mm is shown in figure below. The difference voltage ∆𝑉 = 𝑉₁ − 𝑉₂, where 𝑉₁ and 𝑉₂ are the rms values, for a downward displacement of 10 mm of the intermediate plate from the central position, in volts, is

(A) 0.9

(B) 1.0

(D) 2

Answer: (D)

38. A piezoelectric transducer with sensitivity of 30 mV/kPa is intended to be used in the range of 0 kPa to 100 kPa. The readout circuit has a peak noise amplitude of 0.3 mV and measured signals over the full pressure range are encoded with 10 bits. The smallest pressure that produces a non-zero output, in units of Pa, is approximately

(A) 10

(B) 100

(D) 300

Answer: (B)

39. A 100 W light source emits uniformly in all directions. A photodetector having a circular active area whose diameter is 2 cm is placed 1 m away from the source, normal to the incident light. If the responsivity of the photodetector is 0.4 A/W, the photo-current generated in the detector, in units of mA, is

(A) 1

(B) 4

(D) 400

Answer: (A)

40. A resistance-meter has five measurement range-settings between 200Ω and 2 MΩ in multiples of 10. The meter measures resistance of a device by measuring a full-range voltage of 2 V across the device by passing an appropriate constant current for each range-setting. If a device having a resistance value in the range 8 kΩ to 12 kΩ and a maximum power rating of 100 µW is to be measured safely with this meter, the choice for range-setting on the meter for best resolution in measurement, in kΩ, is

(A) 2

(B) 20

(D) 2000

Answer: (C)

41. A pulsed laser emits rectangular pulses of width 1 nanosecond at a repetition rate of 1 kHz. If the average power output is 1 mW, the average power over a single pulse duration, in watts, is

(A) 1

(B) 10

(D) 1000

Answer: (D)

42. Four identical resistive strain gauges with gauge factor of 2.0 are used in a Wheatstone bridge as shown in the figure below. Only one of the strain gauges R_SENSE changes its resistance due to strain. If the output voltage V_OUT is measured to be 1 mV, the magnitude of strain, in units of microstrain, is

(A) 1

(B) 10

(D) 1000

Answer: (D)

43. The frequency response of a digital filter 𝐻(𝜔) has the following characteristics

Passband: 0.95 ≤ |H(ω)| ≤ 1.05 for 0 ≤ ω ≤ 0.3π and

Stopband: 0 ≤ |H(ω)| ≤ 0.005 for 0.4π ≤ ω ≤ π.

where ω is the normalized angular frequency in rad/sample. If the analog upper cut off frequency for the passband of the above digital filter is to be 1.2 kHz, then the samplingfrequency should be _______kHz.

Answer: (8.0 to 8.0)

44. In the circuit shown below, a step input voltage of magnitude 5 V is applied at node A at time t = 0. If the capacitor has no charge for t ≤ 0 , the voltage at node P at 𝑡 = 6μs is _______ V. (Answer should be rounded off to two decimal places)

Answer: (1.87 to 1.91)

45. In the circuit shown below, the angular frequency 𝜔 at which the current is in phase with the voltage is _______ rad/s.

Answer: (20000 to 20000)

46. The transfer function relating the input x(t) to the output y(t) of a system is given by G(s) = 1/ (s + 3) . A unit-step input is applied to the system at time t = 0 . Assuming that 𝑦(0) = 3, the value of 𝑦(𝑡) at time 𝑡 = 1 is _________ (Answer should be rounded off to two decimal places)

Answer: (0.46 to 0.48)

47. The output of a continuous-time system 𝑦(𝑡) is related to its input 𝑥(𝑡) as If the Fourier transforms of 𝑥(𝑡) and 𝑦(𝑡) are 𝑋(𝜔) and 𝑌(𝜔) respectively, and |𝑋(0)|² = 4, the value of |𝑌(0)|² is ________.

Answer: (9 to 9)

48. A discrete-time signal is down-sampled to the signal x_d[n] such that x_d[n] = x[4n]. The fundamental period of the down-sampled signal xd[n] is____________.

Answer: (6 to 6)

49. In a control system with unity gain feedback, the transfer function of the loop-gain function is L(s) = 9e^−0.1s/s. The phase margin of the loop-gain function L(s) is _________ degree.

Answer: (37 to 39)

50. In the circuit shown below, all transistors are n-channel enhancement mode MOSFETs. They are identical and are biased to operate in saturation mode. Ignoring channel length modulation, the output voltage V_out is _________ V.

Answer: (4 to 4)

51. In the circuit shown below, all OPAMPS are ideal. The current 𝐼 = 0 A when the resistance R = __________kΩ.

Answer: (9.0 to 9.1)

52. The parallel resistance-capacitance bridge shown below has a standard capacitance value of C₁=0.1µF and a resistance value of R₃=10 kΩ. The bridge is balanced at a supply frequency of 100 Hz for R₁=375 kΩ, R₃=10 kΩ and R₄=14.7 kΩ. The value of the dissipation factor 𝐷 = 1/(𝜔𝑅𝑝𝐶𝑝) of the parallel combination of 𝐶_𝑝 and 𝑅_𝑝 is_______.(Answer should be rounded off to THREE decimal places).

Answer: (0.035 to 0.045)

53. In a microprocessor with a 16 bit address bus, the most significant address lines A15 to A12 are used to select a 4096 word memory unit, while lines A0 to A11 are used to address a particular word in the memory unit. If the 3 least significant lines of the address bus A0 to A2 are short-circuited to ground, the addressable number of words in the memory unit is________.

Answer: (512 to 512)

54. A signal x(t) has a bandwidth 2𝐵 about a carrier frequency of f_c = 2 GHz as shown in Figure (a) below. In order to demodulate this signal, it is first mixed (multiplied) with a local oscillator of frequency f_LO = 1.5 GHz, and then passed through an ideal low-pass filter (LPF) with a cut-off frequency of 2.8 GHz. The output of the LPF is sent to a digitizer ADC with a sampling rate of 1.6 GHz as shown in Figure (b) below. The maximum value of B so that the signal x(t) can be reconstructed from its samples according to the Nyquist sampling theorem is _______ MHz.

Answer: (300 to 300)

55. Consider a Michelson interferometer as shown in the figure below. When the wavelength of the laser light source is switched from 400 nanometer to 500 nanometer, it is observed that the intensity measured at the output port P goes from a minimum to a maximum. This observation is possible when the smallest path difference between the two arms of the interferometer is ______ nanometer.

Answer: (500 to 500 OR 1000 to 1000)

GATE Exam 2019 Geology and Geophysics (GG) Question Paper With Answer Key

June 7, 2023December 5, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Geology & Geography

PART A: COMPULSORY SECTION FOR ALL CANDIDATES

Q.1 – Q. 25 carry one mark each.

1. On the present-day global plate tectonic map, the Reunion hotspot is located in the ______.

(a) Indian Plate

(B) Australian Plate

(D) Antarctic Plate

Answer: (C)

2. Which one of the following statements about the planetary motion of the Solar system is INCORRECT?

(A) The orbital-radius of planets sweep out equal areas in equal intervals of time.

(B) The orbital speed of planets is constant throughout their respective orbits.

(D) At least one focus of the elliptical orbit of each planet lies at the same point.

Answer: (B)

3. Choose the CORRECT combination for the following two statements

Statement-I: The correct order of magnetic chrons from the oldest to the youngest is Gilbert-Gauss-Matuyama-and Bruhnes.

Statement -II: Magnetic chrons Gilbert and Matuyama are reverse whereas Gauss and Bruhnes are normal.

(A) Both statements I and II are correct.

(B) Both statements I and II are incorrect.

(D) Statement I is incorrect and statement II is correct.

Answer: (A)

4. Body waves ______.

(A) can travel through vacuum

(B) have cylindrical wavefronts

(D) are known as ground roll

Answer: (C)

5. The acceleration due to gravity (g) begins to fall sharply towards the centre of the Earth from the discontinuity.

(A) Conrad

(B) Mohorovicic

(D) Lehmann

Answer: (C)

6. Which one of the following lists ONLY kinematic parameters?

(A) Force, translation, rotation.

(B) Translation, rotation, distortion.

(D) Force, stress, strain.

Answer: (B)

7. The plunge of the normal to the axial planes of vertical and upright folds is ______.

(A) 0°

(B) 45°

(D) 90°

Answer: (A)

8. Which one of the following rocks is associated with metamorphic thermal aureoles?

(A) Chlorite schist

(B) Amphibolite

(D) Glaucophane schist

Answer: (C)

9. Which one of the following clay minerals contain potassium (K)?

(A) Illite

(B) Kaolinite

(D) Vermiculite

Answer: (A)

10. Which one of the following sequences of minerals CORRECTLY list an increasing rate of dissolution during chemical weathering?

(A) Olivine-Quartz-Pyroxene-Orthoclase

(B) Quartz-Orthoclase-Pyroxene-Olivine

(D) Quartz-Olivine-Orthoclase-Pyroxene

Answer: (B)

11. Which one of the following combination of reservoir and cap rock respectively, is suitable for oil accumulation?

(A) Limestone-Sandstone

(B) Dolomite-Evaporite

(D) Shale-Limestone

Answer: (B)

12. Bituminous coal is found in_________ .

(A) Neyveli

(B) Panandhro

(D) Vastan

Answer: (C)

13. Extinction of Trilobites is associated with which one of the following geological time boundaries?

(A) Ordovician-Silurian

(B) Permian-Triassic

(D) Cretaceous-Palaeogene

Answer: (B)

14. Transmissivity of an aquifer is the product of______ .

(A) saturated thickness and storitivity

(B) hydraulic conductivity and storitivity

(D) saturated thickness and hydraulic head

Answer: (C)

15. Which one of the following is only a correction and not a reduction in the computation of gravity anomalies with respect to a datum?

(A) Free air

(B) Bouguer

(D) Isostatic

Answer: (C)

16. The difference in the mobility of ions in the electrolyte and electrons in metallic conductors in the sub-surface due to applied external electric field gives rise to______ .

(A) electrode polarization

(B) membrane polarization

(D) electro-chemical potential

Answer: (A)

17. A high frequency acoustic wave propagating in a gas saturated sandstone formation exhibits an increase in .

(A) frequency

(B) velocity

(D) wave number

Answer: (C)

18. Which one of the following logging methods uses a radioactive source in the sonde?

(A) Natural Gamma ray

(B) Gamma-Gamma

(D) Nuclear Magnetic Resonance (NMR)

Answer: (B)

19. Isodynamic contours of the geomagnetic field represent lines of equal___________.

(A) inclination

(B) declination

(D) magnetic potential

Answer: (C)

20. A Very Low Frequency (VLF) electromagnetic survey is conducted for the delineation of 2-D conducting mineralization located at 50 m depth from the surface with different geological formations as the overburden layer. For which of the following geological overburden layers given below, will the VLF method fail to yield response?

(A) Granite

(B) Snow

(D) Saline water saturated sand

Answer: (D)

21. Assuming Airy isostatic compensation, the depth to the Moho from a point located 2 km above the mean sea level is ________ km. (round off to 1 decimal place).

Answer: (40.3 to 40.6)

(The depth of compensation T for the crust at mean sea level is 30 km, the density of crust and upper mantle are 2.67 gm/cc and 3.30 gm/cc, respectively).

22. On Survey of India Toposheet number

+ the distance between two points is 18 cm. The actual ground distance between these two points is ________km.

Answer: (9 to 9)

23. For a dam site investigation, drilling was carried out up to a depth of 20 m. The total length of recovered core pieces, each over 100 mm, _____add up to 16 m. The Rock Quality. Designation (RQD) of the foundation rock mass is ______%.

Answer: (80 to 80)

24. Given that of a sample whose (round off to 1 decimal place).

Answer: (2055.1 to 2055.5)

25. The shear wave velocity in an igneous rock with a density of 2.7 gm/cc and rigidity

modulus of 24.3 GPa is _________ km/s. (round off to 1 decimal place).

Answer: (2.9 to 3.1)

PART B (SECTION 1): FOR GEOLOGY CANDIDATES ONLY

Q.26 – Q. 55 carry two marks each.

26. Stream power is the product of specific weight of water with .

(A) hydraulic radius and Manning roughness coefficient

(B) wetted perimeter and slope

(D) discharge and Manning roughness coefficient

Answer: (C)

27. Match the landforms given in Group I to the causative process in Group II

(A) P-2; Q-3; R-1; S-4

(B) P-1; Q-2; R-4; S-3

(D) P-2; Q-1; R-4; S-3

Answer: (D)

28. In a thrust fault exhibiting ramp and flat geometry which one of the following pairs defines a Flat?

(A) I

(B) II
(C) III

(D) IV

Answer: (D)

29. In the given diagram, which one of the combinations CORRECTLY lists structures typically developed at I, II, III, IV?

(A) I-pressure ridge, II-thrust, III-horst, IV-pull-apart basin

(B) I- pull-apart basin, II-thrust, III-horst, IV-pressure ridge

(D) I- pull-apart basin, II- pressure ridge, III-horst, IV-thrust

Answer: (C)

30. The best developed lineation and foliation traces in a L-S tectonite will be observed on a plane .

(A) parallel to the lineation and foliation

(B) perpendicular to the lineation and foliation

(D) perpendicular to the lineation but parallel to the foliation

Answer: (C)

31. Match the type of twinning (Group I) with the mineral (Group II) that best exhibits it

(A) P-3, Q-4, R-2, S-1

(B) P-2, Q-4, R-1, S-3

(D) P-2, Q-1, R-3, S-4

Answer: (A)

32. On inserting a first order red interference filter in SE-NW direction, the interference figure of quartz shows

(A) blue in NE, SW quadrants and yellow in NW, SE quadrants.

(B) yellow in NE, SW quadrants and blue in NW, SE quadrants.

(D) yellow in NE, NW quadrants and blue in SW, SE quadrants.

Answer: (A OR B)

33. Choose the CORRECT combination for the following two statements.

Statement I: Four elements that make up about 90% of the bulk Earth are Fe, O, Si and Mg (in decreasing order of wt % abundance).

Statement II: The four most abundant elements in the Earth’s crust (in decreasing order of wt % abundance) are O, Si, Al and Fe.

(A) Both Statements I and II are correct.

(B) Both Statements I and II are incorrect.

(D) Statement I is incorrect and Statement II is correct.

Answer: (A)

34. Choose the CORRECT combination for the following four statements.

Statement I: Anhydrous partial melting of peridotites produces basaltic magma. Statement II: Hydrous melting of peridotites produces andesitic magma.

Statement III: Congruent melting of minerals produces liquids of compositions identical to the minerals.

Statement IV: Incongruent melting of minerals produces liquids of different compositions and new solids.

(A) All the four statements I to IV are correct.

(B) Statements I, II and III are correct but statement IV is incorrect.

(D) All the four statements I to IV are incorrect.

Answer: (A)

35. The value of salinity, in terms of wt.% NaCl equivalent, of an aqueous saline bi-phase liquid-vapour fluid inclusions is determined by measurement of ________during microthermometry.

(A) last ice-melting temperature

(B) dissolution temperature of halite

(D) homogenization temperature

Answer: (A)

36. Which of the following case (s) represent (s) textural inversion in sandstone? Case I: Rounded grains in clayey matrix.

Case II: Rounded, but poorly sorted grains.

(A) Only case I.

(B) Only case II.

(D) Neither case I nor case II.

Answer: (C)

37. Which of the following set of statements regarding the overall nature of marine shelf succession is CORRECT?

Statement I: Transgressive systems tract deposit is deepening upward

Statement II: Highstand systems tract deposit is deepening upward

Statement III: Falling stage systems tract deposit is deepening upward

Statement IV: Lowstand systems tract deposit is overall shallowing upward

(A) I and II

(B) II and III

(D) I and IV

Answer: (D)

38. Which of the following set of statements is CORRECT?

Statement I: A well sorted sandstone bed showing current ripple, planar laminae, convolute and prod marks.

Statement II: A poorly sorted sandstone bed showing wave ripples, dish structure, pillar e and groove casts.

Statement III: A well sorted sandstone bed showing desiccation cracks, current crescent aminae and convolute laminae.

Statement IV: A poorly sorted sandstone bed showing current ripple, planar laminae, skip marks and load casts.

(A) I, II and III

(B) II,III and IV

(D) I, II and IV

Answer: (D)

39. In metamafites, which one of the following mineral assemblages is stable under green schist facies conditions?

(A) Albite + Chlorite + Actinolite + Epidote

(B) Andesine + Biotite + Hornblende

(D) Oligoclase + Epidote + Biotite + Hornblende

Answer: (A)

40. Match the type of metamorphism listed in Group I with their products in Group II.

(A) P-4, Q-3, R-2, S-1

(B) P-2, Q-3, R-4, S-1

(D) P-1, Q-2, R-3, S-4

Answer: (A)

41. Glaucophane schist forms in _______.

(A) subduction zones

(B) pull-apart basins

(D) mid-oceanic ridges

Answer: (A)

42. Which one of the following statements is CORRECT about bivalve habitat?

(A) Gryphaea is a burrowing variety.

(B) Pholas is a free lying form.

(D) Mytilus is a bysally attached form.

Answer: (D)

43. Match foraminifera in Group I with its wall structure in Group II

(A) P-1, Q-2, R-3, S-4

(B) P-3, Q-2, R-4, S-1

(D) P-3, Q-1, R-4, S-2

Answer: (D)

44. Which one of the following stratigraphic units represents the CORRECT order of younging?

(A) Trichinopally Group – Uttatur Group – Ariyalur Group – Niniyur Group

(B) Kopili Formation – Sylhet Formation – Barail Formation – Boka Bil Formation

(D) Barakar Formation – Talchir Formation – Barren Measures – Raniganj Formation

Answer: (C)

45. Match the Formation names in Group I with their dominant lithology in Group II

(A) P-3, Q-2, R-1, S-4

(B) P-2, Q-1, R-3, S-4

(D) P-4, Q-1, R-2, S-3

Answer: (C)

46. Match the economic deposits in Group I with their occurrence in stratigraphic units in Group II

(A) P-1, Q-3, R-4, S-2

(B) P-3, Q-4, R-2, S-1

(D) P-3, Q-4, R-1, S-2

Answer: (D)

47. Match the basin type in Group I with Indian example provided in Group II

(A) P-3, Q-2, R-4, S-1

(B) P-3, Q-1, R-4, S-2

(D) P-1, Q-2, R-4, S-3

Answer: (B)

48. Choose the CORRECT set of statements.

Statement I: The hydrocarbon source rock in Cambay basin is of Jurassic age.

Statement II: Borholla field is in Assam basin.

Statement IV: Porosity of a reservoir rock increases with increase in sorting.

(A) I, II and III

(B) II, III and IV

(D) I and III only

Answer: (Marks to All)

49. The figure given below represents a scatter plot of Digital Numbers (DN) of Band 4 and Band 5 of a satellite imagery. The fields of Class A and Class B are indicated by the rectangular boxes along with their class means (open circles). Class assignment for the point P by Minimum Distance to Mean (MDM) and Nearest Neighbour (NN) algorithms are_______.

(A) Class A by MDM and class B by NN

(B) Class A by NN and class B by MDM

(D) Class B by both MDM and NN

Answer: (A)

50. Hydrogeological setup of a hypothetical alluvial area (where contact X-Y between two sands is vertical) is given in the schematic section. Hydraulic heads are indicated as h1, h2 and hydraulic conductivities as K1 and K2. The hydraulic head at the contact (X-Y) is _____ m. (round off to 2 decimal places).

Answer: (39.00 to 39.80)

51. The normalized longitudinal profile of a river is given below. The Concavity Index of the river is_______%.

Answer: (64 to 64)

52. For producing 1 kg of gold from an ore having an assay of 2 ppm Au, ______× 10³ kg of ore needs to be processed.

Answer: (500 to 500)

53. A cylindrical core of granite with a radius of 25 mm was subjected to point load test. The load was applied parallel to the diameter of the core and the failure load was 20 kN. The uncorrected point load strength index is _________Mpa.

Answer: (8 to 8)

54. A hypothetical garnet peridotite composed of 60% olivine, 25% orthopyroxene, 10% clinopyroxene and 5% garnet undergoes 10% batch melting described by

where F is degree of melting and D is bulk partition coefficient. The ratio of Ce in the melt to the original rock will be ________. (round off to 2 decimal places).

(The KD values of Ce for olivine, orthopyroxene, clinopyroxene and garnet are 0.001, 0.003, 0.10 and 0.02, respectively)

Answer: (8.90 to 9.10)

55. ⁸⁷Rb decays to ⁸⁷Sr with a decay constant λ = 1.42 × 10^-11 per year. If at the time of formation, a system contains 8× 10⁴ atoms of ⁸⁷Rb and 103 atoms of ⁸⁷Sr, the number of ⁸⁷Sr atoms in this system at the end of 4 half-lives will be _______×10³. Assume close system evolution for parent-daughter pair.

Answer: (75.97 to 76.03)

PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY

Q.56 – Q. 85 carry two marks each.

56. The Young’s modulus ‘E’ is related to the Lame’s parameter ‘’ for a Poisson solid as______.

(A) E = 2.5λ

(B) E = 1.5 λ

(D) E = 0.5 λ

Answer: (A)

57. Which one of the following seismic phases is the earliest arrival in the P shadow zone?

(A) PKiKP

(B) PPP

(D) PKIKP

Answer: (C)

58. A reversed refraction survey was done over a two layered medium with the interface between them dipping at an angle of 15°. The velocities in the upper and lower medium are V₁ and V₂ respectively, with V₂ > V₁. If the critical angle is 45°, then, which one of the following is CORRECT? (V_u and V_d are updip and downdip velocities).

(A) V₁ = V_d = V_u

(B) V_u > V_d > V₁

(D) V_u < V_d > V₁

Answer: (B)

59. In a migrated seismic time section .

(A) both synclines and anticlines appear tighter

(B) both synclines and anticlines appear broader

(D) synclines appear broader and anticlines appear tighter

Answer: (D)

60. Which one of the following is CORRECT for the density porosity (D) and neutron porosity (N) estimated for a finely interbedded organic-rich, shaly sandstone formation relative to those for a shale-free sandstone formation at shallow depths?

(A) ϕN decreases and ϕD increases.

(B) ϕN increases and ϕD decreases.

(D) Both ϕN and ϕD increase.

Answer: (D)

61. Which one of the following statements is INCORRECT with regard to Nuclear Magnetic Resonance (NMR) logging? (ϕNMR – NMR derived total porosity, ϕD – Density porosity)

(A)The relaxation time (T2) decreases with decrease in pore size.

(B)The ϕNMR is greater than ϕD in a water saturated sandstone formation.

(C)The NMR logs provide lithology independent measurement of total porosity.

(D)The ϕNMR is less than ϕD in a gas saturated shaly sandstone formation.

Answer: (B)

62. A 3-D seismic tomography experiment was carried out with an inter-station spacing of ‘X’ km. The subsurface velocity perturbations in three dimensional blocks were estimated with block size of ‘2X’km and ‘0.5X’km in case 1 and case 2, respectively. Which one of the following statements is CORRECT?

(A) The spatial resolution is poor and variance is small for case 1.

(B) The spatial resolution is good and variance is small for case 2.

(D) The spatial resolution is poor and variance is large for case 2.

Answer: (A)

63. A shallow focus, Great earthquake with seismic moment of 2.5 × 10⁴⁰ dyne-cm is recorded at an epicentral distance of 50°. The body wave magnitude (mb), surface wave magnitude (Ms) and moment magnitude (Mw) were estimated. Which one of the following is CORRECT?

(A) mb > Ms > Mw

(B) mb = Ms = Mw

(D) mb < Ms > Mw

Answer: (C)

64. A pair of current electrodes C1 (+I) and C2 (-I) is placed 50m apart (shown in the figure below) over a homogeneous structure of resistivity 100 Ωm and 1 Ampere current flows through the subsurface. Which one of the following is CORRECT for the potential (V_p) and horizontal component of electric field (Ex) at a point P located exactly below the midpoint between C1 and C2 at a depth of 10 m?

(A) V_p = 0 and E_x = 0

(B) V_p = 0 and E_x ≠ 0

(D) V_p ≠ 0 and E_x ≠ 0

Answer: (B)

65. A massive sulphide body in the subsurface is partially above the water table. According to the pH variation hypothesis for the origin of Self Potential, which one of the following statements is CORRECT for such a body?

(A) Acidic above and basic below the water table.

(B) Basic above and acidic below the water table.

(D) Basic above and below the water table.

Answer: (A)

66. The phase difference between the input and output signals for a ‘Compensator device’ used in electromagnetic prospecting to nullify the effect of primary field at the receiver coil is ______.

(A) 0°

(B) 45°

(D) 180°

Answer: (D)

67. In an electromagnetic scale modeling experiment in the lab, the relation between the field and lab geometrical scaling factor (n) with the field and lab resistivity (ρ_f & ρ_m) as well as frequencies (f_f & f_m) will be _______.

(subscripts f and m refer to field and lab systems and n >> 1)

Answer: (A)

68. If G(ω) is the Fourier transform of g(t), then the Fourier transform of g(t + ln 2) will be

(A) e⁻²^j^ωG(ω)

(B) e²^j^ωG(ω)

(D) 2e−jω(ω)

Answer: (Marks to All)

69. The primary objective of ‘Regularization’ in geophysical inversion is to .

(A) improve the resolution

(B) reduce the non-uniqueness

(D) stabilize the inversion process

Answer: (D)

70. P is a point on the Earth’s surface defined by radius (r), colatitude (θ), and longitude (ϕ) in spherical coordinate system. The three components of the magnetic induction ‘B’ at P in Cartesian coordinate system are B_x, B_y and B_z (x-North, y-East and z-downward). For the relation B = −∇V (V is the magnetic potential), the Bx, By, and Bz can be expressed in spherical coordinate system as________.

Answer: (C)

71. In gravity anomalies, the ‘Indirect effect’ mainly arises from .

(A) the sources outside the area of investigation

(B) improper instrument drift

(D) short-wavelength uncompensated masses in the subsurface

Answer: (C)

72. For defining the axial geocentric magnetic dipole of the Earth’s magnetic field using the spherical harmonic expression for magnetic potential, the three non-zero Gauss coefficients for n = 1 are _________.

Answer: (B)

73. The flexural rigidity (D) of the oceanic lithosphere (assuming no secondary thermal perturbations)_________.

(A) increases with both age and plate cooling

(B) decreases with age and increases with plate cooling

(D) decreases with both age and plate thickness

Answer: (A)

74. If ΔJ and Δσ are the uniform magnetization and density contrasts respectively, of a point source, the relation between the vertical components of the gravity(gz) and magnetic (Tz) anomalies can be expressed (neglecting long-wavelength component) as_______.

(G is Gravitational constant)

Answer: (C)

75. Which one of the following statements about the gravity anomalies on land is CORRECT?

(A) Free-air and Bouguer anomalies are always positively correlated with elevation

(B) Isostatic anomalies are not useful to understand the crustal heterogeneities

(D) X-horizontal gradient (∂g/∂x) map enhances / sharpens anomalies of bodies trending N-S (X-East, Y-North, Z-downward).

Answer: (D)

76. An aeromagnetic survey is conducted over an area with outcropping magnetic sources. The aircraft is flying at a height of 250 m with a speed of 200 km/hour. In order to fully define the magnetic anomalies along the flight path, the largest sampling rate of measurement by a Proton Precession Magnetometer will be _______ seconds. (round off to the nearest integer).

Answer: (2 to 2)

77. In an abandoned mine-site, three hollow spherical cavities are located below the surface centered at depths of 50, 100 and 150 metres. Assuming that residual gravity is low due to each one of these cavities are small (~ 0.05 mGal), do not interfere and can be detected by the gravimeter, the most ideal (largest) grid spacing for carrying out the gravity surveys in order to correctly delineate these cavities is ______ metres. (round off to the nearest integer).

Answer: (38 to 39)

78. A split-spread reflection survey is carried out along a profile in the direction of the dipping interface. The difference in arrival times of the reflected waves from the interface at two geophones with an offset distance of 1000 m from the shot-point on both sides is 20 msec. If the velocity of the layer above the dipping interface is 3000 m/s, then the dip of the bed is ______ degrees. (round off to 1 decimal place).

(Assumption 2d >> X, where ‘d’ is depth below the shot-point normal to the interface and X is the source-geophone spacing)

Answer: (1.6 to 1.8)

79. The bulk resistivity of a carbonate formation having 10% porosity which is 75% saturated with hydrocarbons is 500 Ωm. The bulk resistivity of the formation when the porosity is doubled and 100% saturated with water is ohm-metres. (round off to 1 decimal place).

(Assume the tortuosity, cementation factor and saturation exponent to be 1, 2 and 2, respectively).

Answer: (7.7 to 7.9)

80. In a seismogram of a shallow focus (h = 5 km) earthquake, the difference between the arrival times of the S and P phases is 1.34 s. Assuming the average P wave velocity of the crust to be 6.0 km/s and the Poisson’s ratio to be 0.27, the epicentral distance is _______ kilometres. (round off to 1 decimal place)

Answer: (8.8 to 9.2)

81. A Two-electrode array is placed over a vertical contact (2-D) as shown in the given figure (strike of contact is perpendicular to the plane of paper). If 1 Amp current flows through the subsurface, then the potential at the potential electrode P1 will bbe ______ milliVolts. (round off to the nearest integer).

(Consider structures with resistivity ρ1 and ρ2 to be laterally extending to infinity on both sides of the contact and also in the downward direction, C2 and P2 are grounded at infinity) ( Use π = 3.14)

Answer: (880 to 890)

82. In an electrical resistivity imaging survey, Axial Dipole-dipole array is placed over an inhomogeneous structure. The centers of current and potential dipoles are separated by a distance of 100 m. The length of each dipole is 10 m. If 5 Amp current flows through the subsurface and 50 mV potential difference is measured across the potential dipole then apparent resistivity will be ______ ohm-metres. (round off to the nearest integer) (Use π = 3.14)

Answer: (305 to 315)

83. In an electromagnetic land survey, the resultant field (primary and secondary) at any point P makes an angle of 60º from the vertical. A 30 mV signal is observed in the receiver coil placed in a horizontal position at point P. The magnitude of the signal in the receiver coil when the plane of the receiver coil is perpendicular to the resultant field is_________ milliVolts.

Answer: (60 to 60)

84. A vibroseis source sweeps acoustic signal in the frequency range 10 Hz – 100 Hz. The maximum sampling interval to correctly recover the recorded signal will be________ milliseconds.

Answer: (5 to 5)

85. The abundance of ²³⁴U in secular equilibrium with its parent ²³⁸U will be ______ ×10⁻³ %.

(Given Half-life (T_1/2) of ²³⁸U and ²³⁴U are 4.467×10⁹ y and 2.44×10⁵ y, respectively, and abundance of ²³⁸U is 99.28%)(round off to 2 decimal places)

Answer: (5.40 to 5.44)

GATE Exam 2019 Ecology and Evolution (EY) Question Paper With Answer Key

June 7, 2023December 5, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Ecology and Evolution

1. Which of the following is NOT an example of cooperative behaviour?

(A) Biofilm formation

(B) Lek formation

(D) Sentinel behavior

Answer: (B)

2. In a simple linear regression, which of the following statements represents the principle underlying the estimation of the slope and intercept?

(A) The sum of the residuals is minimised

(B) The sum of the residuals is maximised

(D) The sum of the squares of the residuals is maximized

Answer: (C)

3. According to MacArthur and Wilson’s theory of island biogeography, the number species on an of land is a balance between

(A) colonisation and extinction

(B) colonisation and speciation

(D) speciation and extinction

Answer: (A)

4. A researcher wants to sample ant diversity in a landscape consisting of riverine valleys and plateaus. Which among the following is the best sampling strategy for her to employ?

(A) Once an ant is located, lay quadrats in that area

(B) Lay equal number of quadrats in valleys and plateaus

(D) Lay quadrats in both habitats in proportion to their areas

Answer: (D)

5. The rates of non-synonymous and synonymous change per site are 𝑑𝑁 and 𝑑𝑆 respectively. Which of the following mechanisms explains the evolution of a gene with 𝑑𝑁/𝑑𝑆 = 0.2?

(A) Diversifying selection

(B) Neutral evolution

(D) Negative selection

Answer: (D)

6. Which of the following assumptions allows us to use molecular clocks to estimate species divergence times?

(A) Adaptive changes accumulate at a constant rate

(B) Adaptive changes occur episodically

(D) Neutral changes occur episodically

Answer: (C)

7. A large proportion of individuals in a particular population of humans carry the allele for colour-blindness. Assuming colour-blindness does not confer any evolutionary advantage, which of the following mechanisms CANNOT explain the unusual abundance of this allele?

(A) Founder effect

(B) Genetic drift

(D) Purifying selection

Answer: (D)

8. The evolutionary change in the timing of development is known as

(A) heterochrony

(B) heterotopy

(D) homotopy

Answer: (A)

9. Which of the following habitats is best suited for infrasound (low frequency) communication in animals?

(A) Coral reef

(B) Open ocean

(D) Urban area

Answer: (B)

10. Which of the following is typical of the eyes of a nocturnal insect?

(A) High resolution and high sensitivity

(B) High resolution and low sensitivity

(D) Low resolution and low sensitivity

Answer: (C)

11. Gut passage time is defined as the time taken from ingestion to excretion of a food item. Which among the following animals has the longest gut passage time?

(A) Black bear

(B) Gaur

(D) Tiger

Answer: (B)

12. A researcher found 𝑛 number of woody species in a one hectare tropical forest plot. He employs the same method in another one hectare plot in the same forest. Based on the principle of species area curves, the expected number of new species in the second plot is

(A) equal to 𝑛 (the number of species found in the first plot)

(B) less than 𝑛 (the number of species found in the first plot)

(D) always zero

Answer: (B)

13. A phylogenetic study finds that certain plants of peninsular India are more closely related to those in Australia than to those in China. Which of the following statements best explains this result?

(A) China and Australia were part of Laurasia, but India was in Gondwana

(B) India and Australia were part of Gondwana, but China was in Laurasia

(D) India and China were part of Laurasia, but Australia was in Gondwana

Answer: (B)

14. The pattern of net primary productivity in a year for two grassland habitats (P and Q) is shown below. Which of the following statements is consistent with the figure?

(A) Habitat P is in Argentina while Q is in Canada

(B) Habitat P is in Russia while Q is in Canada

(D) Habitat P is in South Africa while Q is in Argentina

Answer: (C)

15. Which of the following statements best explains the patterns of leaf-litter decomposition over time shown in the figure below?

(A) Habitat 1 is cold and wet; Habitat 2 is warm and arid

(B) Habitat 1 is warm and arid; Habitat 2 is cold and wet

(D) Habitat 1 is warm and wet; Habitat 2 is cold and arid

Answer: (C)

16. To compare biomass of a fish species in two lakes, A and B, a researcher records live-weights of 30 individuals from each lake. She assumes that these two datasets are normally distributed and have equal variance. She calculates

where are mean values from the respective lakes, and s is the pooled standard error.

What is this quantity Q?

(A) Correlation coefficient

(B) Regression coefficient

(D) χ2-statistic

Answer: (A)

17. While developing his theory of evolution by natural selection, Charles Darwin was influenced by t he work of

(A) Charles Lyell and Thomas Malthus

(B) Francis Crick and James Watson

(D) Sewall Wright and Ronald Fisher

Answer: (C)

18. Weakly-electric fish typically produce electric voltages of less than 1 volt for communication and navigation. Which of the following features is NOT a characteristic of weakly-electric fish?

(A) Electrocytes

(B) Electroreception capabilities

(D) Mechanisms to avoid signal jamming

Answer: (B)

19. Match the combination of primates and trees to the state/union territory where they can be found.

(A) P – i; Q – iii; R – iv; S – ii

(B) P – iii; Q – i; R – iv; S – ii

(D) P – i; Q – iv; R – ii; S – iii

Answer: (B)

20. Which of the following crops should show the LOWEST proportional increase in photosynthetic rate under rising carbon dioxide levels in the atmosphere?

(A) Barley

(B) Maize

(D) Wheat

Answer: (B)

21. Which among the following is the best indicator of the precision with which a population parameter is estimated?

(A) Degrees of freedom

(B) Mean

(D) Standard error

Answer: (D)

22. Which of the following hormones regulates moulting in arthropods?

(A) Corticosterone

(B) Ecdysone

(D) Hydrocortisone

Answer: (B)

23. A study found that grazing decreased species richness when productivity was low, and increased species richness when productivity was high. Which of the following figures best represents this result? In the figure, the dotted line represents species richness in grazed plots and the solid line represents species richness in plots without grazing.

(A) i

(B) ii

(D) iv

Answer: (B)

24. The mean height of students in a class (number of students, n=10) was initially estimated to be 6 feet and 6 inches. Later an error was detected, where one boy’s height was recorded as 10 feet taller than his actual height. The correct mean height of the students in the class is _______ inches (round off to 1 decimal place).

Answer: (65.9 to 66.1)

25. Two true-breeding lines of a moth, one with black wings and the other with red wings, are crossed. All of the resulting offspring in the F1 generation had red wings. These offspring are crossed to produce the F2 generation of moths where the expected fraction of moths with black wings in the population is _________ (round off to two decimal places).

Answer: (0.24 to 0.26)

Q.26 – Q. 55 carry two marks each.

26. A teacher proposed a null hypothesis (H₀) that there is no difference in the mean heights of boys and girls in his class. His alternative hypothesis (H_a) was that boys are taller than girls.

The figure below shows the probability distribution, i.e. probability density function, of the difference in the mean height of boys and girls if the null hypothesis were true. The observed mean difference in heights is shown by the solid back circle. The dotted line represents the range μ ± 2σ whereas the solid line shows the range μ ± 3σ.

Assuming a significance level of 0.05, which of the following conclusions is correct?

(A) 𝐻₀ is accepted

(B) 𝐻₀ is rejected

(D) 𝐻_𝑎 is rejected

Answer: (B)

27. Females in many birds and mammals mate with multiple males, in addition to their paired- male. Which of the following is an INCORRECT adaptive explanation for such extra-pair mating?

(A) Increased genetic quality of offspring

(B) Increased care of offspring by the paired-male

(D) Increased resources for offspring production

Answer: (B)

28. A researcher hypothesized that females of a bird species prefer to mate with long-tailed males. To test this hypothesis, she assigned male birds of similar tail lengths to one of the following four treatments:

1. Intact – tails left unmanipulated

2. Re-attached – tails cut and re-attached without any change in length

3. Shortened – tails cut, shortened and re-attached

4. Elongated – tails cut, elongated and re-attached

She measured mating success of these experimental birds and the results from this are shown below. Error bars represent 95% confidence intervals. Which of the following inferences are consistent with these results?

i. Experimental manipulation of tails decreased male mating success

ii. Females preferred to mate with males with short tails

iii. Females preferred to mate with males with long tails

(A) i only

(B) i and iii only

(D) iii only

Answer: (B)

29. Highly repetitive sequences are most likely to be prevalent in regions of the genome with ______recombination rate and originate via ______crossing over. Choose the right pair of words that completes this statement correctly.

(A) high; equal

(B) high; unequal

(D) low; unequal

Answer: (D)

30. Which of the following is correct about first and second derivatives at points P, Q and R for f(x) = sin (x) shown below?

Answer: (C)

31. Which of the following is NOT a proximate explanation for group cohesion among animals?

(A) Animals follow a common path while foraging

(B) Animals follow their nearest neighbor while foraging

(D) Animals secrete pheromones to attract conspecifics while foraging

Answer: (C)

32. Which of the following statements is LEAST likely to explain the evolution of dispersal?

(A) Dispersal enhances chances of finding novel habitats

(B) Dispersal regulates population densities

(D) Dispersal reduces sibling conflict

Answer: (B)

33. Which of the following plots describes the expected relationship between population size (y-axis) and generation time (x-axis) in vertebrates? Here, each data point represents a different vertebrate species and the generation time is defined as the average interval between two generations.

(A) i

(B) ii

(D) iv

Answer: (B)

34. Six different species of centipedes represented by the following phylogenetic tree have these single nucleotide polymorphisms (SNPs) at a given locus. Assuming maximum parsimony (or minimum evolutionary changes), what is the most likely nucleotide in the ancestor ‘P’?

(A) A or C

(B) A or G

(D) C or T

Answer: (A)

35. Garter snakes have evolved resistance to the poisonous secretions of the rough-skinned newts. The following figure describes poison production in newts and the resistance (measured as amount of poison tolerated) in garter snakes in three different geographical areas. Given this information, which of the following statements is correct regarding the evolution of poison resistance in garter snakes?

(A) Evolution of resistance is neutral

(B) Snakes in Area 2 are more adapted than the others

(D) The resistance mechanism is costly

Answer: (D)

36. Many bird species show cooperative breeding. Offspring are cared for by parents and other individuals (helpers) who are typically offspring from previous years. Which of the following is NOT an appropriate evolutionary explanation for why helpers do not leave and breed on their own?

(A) At high population density new breeding territories are difficult to obtain and helpers gain more from staying and helping than from dispersing to breed

(B) In environments where resources are scarce, helpers gain more by suppressing their reproduction and minimizing population extinction than from dispersing to breed

(C) When complex parental care is required for offspring survival, helpers gain more by staying and learning to care than from dispersing to breed

(D) When predation risk during dispersal is high, helpers gain more by staying and helping than from dispersing to breed

Answer: (B)

37. The relative performance of amphibians adapted to tropical (dashed line) and temperate (solid line) climates as a function of temperature is shown below. Assume that global warming will result in an equal increase in mean temperatures over the next 30 years in both regions. Which of the following statements about the effects of global warming on these two amphibians is most likely?

(A) Temperate and tropical amphibians will be similarly impacted

(B) Temperate amphibians will be more negatively impacted than tropical amphibians

(D) Tropical amphibians will be positively impacted, while temperate amphibians will be negatively impacted

Answer: (C)

38. Global warming potential of different greenhouse gases (CO2, CH4, N2O, etc) is determined by their:

P: ability to absorb infrared radiation

Q: concentration in the atmosphere

R: residence time in the atmosphere

S: source of origin (whether natural, or anthropogenic)

(A) P & R only

(B) P, Q & R only

(D) Q & S only

Answer: (B)

39. A hornbill foraging exclusively on figs in a tropical forest spends an average of 36 minutes on a tree before moving to the next tree. The density of fig trees in the forest decreases by half. In accordance with optimal foraging theory, which of following represents a possible duration (in minutes) that the hornbill may spend per tree?

(A) 6

(B) 18

(D) 54

Answer: (D)

40. Type-I errors in statistical tests represent false positives, where a true null hypothesis is falsely rejected. Type-II errors represent false negatives where we fail to reject a false null hypothesis. For a given experimental system, increasing sample size will

(A) decrease both Type-I and Type-II errors

(B) decrease Type-I and increase Type-II errors

(D) increase Type-I and decrease Type-II errors

Answer: (D)

41. Semelparous species are those that produce all of their offspring in a single reproductive event. The survivorship curve of a population of a semelparous species would most likely resemble which of the following?

(A) i

(B) ii

(D) iv

Answer: (C)

42. Bergmann’s rule describes the increase in body size observed in related organisms as we go from the equator to the poles. Which of the following is a possible explanation for this pattern?

(A) Decreased body mass in smaller organisms helps generate less heat

(B) Decreased surface area to volume ratios in larger organisms helps conserve heat

(D) Increased surface area in larger organisms helps efficient gas exchange in the poles

Answer: (B)

43. To estimate the number of foxes in an area, a researcher conducted a mark-recapture survey. In the first survey, he caught and marked 90 foxes. In his second survey a week later, he caught 120 foxes of which 40 were marked (recaptures). If you are told that the actual number of foxes in this area is 400, which of the following is a plausible explanation for the anomaly in the researcher’s data?

(A) Capture increased mortality in the marked foxes

(B) Large mortality of foxes between the two surveys

(D) The marked foxes were more likely to be recaptured

Answer: (D)

44. Which one of the statements below best describes a plant species with the timing of reproductive events shown in the following figure?

(A) The plant does not require animal pollinators

(B) The plant relies on diurnal pollinators only

(D) The plant relies on nocturnal pollinators only

Answer: (D)

45. Match species in column A to its phylogenetically closest relative in column B.

(A)P – W; Q – V; R – Z; S – X; T – Y

(B) P – Y; Q – V; R – Z; S – X; T – W

(D) P – Y; Q – V; R – Z; S – W; T – X

Answer: (B)

46. Under which of the following conditions is rapid pollen tubes growth most likely to evolve?

(A) In a self-compatible species with few ovules

(B) In a self-compatible species with many ovules

(D) In a self-incompatible species with many ovules

Answer: (C)

47. Which of the following correctly represents a decreasing order of tree species richness?

P – Dry tropical forests in Maharahstra

Q – Lowland wet tropical forests in Arunachal Pradesh

R – Scrub Forest in Rajasthan

S – Wet tropical forests in Kerala

(A) Q > R > S > P

(B) Q > S > P > R

(D) S > Q > R > P

Answer: (B)

48. A forester, pictured below, is trying to measure the height of a tree. Her height is x =1.5 m. She stands y = 10 m away from a tree, from where the angle subtended to the top of the tree is z = 45°. The height of the tree is_______m (round off to 1 decimal place).

Answer: (11.49 to 11.51)

49. In a recently discovered fossil, only 0.39% of 𝐶14 found in living fossils is present. If the half-life of 𝐶¹⁴ is 5730 years, the age of the fossil is expected to be __________years (round off to the nearest integer).

Answer: (45800 to 45900)

50. A beaker contains a large number of spherical nuts of two types, one with radius 1 cm and the other with 2 cm, in the ratio 2:1. A squirrel picks one nut from a random point in this beaker. Assuming that the beaker is well-mixed, the probability of picking the smaller nut is _______(round off to 1 decimal place).

Answer: (0.19 to 0.35)

51. In a closed population following logistic growth, per capita birth rate 𝑏 and per capita death rate 𝑑 vary with population size 𝑁 as 𝑏 = 0.1 − 0.0001𝑁 and 𝑑 = 0.01 + 0.00002𝑁, respectively. The carrying capacity 𝐾 of this population is________ individuals.

Answer: (750 to 750)

52. A population of birds has a 3:2 male to female adult sex ratio at the beginning of the breeding season. During the breeding season, every female produces 8 eggs of which 4 survive to become juveniles. A census at the end of the breeding season accurately estimates the bird population to be 1300 individuals. Assuming no deaths, the number of adult males in this population is _______ individuals.

Answer: (300 to 300)

53. The coordinates of P is (0,1), Q is (0,3), R is (2,0) and S is (1,0). The area of the trapezoid PQRS is ___________ (round off to 1 decimal place).

Answer: (2.49 to 2.51)

54. Trees in two patches A and B can disperse seeds to a bare patch C. The probability of a seed being dispersed from A to C is 0.5 and the probability of germination of such a seed is 0.1. Likewise, the probability of a seed being dispersed from B to C is 0.4 and the probability of germination of such a seed is 0.2. If the number of seeds produced in patch A is 100 and that in B is 200, the expected number of germinated seeds in patch C is________.

Answer: (21 to 21)

55. A bacterial population grows from 106 cells to 5.5 × 107 cells in 20 minutes. Assuming that the growth was not resource limited, the per-capita growth rate of bacteria is ______ per minute (round off to 2 decimal places).

Answer: (0.19 to 0.21)

GATE Exam 2019 Electrical Engineering (EE) Question Paper With Answer Key

June 7, 2023December 4, 2019 by suresh84

General Aptitude

Q.1 – Q. 5 carry one mark each.

1. I am not sure if the bus that has been booked will be able to ______all the students.

(A) sit

(B) deteriorate

(D) accommodate

Answer: (D)

2. The passengers were angry______ the airline staff about the delay.

(A) on

(B) about

(D) towards

Answer: (C)

3. The missing number in the given sequence 343, 1331, _____, 4913 is

(A) 3375

(B) 2744

(D) 4096

Answer: (C)

4. It takes two hours for a person X to mow the lawn. Y can mow the same lawn in four hours. How long (in minutes) will it take X and Y, if they work together to mow the lawn?

(A) 60

(B) 80

(D) 120

Answer: (B)

5. Newspapers are a constant source of delight and recreation for me. The _______trouble is that many I read ____ of them.

(A) even, quite

(B) even, too

(D) only, too

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. How many integers are there between 100 and 1000 all of whose digits are even?

(A) 60

(B) 80

(D) 90

Answer: (C)

7. The ratio of the number of boys and girls who participated in an examination is 4:3. The total percentage of candidates who passed the examination is 80 and the percentage of girls who passed is 90. The percentage of boys who passed is _____.

(A) 55.50

(B) 72.50

(D) 90.00

Answer: (B)

8. An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women but women feel more guilty about shopping.

Which one of the following statements can be inferred from the given text?

(A) Some men and women indulge in buying on impulse

(B) All men and women indulge in buying on impulse

(D) Many men and women indulge in buying on impulse

Answer: (A)

9. Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The product of elements having minimum and maximum values in the set Z is_____ .

(A) 1/12

(B) 1/8

(D) 3/8

Answer: (D)

10. Consider five people – Mita, Ganga, Rekha, Lakshmi and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.

Which of the following conclusions are true?

1.Lakshmi is taller than Rekha

2.Rekha is shorter than Mita

3.Rekha is taller than Sana

4.Sana is shorter than Ganga

(A) 1 and 3

(B) 3 only

(D) 1 only

Answer: (C)

Electrical Engineering

Q.1 – Q. 25 carry ONE mark each.

1. The inverse Laplace transform of is

(A) 3te^−t + e^−t

(b) 3e^−t

(D) 4te^−t + e^−t

Answer: (C)

2. M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of M² are

(A) heat equation

(B) wave equation

(D) Laplace equation

Answer: (D)

3. The partial differential equation

where c ≠ 0

is known as

(A) heat equation

(B) wave equation

(D) Laplace equation

Answer: (D)

4. Which one of the following functions is analytic in the region |z| ≤ 1?

Answer: (B)

5. The mean-square of a zero-mean random process is kT/C, where k is where 𝑘 is Boltzmann’s constant, T is the absolute temperature, and C is a capacitance. The standard deviation of the random process is

(A) kT/C

(B)

(D) √kT/C

Answer: (B)

6. A system transfer function is . If a₁ = b₁ =0, and the other coefficients are positive, the transfer function represents a

(A) low pass filter

(B) high pass filter

(D) notch filter

Answer: (A)

7. The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

(A) e^+atu(t)

(B)e^{−a(t + T)}u(t)

(D) e^−a(t−T) u(t)

Answer: (C)

8. A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is

(A) 4.5%

(B) 9%

(D) 1%

Answer: (C)

9. A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50 Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is

(A) 100 Hz

(B) 150 Hz

(D) 300 Hz

Answer: (C)

10. The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is

(A) rotor resistance

(B) rotor leakage reactance

(D) stator resistance

Answer: (C)

11. A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of 0.5 leading is

(A) 100 A

(B) 200 A

(D) 400 A

Answer: (D)

12. In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is

(A) 60

(B) −45

(D) −30

Answer: (B)

13. The output response of a system is denoted as y(t), and its Laplace transform is given by

The steady state value of y(t) is

(A) 1/10√2

(B)10√2

(D) 100√2

Answer: (A)

14. The open loop transfer function of a unity feedback system is given by

In G(s) place, the Nyquist plot of G(s) passes through the negative real axis at the point

(A) (−0.5, j0)

(B)(−0.75, j0)

(D) (−1.5, j0)

Answer: (A)

15. The characteristic equation of a linear time-invariant (LTI) system is given by

∆(s) = s⁴ + 3s³ + 3s² + s + k = 0.

The system is BIBO stable if

(A) 0 < k < 12/9

(B) k > 3

(D) k > 6

Answer: (C)

16. Given, V_gs is the gate-source voltage, V_ds is the drain source voltage, and V_th is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are

(A) V_gs < v_th ; V_ds ≥ V_gs – V_th

(B) V_gs > v_th ; V_ds ≥ V_gs – V_th

(D) V_gs < v_th ; V_ds ≤ V_gs – V_th

Answer: (B)

17. A current controlled current source (CCCS) has an input impedance of 10 Ω and output impedance of 100 kΩ. When this CCCS is used in a negative feedback closed loop with a loop gain of 9, the closed loop output impedance is

(A) 10 Ω

(B) 100Ω

(D) 1000 kΩ

Answer: (D)

18. If 𝑓 = 2𝑥³ + 3𝑦² + 4𝑧, the value of line integral ∫_𝐶 grad𝑓 ∙ 𝑑𝐫 evaluated over contour C formed by the segments (-3, -3, 2)→(2, -3, 2) →(2, 6, 2) →(2, 6, -1) is _________.

Answer: (139 to 139)

19. The current 𝐼 flowing in the circuit shown below in amperes (round off to one decimal place) is __________.

Answer: (1.3 to 1.5)

20. A co-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity ε_r1 = 2. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity ε_r2, as shown in Figure (ii), the capacitance is doubled. The value of ε_r2 is _______.

Answer: (9 to 11)

21. The 𝑌𝑏𝑢𝑠 matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as_________.

Answer: (0.095 to 0.105)

22. Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is ______.

Answer: (100 to 100)

23. The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 Ω. If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is________.

Answer: (100 to 100)

24. The rank of the matrix, is ______.

Answer: (3 to 3)

25. The output voltage of a single-phase full bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms component of output voltage to be 75% of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ___________.

Answer: (111.0 to 115.0)

Q.26 – Q. 55 carry TWO marks each.

26. Consider a 2 × 2 matrix 𝑴 = [𝒗_𝟏 𝒗_𝟐], where, 𝒗_𝟏 and 𝒗_𝟐 are the column vectors. Suppose are the row vectors. Consider the following statements:

Which of the following options is correct?

(A) Statement 1 is true and statement 2 is false

(B) Statement 2 is true and statement 1 is false

(D) Both the statements are false

Answer: (C)

27. The closed loop line integral

evaluated counter-clockwise, is

(A) +8jπ

(B) −8jπ

(D) +4jπ

Answer: (A)

28. A periodic function f(t), with a period of 2π, is represented as its Fourier series,

the Fourier series coefficients a₁ and b₁ of f(t) are

(A) a₁ = a/π; b₁ = 0

(B)a₁= A/2, b₁ = 0

(D) a₁ = 0; b₁ = A/2

Answer: (D)

29. The asymptotic Bode magnitude plot of a minimum phase transfer function 𝐺(𝑠) is shown below.

Consider the following two statements.

Statement I: Transfer function G(s) has three poles and one zero.

Statement II: At very high frequency (ω−∞), the phase angle ∠G (jω) = −3π/2.

Which one of the following options is correct?

(A) Statement I is true and statement II is false.

(B) Statement I is false and statement II is true.

(D) Both the statements are false.

Answer: (B)

30. The transfer function of a phase lead compensator is given by

The frequency (in rad/sec), at which ∠D(jω) is maximum, is

Answer: (B)

31. Consider a state-variable model of a system

where y is the output, and r is the input. The damping ratio ξ and the undamped natural frequency ω_n (rad/sec) of the system are given by

Answer: (A)

32. A moving coil instrument having a resistance of 10 Ω, gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to 100 V?

(A) 9 Ω

(B) 99 Ω

(D) 9990 Ω

Answer: (D)

33. The enhancement type MOSFET in the circuit below operates according to the square law. μ_nC_ox = 100 μA/V², the threshold voltage (VT) is 500 mV. Ignore channel length modulation. The output voltage V_out is

(A) 100 mV

(B)500 mV

(D) 2 V

Answer: (C)

34. In the circuit below, the operational amplifier is ideal. If V1 = 10 mV and V2 = 50 mV, the output voltage (V_out) is

(A) 100 mV

(B) 400 mV

(D) 600 mV

Answer: (B)

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

Answer: (A)

36. In the circuit shown below, X and Y are digital inputs, and Z is a digital output. The equivalent circuit is a

(A) NAND gate

(B)NOR gate

(D) XNOR gate

Answer: (C)

37. A DC-DC buck converter operates in continuous conduction mode. It has 48 V input voltage, and it feeds a resistive load of 24 Ω. The switching frequency of the converter is 250 Hz. If switch-on duration is 1 ms, the load power is

(A) 6 W

(B)12 W

(D) 48 W

Answer: (A OR C)

38. The line currents of a three-phase four wire system are square waves with amplitude of 100A. These three currents are phase shifted by 120° with respect to each other. The rms value of neutral current is

(A) 0 A

(B)100/√3A

(D) 300 A

Answer: (C)

39. If 𝐀 = 2𝑥𝐢 + 3𝑦𝐣 + 4𝑧𝐤 and 𝑢 = 𝑥2 + 𝑦2 + 𝑧2, then div(𝑢𝐀) at (1, 1, 1) is _____________.

Answer: (45 to 45)

40. The probability of a resistor being defective is 0.02. There are 50 such resistors in a circuit.

The probability of two or more defective resistors in the circuit (round off to two decimal places) is ____________.

Answer: (0.25 to 0.27)

41. A 0.1 µF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1 V is ________.

Answer: (0.45 to 0.47)

42. The current I flowing in the circuit shown below in amperes is _________.

Answer: (0 to 0)

43. The voltage across and the current through a load are expressed as follows

The average power in watts (round off to one decimal place) consumed by the load is _______

Answer: (585.0 to 590.0)

44. The magnetic circuit shown below has uniform cross-sectional area and air gap of 0.2 cm. The mean path length of the core is 40 cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the magnetic flux density computed in the air gap is 1 tesla. With same Ampere-turns, if the core relative permeability is assumed to be 1000 (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _________.

Answer: (0.820 to 0.850)

45. A single-phase transformer of rating 25 kVA, supplies a 12 kW load at power factor of 0.6 The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________.

Answer: (7.10 to 7.30)

46. A 220 V DC shunt motor takes 3 A at no-load. It draws 25 A when running at full-load at 1500 rpm. The armature and shunt resistances are 0.5 Ω and 220 Ω, respectively. The no- load speed in rpm (round off to two decimal places) is ________.

Answer: (1564.00 to 1596.00)

47. A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator: 𝑅₁ = 5.39 Ω, 𝑅₂ = 5.72 Ω, 𝑋₁ = 𝑋₂ = 8.22 Ω. Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to a 100 V (line), 10 Hz, three-phase AC source is__________.

Answer: (13.00 to 16.00)

48. A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of (0.25 + 𝑗2.5) Ω/phase. The motor draws the rated current of 10 A at 0.8 pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _______.

Answer: (240.00 to 250.00)

49. A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 µF/km per phase. The line is under open circuit ondition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be______.

Answer: (414.00 to 423.00)

50. A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a eactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is________.

Answer: (1.7 to 1.9)

51. In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8 pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is_______.

Answer: (19.0 to 22.0)

52. In a 132 kV system, the series inductance up to the point of circuit breaker location is 50 mH. The shunt capacitance at the circuit breaker terminal is 0.05 µF. The critical value of

resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is______.

Answer: (500 to 500)

53. In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at 48 V. The input DC voltage is 24 V. The output power is 120 W. The switching frequency is 50 kHz. Assume ideal components and a very large output filter capacitor. The converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in µH) is_________.

Answer: (24 to 24)

54. A fully-controlled three-phase bridge converter is working from a 415 V, 50 Hz AC supply. It is supplying constant current of 100 A at 400 V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is _________

Answer: (81.00 to 82.00)

55. A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC supply of 230 V, 50 Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________.

Answer: (0.75 to 0.80)

GATE Exam 2019 Electronics and Communication Engineering (EC) Question Paper With Answer Key

June 7, 2023December 4, 2019 by suresh84

General Aptitude

Q.1 – Q. 5 carry one mark each.

1. The strategies that the company to sell its products house-to-house marketing.

(A) use, includes

(B) uses, include

(D) uses, including

Answer: (B)

2. The boat arrived dawn.

(A) in

(B) at

(D) under

Answer: (B)

3. It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is hours.

(A) 2/3

(B) 3/4

(D) 7/3

Answer: (C)

4. Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is_______.

(A) 2

(B) 6

(D) 120

Answer: (B)

5. When he did not come home, she _______him lying dead on the roadside somewhere.

(A) concluded

(B) looked

(D) pictured

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. Four One people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. is an engineer, one is a doctor, one a teacher and another a dancer. You are told that:

1.Mathew is not standing next to Seema

2.There are two people standing between Lohit and the engineer

3.Rahul is not a doctor

4 The teacher and the dancer are standing next to each other

5.Seema is turning to her right to speak to the doctor standing next to her

Who among them is an engineer?

(A) Seema

(B) Lohit

(D) Mathew

Answer: (D)

7. The bar graph in Panel (a) shows the proportion of male and female illiterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c), respectively. The total population did not change during this period.

The percentage increase in the total number of literates from 2001 to 2011 is_______ .

(A) 30.43

(B) 33.43

(D) 35.43

Answer: (A)

8. “Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latter-day Indian scholars presented a contrary picture.”

From the text above, we can infer that:

Indian history written by British historians ________

(A) was well documented and not researched but was always biased

(B) was not well documented and researched and was always biased

(D) was not well documented and researched and was sometimes biased

Answer: (C)

9. Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_____ remaining in the budget.

(A) 000.00

(B) 166.67

(D) 433.33

Answer: (B)

10. Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, who is currently sharing an office with T wants to move to the adjacent office with S, the handsome new intern. Given the floor plan, what is the current location of Q, R and T?

(O = Office, WR = Washroom)

Answer: (C)

Electronics and Communication Engineering

Q.1 – Q. 25 carry ONE mark each.

1. Which one of the following functions is analytic over the entire complex plane?

(A) ln(Z)

(B) e^1/z

(D) cos(z)

Answer: (D)

2. The families of curves represented by the solution of the equation

(A) Parabolas and Circles

(B) Circles and Hyperbolas

(D) Hyperbolas and Parabolas

Answer: (C)

3. Let H(z) be t he z-transform of a real-valued discrete-time signal ℎ[𝑛]. If P(z) = H(z)H(1/z) has a zero at and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly ?

Answer: (D)

4. Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).

Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?

(A) 0.5 A

(B) 1 A

(D) 2.5 A

Answer: (B)

5. Let Y(s) be unit-step response of a casual system having a transfer function

that is, The forced response of the system is

(A) u(t) – 2e^−tu(t) + e^−3tu(t)

(B) 2u(t) – 2e^−tu(t) + e^−3tu(t)

(D) u(t)

Answer: (D OR A)

6. For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles 𝑁𝑝 and the number of system zeros 𝑁𝑧 in the frequency range 1 Hz ≤ f ≤ 10⁷ Hz is

(A) N_p = 5, N_z = 2

(B) N_p = 6, N_z = 3

(D) N_p = 4, N_z = 2

Answer: (B)

7. A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to

(A) 0010011

(B) 1100001

(D) 1111111

Answer: (B)

8. Which one of the following options describes correctly the equilibrium band diagram at T = 300 K of a Silicon pnn⁺p⁺⁺ configuration shown in the figure?

Answer: (A)

9. The correct circuit representation of the structure shown in the figure is

Answer: (A)

10. The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with Φ_ms = 0 V and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points

(A) P, Q, R

(B) Q, R, P

(D) Q, P, R

Answer: (B)

11. What is the electric flux through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of Q?

(A) HQ/ε₀

(B) HQ/4ε₀

(D) 4H/Qε₀

Answer: (B)

12. In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side.

(A) 1 – P, 2 – R, 3 – Q, 4 – S

(B) 1 – Q, 2 – R, 3 – P, 4 – S

(D) 1 – R, 2 – Q, 3 – S, 4 – P

Answer: (B)

13. A standard CMOS inverter is designed with equal rise and fall times (β_n = β_p). If the width of the pMOS transistor in the inverter is increased, what would be the effect on the LOW noise margin (𝑁𝑀𝐿) and the HIGH noise margin NM_H?

(A) NM_L increases and NM_H decreases.

(B) NM_L decreases and NM_H increases.

(D) No change in the noise margins.

Answer: (A)

14. In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?

(A) 0 and D

(B) Hi-Z and D

(D)

Answer: (B)

15. In the circuit shown, A and B are the inputs and the circuit?

(A) Latch

(B) XNOR

(D) XOR

Answer: (B)

16. The value of the contour integral

evaluated over the unit circle |z| = 1 is________

Answer: (−0.0001 to .0001)

17. The number of distinct eigenvalues of the matrix

is equal to______.

Answer: (3 to 3)

18. If 𝑋 and 𝑌 are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] =_______.

Answer: (11 to 11)

19. The value of the integral is equal to ________.

Answer: (1.99 to 2.01)

20. Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by

Then Pr(Z > 2| Z > 1), rounded off to two decimal places, is equal to ________.

Answer: (0.36 to 0.38)

21. Consider the signal where t is in seconds. Its fundamental time period, in seconds, is ________.

Answer: (11.99 to 12.01)

22. The baseband signal 𝑚(𝑡) shown in the figure is phase-modulated to generate the PM signal φ(t) = cos(2πf_ct + k m(t)). The time 𝑡 on the x-axis in the figure is in milliseconds. If the carrier frequency is f_c = 50 kHz and k = 10π, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _______(rounded off to 2 decimal places).

Answer: (0.74 to 0.76)

23. Radiation resistance of a small dipole current element of length l at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is ______%.

Answer: (1.98 to 2.02)

24. In the circuit shown, V_s is a square wave of period 𝑇 with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and R₁ = R₂ = 50 Ω. The average value of V_L is ______-volts (rounded off to 1 decimal place).

Answer: (−3.1 to −2.9)

25. In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at Q₂ is_______kHz.

Answer: (4 to 4)

Q.26 – Q. 55 carry TWO marks each.

26. Consider a differentiable function f(x) on the set of real numbers such that f(−1) = 0 and |f′(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x ∈ [−2, 2]?

(A) f(x) ≤ 1/2|x + 1|

(B) f(x) ≤ 2|x + 1|

(D) f(x) ≤ 2|x|

Answer: (B)

27. Consider the line integral

the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in the figure below. The region R is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to

(A) 6 + π/2

(B) 8 + π

(D) 16 +2π

Answer: (C)

28. Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal flow graph corresponding to X[1] is shown in the figure. Let In the figure, what should be the values of the coefficients a₁, a₂, a₃ in terms of W₆ so that X[1] is obtained correctly?

(A) a₁ = −1, a₂ = W₆, a₃ = W₆²

(B) a₁ = 1, a₂ = W², a₃= W₆

(D) a₁ = −1, a₂ = W²₆, a₃ = W₆

Answer: (C)

29. It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

where c₁ and c₂ are arbitrary real numbers. The desired three-tap filter is given by

h[0] = 1, h[1] = a, h[2] = b

and

h[n] = 0, n < 0 or n > 2.

What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above?

(A) a = 1, b = 1

(B) a = 0, b = −1

(D) a = 0, b = 1

Answer: (D)

30. In the circuit shown, if v(t) = 2 sin(1000 t) volts, R = 1 kΩ and C = 1μF, t hen the steady-state current i(t) in miliamperes (mA), is

(A) sin(1000 t) + cos (1000 t)

(B) 2 sin(1000 t) + 2 cos(1000 t)

(D) sin(1000 t) + 3 cos(1000 t)

Answer: (C)

31. Consider a causal second-order system with the transfer function

with a unit-step R(s) = 1/s as an input. Let 𝐶(𝑠) be the corresponding output. The time taken by the system output 𝑐(𝑡) to reach 94% of its steady-state value rounded off to two decimal places, is

(A) 5.25

(B) 4.50

(D) 2.81

Answer: (B)

32. The block diagram of a system is illustrated in the figure shown, where X(𝑠) is the input and Y(s) is the output. The transfer function is

Answer: (B)

33. Let the state-space representation of an LTI system be , y(t) = C x(t) + d u(t) where A, B, C are matrices, d is a scalar d is a scalar, u (t) is the input to the system, and y(t) is its output. Let B = [0 0 1]^T and d = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is

Answer: (A)

34. A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density N₀/2. Binary signaling, with minimizes the bit-error probability.

Let φ₁(t), φ₂(t) form an orthonormal signal set.

It we choose p(t) = φ₁(t) and q(t) = − φ₁(t), we would obtain a certain bit-error probability P_b.

If we keep p(t) = φ₁(t), but take q(t) = √E φ₂(t), for what value of E would we obtain the same bit-error probability P_b?

(A) 0

(B) 1

(D) 3

Answer: (D)

35. The quantum efficiency (η) and responsivity (R) at a wavelength λ (in µm) in a p-i-n photodetector are related by

Answer: (A)

36. Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents I and 2I, respectively, in opposite directions. If the two wires are separated by a distance of 4r, then the magnitude of the magnetic field between the wires at a distance r from W1 is

Answer: (C)

37. The dispersion equation of a waveguide, which relates the wave number k to the frequency ω, is

where the speed of light c = 3 × 10⁸ m/s, and ω₀ is a constant. If the group velocity is 2 × 10⁸ m/s, then the phase velocity is

(A) 1.5 × 10⁸ m/s

(B) 2 × 10⁸ m/s

(D) 4.5 × 10⁸ m/s

Answer: (D)

38. In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are 20 V and 60 mA, respectively. The values of R₁ and R_L are 200 Ω and 1 kΩ, respectively. What is the range of Vi that will maintain the Zener diode in the ‘on’ state?

(A) 22 V to 34 V

(B) 24 V to 36 V

(D) 20 V to 28 V

Answer: (B)

39. The state transition diagram for the circuit shown is

Answer: (C)

40. In the circuits shown, the threshold voltage of each nMOS transistor is 0.6 V. Ignoring the effect of channel length modulation and body bias, the values of Vout1 and Vout2, respectively, in volts, are

(A) 1.8 and 1.2

(B) 2.4 and 2.4

(D) 2.4 and 1.2

Answer: (C)

41. The RC circuit shown below has a variable resistance 𝑅(𝑡) given by the following expression:

where R₀ = 1 Ω, and 𝐶 = 1 F. We are also given that T = 3 R₀C and the source voltage is V_s = 1 V. If the current at time t = 0 is 1 A, then the current I(t), in amperes, at time t = T/2 is _____(rounded off to 2 decimal places)

Answer: (0.23 to 0.27)

42. Consider a unity feedback system, as in the figure shown, with an integral compensator k/s and open-loop transfer function

where K > 0. The positive value of 𝐾 for which there are exactly two poles of the unity feedback system on the 𝑗𝜔 axis is equal to _______ (rounded off to two decimal places)

Answer: (5.99 to 6.01)

43. Consider the homogeneous ordinary differential equation

with y(x) as a general solution. Given that

y(1) = 1 and y(2) = 14

the value of y(1.5), rounded off to two decimal places, is________.

Answer: (5.24 to 5.26)

44. Let h[n] be a length-7 discrete-time finite impulse response filter, given by

h[0] = 4, h[1] = 3, h[2] = 2, h[3] = 1,

h[−1] = −3, h[−2] = −2, h[−3] = −1,

and h[n] is zero for |n| ≥ 4. A length-3 finite impulse response approximation g[n] of h[n] has to be obtained such that

is minimized, where H(e^jω) and G(e^jω) are the discrete-time Fourier transforms of h[n] and g[n], respectively. For the filter that minimizes E(h, h), the value of 10g[−1] + g[1], rounded off to 2 decimal places, is ________.

Answer: (−27.01 to 26.99)

45. Let a random process 𝑌(𝑡) be described as 𝑌(𝑡) = ℎ(𝑡) ∗ 𝑋(𝑡) + 𝑍(t), where 𝑋(𝑡) is a white noise process with power spectral density 𝑆𝑋(𝑓) = 5 W/Hz. The filter ℎ(𝑡) has a magnitude response given by |𝐻(𝑓)| = 0.5 for −5 ≤ 𝑓 ≤ 5, and zero elsewhere. 𝑍(𝑡) is a stationary random process, uncorrelated with 𝑋(𝑡), with power spectral density as shown in the figure. The power in 𝑌(𝑡), in watts, is equal to_____W (rounded off to two decimal places).

Answer: (17.40 to 17.60)

46. A voice signal 𝑚(𝑡) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude- modulated to generate an AM signal 𝑓(𝑡) = 𝐴(1 + 𝑚(𝑡)) cos 2𝜋𝑓𝑐𝑡, where 𝑓_𝑐 = 600 kHz. The AM signal 𝑓(𝑡) is to be digitized and archived. This is done by first sampling 𝑓(𝑡) at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using 𝐾 bits, where 𝐾 is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is _______Mbps.

Answer: (11.80 to 11.82)

47. A random variable 𝑋 takes values −1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise 𝑁, so that the random variable at the channel output is 𝑌 = 𝑋 + 𝑁. The noise 𝑁 is independent of 𝑋, and is uniformly distributed over the interval [−2 , 2]. The receiver makes a decision

where the threshold 𝜃 ∈ [−1,1] is chosen so as to minimize the probability of error The minimum probability of error, rounded off to 1 decimal place, is _____.

Answer: (0.1 to 0.1)

48. A Germanium sample of dimensions 1 cm × 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dioxide- Germanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is 3 × 10⁴ cm⁻¹ and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is ______µm.

Answer: (0.230 to 0.232)

49. In an ideal pn junction with an ideality factor of 1 at T=300 K, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2 decimal places, is _______mV.

[𝑘 = 1.38 × 10⁻²³ JK⁻¹, ℎ = 6.625 × 10⁻³⁴ J-s, 𝑞 = 1.602 × 10⁻¹⁹C].

Answer: (34.00 to 38.00)

50. Consider a long-channel MOSFET with a channel length 1 µm and width 10 µm. The device parameters are acceptor concentration NA= 5 × 10¹⁶ cm^-3, electron mobility µn=800 cm2/V-s, oxide capacitance/area Cox= 3.45 × 10⁻⁷ F/cm², threshold voltage VT=0.7 V. The drain saturation current (IDsat) for a gate voltage of 5 V is ______ mA (rounded off to two decimal places). [𝜀₀ = 8.854 × 10⁻¹⁴F/cm, 𝜀_𝑆𝑖 = 11.9]

Answer: (25.40 to 25.60)

51. A rectangular waveguide of width w and height h has cut-off frequencies for TE₁₀ and TE₁₁ modes in the ratio 1: 2. The aspect ratio w/h, rounded off to two decimal places, is______.

Answer: (1.71 to 1.75)

52. In the circuit shown, Vs is a 10 V square wave of period, T = 4 ms with R = 500 Ω and C = 10 µF. The capacitor is initially uncharged at t=0, and the diode is assumed to be ideal. The voltage across the capacitor (V_c) at 3 ms is equal to ______volts (rounded off to one decimal place).

Answer: (3.2 to 3.4)

53. A CMOS inverter, designed to have a mid-point voltage V_I equal to half of V_dd, as shown in the figure, has the following parameters:

V_dd = 3 V

μ_nC_ox = 100 μA/V²; V_tn = 0.7 V forn MOS

μ_pC_ox = 40 μA/V²; |V_tp| = 0.9 V for pMOS

The ratio of (W/L)_n to (W/L)_p is equal to ________(rounded off to 3 decimal places).

Answer: (0.210 to 0.230)

54. In the circuit shown, the threshold voltages of the pMOS (|V_tp|) and nMOS (𝑉_tn) transistors are both equal to 1 V. All the transistors have the same output resistance r_ds of 6 MΩ. The other parameters are listed below:

μ_nC_ox = 60 μA/V² ; (W/L)_nMOS = 5

μ_pC_ox = 30 μA/V² ; (W/L)_pMOS = 10

μ_n and μ_p are the carrier mobilities, and 𝐶ox is the oxide capacitance per unit area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is (rounded off to 1 decimal place).

Answer: (-905 to -895 OR 895.0 to 905.0)

55. In the circuit shown, V₁ = 0 and V₂ = V_dd. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of Iout is _______ mA (rounded off to 1 decimal place).

Answer: (5.9 to 6.1)

GATE Exam 2019 Chemistry (CY) Question Paper With Answer Key

June 7, 2023December 3, 2019 by suresh84

General Aptitude

Q.1 – Q. 5 carry one mark each.

1. John Thomas, an writer, passed away in 2018.

(A) imminent

(B) prominent

(D) dominant

Answer: (C)

2. _________I permitted him to leave, I wouldn’t have had any problem with him being absent, _________I?

(A) Had, wouldn’t

(B) Have, would

(D) Have, wouldn’t

Answer: (C)

3. A work her staer noticed that the hour hand on the factory clock had moved by 225 degrees during y at the factory. For how long did she stay in the factory?

(A) 3.7 5 hours

(B) 4 hours and 15 mins

(D) 7.5 hours

Answer: (D)

4. The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is _______.

(A) 2

(B) 3

(D) 6

Answer: (C)

5. The minister avoided any mention of the issue of women’s reservation in the private sector. He was accused of_______the issue.

(A) collaring

(B) skirting

(D) belting

Answer: (B)

Q.6 – Q. 10 carry two marks each.

(A) I did not commit the crime

(B) I committed the crime

(D) You committed the crime

Answer: (C)

(A) 9 : 16

(B) 11 : 14

(D) 47 : 53

Answer: (D)

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

(A) Mobuto was not entirely successful in Africanising the name of his country

(B) The term Nzadi o Nzere was of Portuguese origin

(D) As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire

Answer: (A)

(A) 30

(B) 35

(D) 72

Answer: (C)

(A) M is the grandmother of Y

(B) R is the father of Y

(D) W is the wife of P

Answer: (D)

Chemistry

Q .1 – Q. 25 carry one mark each.

1. The INCORRECT statement about the solid-state structure of CsCl and CaF2 is:

(A) Cations in both solids exhibit coordination number 8.

(B) CsCl has bcc type structure and CaF2 has cubic close pack structure.

(D) Both exhibit close pack structure.

Answer: (D)

2. The INCORRECT statement about the interhalogen compound ICl3 is:

(A) It exists as a dimer.

(B) Geometry around the iodine is tetrahedral in solid-state.

(D) Liquid ICl3 conducts electricity.

Answer: (B)

3. Among the following carbon allotropes, the one with discrete molecular structure is

(A) Diamond

(B) α-Graphite

(D) Fullerene

Answer: (D)

4. The INCORRECT statement about the silicones is:

(A) They are thermally unstable because of the Si–C bond.

(B) They are insoluble in water.

(D) They have stable silica-like skeleton (–Si–O–Si–O–Si–).

Answer: (A)

5. The ∆_o value of [Ni(H₂O)₆]²⁺ is 8500 cm⁻¹. The ∆₀values for [NiCl₆]⁴⁻ and [Ni(NH₃)₆]²⁺ compared to [Ni(H₂O)₆]²⁺ are

(A) higher and lower, respectively.

(B) lower and higher, respectively.

(D) lower in both complex ions.

Answer: (B)

6. The Freundich isotherm, a linear relationship is obtained in the plot of

(θ = surface coverage and p = partial pressure of the gas)

(A) θ vs p.

(B) ln (θ) vs ln(p).

(D) θ vs ln(p).

Answer: (B)

7. Micelle formation is accompanied by the

(A) decrease in overall entropy due to ordering.

(B) increase in overall entropy mostly due to increase in solvent entropy.

(D) increase in overall entropy and decrease in enthalpy.

Answer: (B)

8. Consider the following phase diagram of CO₂ (not to scale). At equilibrium, the INCORRECT statement is:

(A) At 200 K, on increasing the pressure from 1 to 50 atm, CO₂ gas condenses to liquid.

(B) It is not possible to obtain liquid CO₂ from gaseous CO2 below 5.11 atm.

(D) With increasing pressure, the melting point of solid CO₂ increases.

Answer: (A)

9. The major product formed in the following reaction is

Answer: (B)

10. The Woodward-Hoffmann condition to bring out the following transformation is

(A) ∆, conrotatory

(B) ∆, disrotatory

(D) hν, conrotatory

Answer: (D)

11. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (B)

12. In the following reaction, the stereochemistry of the major product is predicted by the

(A) Cram ’s model

(B) Cram’s chelation model

(D) Felkin-Anh model

Answer: (B)

13. The product(s) formed in the following reaction is (are)

(A) I only

(B) II only

(D) mixture of I and II

Answer: (C)

14. Among the following compounds, the number of compounds that DO NOT exhibit optical

activity at room temperature is _________.

Answer: (4 to 4)

15. The number of following diene(s) that undergo Diels-Alder reaction with methyl acrylate is______.

Answer: (5 to 5)

16. The number of 1H NMR signals observed for the following compound is_________ .

Answer: (6 to 6)

17. The number of CO stretching bands in IR spectrum of trigonal bipyramidal cis-M(CO)₃L₂ is _______.

(M = metal and L = monodentate ligand)

Answer: (3 to 3)

18. On heating a sample of 25 mg hydrated compound (molecular weight = 250 g/mol) in thermogravimetric analysis, 16 mg of dehydrated compound remains. The number of water molecules lost per molecule of hydrated compound is __________.

(Molecular weight of water = 18 g/mol)

Answer: (5 to 5)

19. The total number of α and β particles emitted in the following radioactive decay is ________.

Answer: (11 to 11)

20. An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ________cal. (Round off to two decimal places)

(Gas constant R = 0.082 L atm mol^–1 K^–1 = 2 cal mol^–1 K^–1)

Answer: (-126.00 to -120.00)

21. The entropy change for the melting of ‘x’ moles of ice (heat of fusion is 80 cal g^–1) at 273 K and 1 atm pressure is 28.80 cal K^–1. The value of ‘x’ is ______. (Round off to two decimal places)

(Molecular weight of water =18 g/mol)

Answer: (5.410 to 5.55)

22. Consider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is _______. (Round off to two decimal places)

(kB is the Boltzmann constant)

Answer: (1.25 to 1.30)

23. Consider a system of three identical and distinguishable non-interacting particles and three available nondegenerate single particle energy levels having energies 0, ε and 2εThe system is in contact with a heat bath of temperature T K. A total energy of 2ɛ is shared by these three particles. The number of ways the particles can be distributed is_______.

Answer: (6 to 6)

24. In a 400 MHz 1H NMR spectrometer, a proton resonates at 1560 Hz higher than that of tetramethylsilane. The chemical shift value of this proton is _____ ppm. (Round off to one decimal place)

(Chemical shift of tetramethylsilane is fixed at zero ppm)

Answer: (3.9 to 3.9)

25. Gas phase bond length and dipole moment of a compound (MX) is 3 Å and 10.8 D, respectively. The ionic character in gas phase MX is _______%. (Round off to one decimal place)

(1D = 3.336 × 10^–30 C m)

Answer: (74.0 to 76.0)

Q.26 – Q. 55 carry two marks each.

26. The experimentally observed magnetic moment values, which match well with the spin-only values for the pair of aqueous ions is

(Atomic number: Cr = 24, Co = 27, Gd = 64, Tb = 65, Dy = 66 and Lu = 71)

(A) Cr(III)and Gd(III)

(B) Co(II) and Gd (III)

(D) Lu(III) and Tb(III)

Answer: (A)

27. Among the following compounds, a normal spinel is

(A) MgFe₂O₄

(B) ZnFe₂O4

(D) CuFe₂O₄

Answer: (B)

28. Following are the examples of silicate minerals

The correct structural description of the minerals is

(A) I – Ortho silicate, II – Cyclic silicate and III – Sheet silicate

(B) I – Ortho silicate, II – Sheet silicate and III – Cyclic silicate

(D) I – Sheet silicate, II – Ortho silicate and III – Cyclic silicate

Answer: (A)

29. In the EPR spectrum of a methyl radical, the number of lines and their relative intensities, respectively, are

(A) 1 and 1

(B) 3 and 1:2:1

(D) 4 and 1:3:3:1

Answer: (D)

30. The product obtained in the reaction of Mn₂(CO)₁₀ with Br₂ is

(A) Mn(CO)5Br

(B) Mn₂(CO)₈Br₂

(D) Mn₂(CO)₉Br

Answer: (A)

31. The correct molecular representation of W(Cp)₂(CO)₂ is

(Cp = cyclopentadienyl)

32. Match the metalloproteins with their respective functions.

(A) P – III; Q – II; R – I; S – IV

(B) P – III; Q – I; R – IV; S – II

(D) P – IV; Q – II; R – I; S – III

Answer: (B)

33. Suppose the wave function of a one dimensional system is

Ψ = sin(kx)exp(3ikx).

In an experiment measuring the momentum of the system, one of the expected outcomes is

(A) 0

(B) ћk

(D) 3 ћk

Answer: (C)

34. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (A)

35. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (B)

36. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (D)

37. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (D)

38. In the following reaction sequence, the products P and Q are

(A)

(B)

(C)

(D)

Answer: (C)

39. The major product formed in the following reaction is.

(PCC = pyridinium chlorochromate)

(A)

(B)

(C)

(D)

Answer: (C)

40. In the following reactions, the major products P and Q are

(A)

(B)

(C)

(D)

Answer: (B)

41. In the following reaction sequence, the products P and Q are

(A)

(B)

(C)

(D)

Answer: (B)

42. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (C)

43. The rate of the following redox reaction is slowest when X is

(A) H₂O

(B) NH₃

(D) N₃^–

Answer: (B)

44. A complex is composed of one chromium ion, three bromides and six water molecules. Upon addition of excess AgNO₃, 1.0 g aqueous solution of the complex gave 0.94 g of AgBr. The molecular formula of the complex is

(Atomic weight: Cr = 52, Br = 80, Ag = 108, O = 16 and H = 1)

(A) [Cr(H₂O)₆]Br₃

(B) [Cr(H₂O)₅Br]Br₂•H₂O

(D) [Cr(H₂O)₃Br₃]•3H₂O

Answer: (B)

45. The number of possible optically active isomer(s) for the following complex is ________.

en = ethylenediamine

Answer: (2 to 2 OR 4 to 4)

46. The specific rotation of optically pure (R)-2-bromobutane is –112.00. A given sample of 2-bromobutane exhibited a specific rotation of –82.88. The percentage of (S)-(+)-enantiomer present in this sample is_______.

Answer: (13 to 13)

47. Consider the following two parallel irreversible first order reactions at temperature T,

where 𝑘₁and 𝑘₂ are the rate constants and their values are 5 × 10^–2 and 15 × 10^–2 min^–1, respectively, at temperature T. If the initial concentration of the reactant ‘P’ is 4 mol L^–1, then the concentration of product ‘R’ after 10 min of reaction is _____ mol L^–1. (Round off to two decimal places)

(Assume only P is present at the beginning of the reaction.)

Answer: (2.50 to 2.65)

48. Consider the following equilibrium

At 298 K, the standard molar Gibbs energies of formation, ∆_fG⁰, of SO₂ (g) and SO₃ (g) are –300 and –371 kJ mol^{– 1}, respectively. The value of the equilibrium constant, KP, at this temperature is ______× 10¹⁰. (Round off to the nearest integer)

(Gas constant R = 8.31 J mol^–1 K^–1)

Answer: (265 to 295)

49. Consider the electrochemical cell

M(s)|MI₂(s)|MI₂(aq)|M(s)

where ‘M’ is a metal. At 298 K, the standard reduction potentials are

and the temperature coefficient is

At this temperature the standard enthalpy change for the

overall cell reaction, ∆_rH⁰, is _____kJ mol^–1. (Round off to two decimal places)

(Faraday constant F = 96500 C mol^–1)

Answer: (-38.00 to -37.00)

50. The normal boiling point of a compound (X) is 350 K (heat of vaporization, ∆_vapH, = 30 kJ mol–1). The pressure required to boil ‘X’ at 300 K is_______ Torr. (Round off to two decimal places)

(Ignore the temperature variation of ∆vapH; Gas constant R = 8.31 J mol^–1 K^–1 and 1 atm = 760 Torr)

Answer: (120.00 to 140.00)

51. For a bimolecular gas phase reaction P + Q → R, the pre-exponential factor is 1 × 10¹³ dm³ mol^–1 s^–1. The standard entropy of activation at 25°C is ______ J K^–1 mol^–1. (Round off to two decimal points)

(The standard concentration c^o = 1 mol dm^–3; Planck constant h = 6.62 × 10^–34 J s; Boltzmann constant k_B = 1.38 × 10^–23 JK^–1; Gas constant R = 8.31 J mol^–1 K^–1)

Answer: (-12.90 to -12.40)

52. Character table of point group D8 is given below.

Value of (a + b + c + d + e + f + g + h + i + j + k) is equal to _______.

Answer: (9 to 9)

53. If are spin angular momentum operators and is spin up eigen function, then the value of ‘a’ is _____ . (Round off to one decimal place)

Answer: (0.5 to 0.5)

54. A particle in one dimensional box of length 2a with potential energy

is perturbed by the potential V’ = cx eV, where c is a constant. The 1st order correction to the 1st excited state of the system is ______× c eV.

Answer: (0 to 0)

55. Consider a two dimensional harmonic oscillator with angular frequency ω_x = 2ω_y = 6.5 × 10¹⁴ rad s^–1. The wavelength of x polarized light required for the excitation of a particle from its ground state to the next allowed excited state is _____ × 10⁻⁶ m. (Round off to one decimal place)

(Speed of light c = 3.0 × 10⁸ ms^–1)

Answer: (2.8 to 3.0)

GATE Exam 2019 Computer Science and Information Technology (CS) Question Paper With Answer Key

June 7, 2023December 3, 2019 by suresh84

General Aptitude

Q. 1 – Q. 5 carry one mark each.

1. The expenditure on the project as follows: equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.

(A) break down

(B) break

(D) breaks

Answer: (C)

2. The search engine’s business model around the fulcrum of trust.

(A) revolves

(B) plays

(D) burst

Answer: (A)

3. Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ____.

(A) 1

(B) 2

(D) 6

Answer: (B)

4. Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ______.

(A) 666

(B) 3000

(D) 12000

Answer: (C)

5. A court is to a judge as ______ is to a teacher.

(A) a student

(B) a punishment

(D) a school

Answer: (D)

Q. 6 – Q. 10 carry two marks each.6

6. The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:

P says “Q committed the crime.”

Q says “S committed the crime.”

R says “I did not do it.”

S says “What Q said about me is false.”

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

(A) P

(B) R

(D) Q

Answer: (B)

7. In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of _____.

(A) 0 to 15

(B) 16 to 30

(D) 46 to 60

Answer: (C)

8. “A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net.”

Which one of the following statements can be inferred from the given passage?

(A) Beggars are lazy people who beg because they are unwilling to work

(B) Beggars are created because of the lack of social welfare schemes

(D) Begging has to be banned because it adversely affects the welfare of the state

Answer: (B)

9. In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is .

(A) 1000

(B) 975

(D) 225

Answer: (C)

10. Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests. Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell. Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

The shaded rooms are already occupied. WR is washroom.

(A)

(B)

(C)

(D)

Answer: (D)

Computer Science and Information Technology

1. A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor?

(A) 24 bits and 0 bits

(B) 28 bits and 4 bits

(D) 28 bits and 0 bits

Answer: (D)

2. The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system has 16 address lines denoted by A15 to A0. What is the range of addresses (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal?

(A) C800 to CFFF

(B) CA00 to CAFF

(D) DA00 to DFFF

Answer: (A)

3. Which one of the following kinds of derivation is used by LR parsers?

(A) Left most

(B) Leftmost in reverse

(D) Rightmost in reverse

Answer: (D)

4. Which one of the following kinds of derivation is used by LR parsers?

(A) Leftmost

(B) Leftmost in reverse

(D) Rightmost in reverse

Answer: (C)

5. Let U = {1, 2, …., n}. Let A = {(x, X)|x ∈ X, X ⊆}. Consider the following two statements on |A|.

Which of the above statements is/are TRUE?

(A) Only I

(B) Only II

(D) Neither I nor II

Answer: (C)

6. Which one of the following is NOT a valid identity?

Answer: (B)

7. If 𝐿 is a regular language over ∑ = {a, b}, which one of the following languages is NOT regular ?

8.Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in 𝑛 bits. To avoid overflow, the representation of Z would require a minimum of:

(A) 𝑛 bits

(B) 𝑛 − 1 bits

(D) 𝑛 + 2 bits

Answer: (B)

9. Let 𝑋 be a square matrix. Consider the following two statements on 𝑋.

I. 𝑋 is invertible.

Determinant of 𝑋 is non-zero.

Which one of the following is TRUE?

(A) I implies II; II does not imply I.

(B) II implies I; I does not imply II.

(D) I and II are equivalent statements.

Answer: (D)

10. Let 𝐺 be an arbitrary group. Consider the following relations on 𝐺:

Which of the above is/are equivalence relation/relations?

(A) 𝑅₁ and 𝑅₂

(B) 𝑅₁ only

(D) Neither 𝑅₁ nor 𝑅₂

Answer: (B)

11. Consider the following two statements about database transaction schedules:

I. Strict two-phase locking protocol generates conflict serializable schedules that are also recoverable.

II. Timestamp-ordering concurrency control protocol with Thomas’ Write Rule can generate view serializable schedules that are not conflict serializable.

Which of the above statements is/are TRUE?

(A) I only

(B) II only

(D) Neither I nor II

Answer: (C)

12. Let 𝐺 be an undirected complete graph on 𝑛 vertices, where 𝑛 > 2. Then, the number of different Hamiltonian cycles in 𝐺 is equal to

(A) 𝑛!

(B) (𝑛 − 1)!

(D)

Answer: (C OR D)

13.

(A) 1

(B) 53/12

(D) Limit does not exist

Answer: (C)

14. Which one of the following statements is NOT correct about the B+ tree data structure used for creating an index of a relational database table?

(A) B+ Tree is a height-balanced tree

(B) Non-leaf nodes have pointers to data records

(D) Each leaf node has a pointer to the next leaf node

Answer: (B)

15. For Σ = {𝑎, 𝑏}, let us consider the regular language 𝐿 = { 𝑥 |𝑥 = 𝑎²⁺³^𝑘 or 𝑥 = 𝑏¹⁰⁺¹²^𝑘,

𝑘 ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for 𝐿 ?

(A) 3

(B) 5

(D) 24

Answer: (D)

16. Which of the following protocol pairs can be used to send and retrieve e-mails (in that order)?

(A) IMAP, POP3

(B) SMTP, POP3

(D) IMAP, SMTP

Answer: (B)

17. The following C program is executed on a Unix/Linux system:

The total number of child processes created is______.

Answer: (31 to 31)

18. Consider the following C program:

The value printed by the program is_______.

Answer: (26 to 26)

19. Consider the grammar given below: S → Aa

Let a, b, d, and $ be indexed as follows:

Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210) Answer: _______.

Answer: (31 to 31)

20. An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is ______.

Answer: (0.08 to 0.08)

21. The value of 3⁵¹ mod 5 is _______.

Answer: (2 to 2)

22. Two numbers are chosen independently and uniformly at random from the set {1, 2 , . . . , 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ________.

Answer: (0.502 to 0.504)

23. Consider three concurrent processes P1, P2 and P3 as shown below, which access a shared variable D that has been initialized to 100.

The processes are executed on a uniprocessor system running a time-shared operating system. If the minimum and maximum possible values of D after the three processes have completed execution are X and Y respectively, then the value of Y – X is _______.

Answer: (80 to 80)

24. Consider the following C program:

The number that will be displayed on execution of the program is_______.

Answer: (6 to 6)

25. Consider a sequence of 14 elements: A = [−5, −10, 6, 3, −1, −2, 13, 4, −9, −1, 4, 12, −3, 0]. The subsequence sum Determine the maximum of 𝑆(𝑖, 𝑗), where 0 ≤ 𝑖 ≤ 𝑗 < 14. (Divide and conquer approach may be used.)

Answer: _____.

Answer: (29 to 29)

26. Consider the following C function.

Which one of the following will happen when the function convert is called with any positive integer n as argument?

(A) It will print the binary representation of n and terminate

(B) It will print the binary representation of n in the reverse order and terminate

(D) It will not print anything and will not terminate

Answer: (D)

27. Consider the following C program:

Which one of the following values will be displayed on execution of the programs?

(A) 41

(B) 52

(D) 630

Answer: (B)

28. Consider three machines M, N, and P with IP addresses 100.10.5.2, 100.10.5.5, and 100.10.5.6 respectively. The subnet mask is set to 255.255.255.252 for all the three machines. Which one of the following is true?

(A) M, N, and P all belong to the same subnet

(B) Only M and N belong to the same subnet

(D) M, N, and P belong to three different subnets

Answer: (C)

29. Suppose that in an IP-over-Ethernet network, a machine X wishes to find the MAC address of another machine Y in its subnet. Which one of the following techniques can be used for this?

(A) X sends an ARP request packet to the local gateway’s IP address which then finds the MAC address of Y and sends to X

(B) X sends an ARP request packet to the local gateway’s MAC address which then finds the MAC address of Y and sends to X

(D) X sends an ARP request packet with broadcast IP address in its local subnet

Answer: (C)

30. Consider three 4-variable functions f₁, f₂, and f₃, which are expressed in sum-of-minterms as

f1 = ∑ (0, 2, 5, 8, 14), f2 = ∑ (2, 3, 6, 8, 14, 15), f3 = ∑ (2, 7, 11, 14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

(A) ∑ (7, 8, 11)

(B) ∑ (2, 7, 8, 11, 14)

(D) ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)

Answer: (A)

31. Which one of the following languages over Σ = {𝑎, 𝑏} is NOT context-free?

Answer: (C)

32. Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS).

Consider the two statements given below.

(I) Both Y and Z are in BCNF

(II) Decomposition of X into Y and Z is dependency preserving and lossless

Which of the above statements is/are correct?

(A) Both I and II

(B) I only

(D) Neither I nor II

Answer: (C)

33. Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressible. The page size is 8 kB and the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss?

(A) 16 × 2¹⁰

(B) 256 × 2¹⁰

(D) 8 × 2²⁰

Answer: (B)

34. Consider the following sets:

S1 Set of all recursively enumerable languages over the alphabet {0,1}

S2 Set of all syntactically valid C programs S3. Set of all languages over the alphabet {0,1}

S4 Set of all non-regular languages over the alphabet {0,1}

Which of the above sets are uncountable?

(A) S1 and S2

(B) S3 and S4

(D) S1 and S4

Answer: (B)

35. Consider the first order predicate formula 𝜑:

∀𝑥 [(∀𝑧 𝑧|𝑥 ⇒ ((𝑧 = 𝑥) ∨ (𝑧 = 1))) ⇒ ∃𝑤 (𝑤 > 𝑥) ∧ (∀𝑧 𝑧|𝑤 ⇒ ((𝑤 = 𝑧) ∨ (𝑧 = 1)))] Here ‘𝑎|𝑏’ denotes that ‘𝑎 divides 𝑏’, where 𝑎 and 𝑏 are integers. Consider the following sets:

S1. {1,2,3, … , 100}

S2. Set of all positive integers

S3. Set of all integers

Which of the above sets satisfy 𝜑?

(A) S1 and S2

(B) S1 and S3

(D) S1, S2 and S3

Answer: (C)

36. Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let 𝑋₁, 𝑋₂, 𝑋₃, 𝑋₄, 𝑋₅, and 𝑋₆ be the placeholders for the non- terminals D, T, L or L₁ in the following table:

Which one of the following are the appropriate choices for 𝑋1, 𝑋2, 𝑋3 and 𝑋4?

(A) 𝑋₁ = 𝐿 , 𝑋₂ = 𝑇, 𝑋₃ = 𝐿₁, 𝑋₄ = 𝐿

(B) 𝑋₁ = 𝑇 , 𝑋₂ = 𝐿, 𝑋₃ = 𝐿₁, 𝑋₄ = 𝑇

(D) 𝑋₁ = 𝑇 , 𝑋₂ = 𝐿, 𝑋₃ = 𝑇, 𝑋₄ = 𝐿1

Answer: (A)

37. There are n unsorted arrays: A₁, A₂, …, An. Assume that n is odd. Each of A₁, A₂, …, An contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A₁, A₂, …, An is

(A) O(n)

(B) O(n log n)

(D) Ω(n² log n)

Answer: (C)

38. Let 𝐺 be any connected, weighted, undirected graph.

I. 𝐺 has a unique minimum spanning tree, if no two edges of 𝐺 have the same weight.

II. 𝐺 has a unique minimum spanning tree, if, for every cut of 𝐺, there is a unique minimum-weight edge crossing the cut.

Which of the above two statements is/are TRUE?

(A) I only

(B) II only

(D) Neither I nor II

Answer: (C)

39. Consider the following snapshot of a system running 𝑛 concurrent processes. Process 𝑖 is holding 𝑋𝑖 instances of a resource R, 1 ≤ 𝑖 ≤ 𝑛. Assume that all instances of R are currently in use. Further, for all 𝑖, process 𝑖 can place a request for at most 𝑌𝑖 additional instances of R while holding the 𝑋𝑖 instances it already has. Of the 𝑛 processes, there are exactly two processes 𝑝 and 𝑞 such that 𝑌_𝑝 = 𝑌_𝑞 = 0. Which one of the following conditions guarantees that no other process apart from 𝑝 and 𝑞 can complete execution?

Answer: (A)

40. Consider the following statements:

I. The smallest element in a max-heap is always at a leaf node

II. The second largest element in a max-heap is always a child of the root node

III. A max-heap can be constructed from a binary search tree in Θ(𝑛) time

IV. A binary search tree can be constructed from a max-heap in Θ(𝑛) time

Which of the above statements are TRUE?

(A) I, II and III

(B) I, II and IV

(D) II, III and IV

Answer: (A)

41. Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in milliseconds) as shown below:

These processes are run on a single processor using preemptive Shortest Remaining Time First scheduling algorithm. If the average waiting time of the processes is 1 millisecond, then the value of Z is______.

Answer: (2 to 2)

42. The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointers. The disk block size is 4 kB, and the disk block address is 32-bits long. The maximum possible file size is (rounded off to 1 decimal place)_____GB.

Answer: (3.7 to 3.8 OR 4.0 to 4.1)

43. Consider the augmented grammar given below

Let I0 = CLOSURE ({[S’ → •S]}). The number of items in the set GOTO (I₀ , 〈 ) is:_____.

Answer: (5 to 5)

44. Consider the following matrix:

The absolute value of the product of Eigen values of 𝑅 is_______.

Answer: (12 to 12)

45. A certain processor deploys a single-level cache. The cache block size is 8 words and the word size is 4 bytes. The memory system uses a 60-MHz clock. To service a cache miss, the memory controller first takes 1 cycle to accept the starting address of the block, it then takes 3 cycles to fetch all the eight words of the block, and finally transmits the words of the requested block at the rate of 1 word per cycle. The maximum bandwidth for the memory system when the program running on the processor issues a series of read operations is _______× 10⁰⁰ bytes/sec.

Answer: (160 to 160)

46. Let 𝑇 be a full binary tree with 8 leaves. (A full binary tree has every level full.) Suppose two leaves 𝑎 and 𝑏 of 𝑇 are chosen uniformly and independently at random. The expected value of the distance between 𝑎 and 𝑏 in 𝑇 (i.e., the number of edges in the unique path between 𝑎 and 𝑏) is (rounded off to 2 decimal places)______.

Answer: (4.25 to 4.25)

47. Suppose 𝑌 is distributed uniformly in the open interval (1,6). The probability that the polynomial 3𝑥² + 6𝑥𝑌 + 3𝑌 + 6 has only real roots is (rounded off to 1 decimal place) _____.

Answer: (0.8 to 0.8)

48. Let Σ be the set of all bijections from {1, … , 5} to {1, … , 5}, where 𝑖𝑑 denotes the identity function, i.e. 𝑖𝑑(𝑗) = 𝑗, ∀𝑗. Let ∘ denote composition on functions. For a string 𝑥 = 𝑥1 𝑥2 ⋯ 𝑥𝑛 ∈ Σ𝑛, 𝑛 ≥ 0 , let 𝜋(𝑥) = 𝑥1 ∘ 𝑥2 ∘ ⋯ ∘ 𝑥𝑛.

Consider the language 𝐿 = {𝑥 ∈ Σ∗| 𝜋(𝑥) = 𝑖𝑑 }. The minimum number of states in any DFA accepting 𝐿 is ________.

Answer: (120 to 120)

49. Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches.

Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is _________.

Answer: (3 to 3)

50. What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = ∑ (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer: ______.

Answer: (3 to 3)

51. A relational database contains two tables Student and Performance as shown below:

The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together form the primary key. Consider the SQL query given below:

The number of rows returned by the above SQL query is______ .

Answer: (5 to 5)

52. Consider the following C program:

The number of times the variable sum will be printed, when the above program is executed, is ________.

Answer: (5 to 5)

53. Consider the following C program:

The output of the above C program is _______.

Answer: (10 to 10)

54. In an RSA cryptosystem, the value of the public modulus parameter 𝑛 is 3007. If it is also known that φ(𝑛) = 2880, where φ () denotes Euler’s Totient Function, then the prime factor of 𝑛 which is greater than 50 is ______.

Answer: (97 to 97)

55. Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).

How many tuples will be returned by the following relational algebra query?

Answer: ________.

Answer: (1 to 1)

GATE Exam 2019 Chemical Engineering (CH) Question Paper With Answer Key

June 7, 2023December 3, 2019 by suresh84

General Aptitude

Q. 1 – Q. 5 carry one mark each.

1. The expenditure on the project as follows: equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.

(A) break down

(B) break

(D) breaks

Answer: (C)

2. The search engine’s business model around the fulcrum of trust.

(A) revolves

(B) plays

(D) burst

Answer: (A)

(A) 1

(B) 2

(D) 6

Answer: (B)

(A) 666

(B) 3000

(D) 12000

Answer: (C)

5. A court is to a judge as ______ is to a teacher.

(A) a student

(B) a punishment

(D) a school

Answer: (D)

Q. 6 – Q. 10 carry two marks each.6

6. The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:

P says “Q committed the crime.”

Q says “S committed the crime.”

R says “I did not do it.”

S says “What Q said about me is false.”

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

(A) P

(B) R

(D) Q

Answer: (B)

(A) 0 to 15

(B) 16 to 30

(D) 46 to 60

Answer: (C)

Which one of the following statements can be inferred from the given passage?

(A) Beggars are lazy people who beg because they are unwilling to work

(B) Beggars are created because of the lack of social welfare schemes

(D) Begging has to be banned because it adversely affects the welfare of the state

Answer: (B)

(A) 1000

(B) 975

(D) 225

Answer: (C)

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell. Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

The shaded rooms are already occupied. WR is washroom.

(A)

(B)

(C)

(D)

Answer: (D)

Chemical Engineering

1. A system of n homogeneous linear equations containing n unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is

(A) 1

(B) −1

(D) ∞

Answer: (D)

2. The value of the expression is

(A) ∞

(B) 0

(D) −1

Answer: (C)

3. Consider a rigid, perfectly insulated, container partitioned into two unequal parts by a thin membrane (see figure). One part contains one mole of an ideal gas at pressure 𝑃_𝑖 and temperature 𝑇_𝑖 while the other part is evacuated. The membrane ruptures, the gas fills the entire volume and the equilibrium pressure is 𝑃_𝑓 = 𝑃𝑖⁄4. If 𝐶_𝑝 (molar specific heat capacity at constant pressure), 𝐶_𝑣 (molar specific heat capacity at constant volume) and 𝑅 (universal gas constant) have the same units as molar entropy, the change in molar entropy (𝑆_𝑓 − 𝑆_𝑖) is

(A) C_𝑝ln2 + Rln4

(B) −C_𝑣ln2 + Rln4

(D) C_𝑝ln2

Answer: (A)

4. For a single component system, vapor (subscript 𝑔) and liquid (subscript 𝑓) coexist in mechanical, thermal and phase equilibrium when

(A) 𝑢_𝑔 = u_f (equality of specific internal energy)

(B) h_𝑔 = h_f(equality of specific enthalpy)

(D) g_g= g_f (equality of specific Gibbs free energy)

Answer: (D)

5. For a binary nonideal A-B mixture exhibiting a minimum boiling azeotrope, the activity coefficients, 𝛾𝑖 (i = A, B), must satisfy

(A) γ_A > 1, γ_B > 1

(B) γ_A < 1, γ_B > 1

(D) γ_A < 1, γ_B < 1

Answer: (A)

6. For a fully-developed turbulent hydrodynamic boundary layer for flow past a flat plate, the thickness of the boundary layer increases with distance x from the leading edge of the plate, along the free-stream flow direction, as

(A) 𝑥^0.5

(B) 𝑥^1.5

(D) 𝑥^0.8

Answer: (D)

7. Consider a cylinder (diameter D and length D ), a sphere (diameter D ) and a cube length D ). objects is true (side Which of the following statements concerning the sphericity ( Φ ) of the above :

(A) Φ_sphere > Φ_cylinder > Φ_cube

(B) Φ_sphere = Φ_cylinder = Φ_cube

(D) Φ_sphere > Φ_cylinder = Φ_cube

Answer: (A)

8. Prandtl number signifies the ratio of

Answer: (A)

9. Pool boiling equipment operating above ambient temperature is usually designed to operate

(A) far above the critical heat flux

(B) near the critical heat flux

(D) near the Leidenfrost point

Answer: (B)

10. The desired liquid-phase reaction

is accompanied by an undesired side reaction

Four isothermal reactors schemes (CS TR: ideal Continuous-Stirred Tank Reactor. PFR: ideal Plug Flow Reactor) for processing equal molar feed rates of D and E are show in figure. Each scheme is designed for t he same conversion. The scheme that gives the most favorable product distribution is

Answer: (C)

11. For a first order reaction in a porous spherical catalyst pellet, diffusional effects are most likely to lower the observed rate of reaction for

(A) slow reaction in a pellet of small diameter

(B) slow reaction in a pellet of large diameter

(D) fast reaction in a pellet of large diameter

Answer: (D)

12. A thermocouple senses temperature based on the

(A) Nernst Effect

(B) Maxwell Effect

(D) Peltier Effect

Answer: (C)

13. The correct expression for the Colburn j-factor for mass transfer that relates Sherwood number (Sh), Reynolds number (Re) and Schmidt number (Sc) is

Answer: (A)

14. In the drying of non-dissolving solids at constant drying conditions, the internal movement of moisture in the solid has a dominant effect on the drying rate during

(A) the initial adjustment period only

(B) the constant rate period only

(D) both the initial adjustment and constant rate periods

Answer: (C)

15. Three distillation schemes for separating an equimolar, constant relative volatility ABC mixture into nearly pure components are shown. The usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays are valid. All the schemes are designed for minimum total reboiler duty. Given that the relative volatilities are in the ratio α_A : α_B : α_C = 8:2:1, the correct option that arranges the optimally-designed schemes in ascending order of total reboiler duty is

(A) I, II, III

(B) III, I, II

(D) III, II, I

Answer: (B)

16. Consider the two countercurrent heat exchanger designs for heating a cold stream from 𝑡_𝑖𝑛 to 𝑡_out , as shown in figure. The hot process stream is available at 𝑇 . The inlet stream conditions and overall heat transfer coefficients are identical in both the designs. The heat transfer area in Design I and Design II are respectivel

If heat losses are neglected, and if both the designs are feasible, which of the following statements holds true:

Answer: (D)

17. Producer gas is obtained by

(A) passing air through red hot coke

(B) thermal cracking of naphtha

(D) passing air and steam through red hot coke

Answer: (D)

18. In Kraft process, the essential chemical reagents used in the digester are

(A) caustic soda, mercaptans and ethylene oxide

(B) caustic soda, sodium sulphide and soda ash

(D) baking soda, sodium sulphide and mercaptans

Answer: (B)

19. The most common catalyst used for oxidation of o-xylene to phthalic anhydride is

(A) V₂O₅

(B) Pd

(D) Ag

Answer: (A)

20.In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics is

(A) alkylation

(B) catalytic reforming

(D) isomerization

Answer: (B)

21. The combination that correctly matches the polymer in Group-1 with the polymerization type in reaction Group-2 is

(A) P-II, Q-I, R-III

(B) P-I, Q-III, R-II

(D) P-II, Q-III, R-I

Answer: (D)

22. The product of the eigenvalues of the matrix is ______ (rounded off to one decimal place).

Answer: (13.9 to 14.1)

23. For a hydraulic lift with dimensions shown in figure, assuming g =10 m/s² , the maximum diameter D_left (in m) that lifts a vehicle of mass 1000 kg using a force of 100 N is _____ (rounded off to two decimal places).

Answer: (0.19 to 0.21)

24. The liquid flow rate through an equal percentage control valve, when fully open, is 150 gal/min and the corresponding pressure drop is 50 psi. If the specific gravity of the liquid is 0.8, then the valve coefficient, C_v, in gal/(min psi^0.5) is ______ (rounded off to two decimal places).

Answer: (18.96 to 18.98)

25. Consider a sealed rigid bottle containing CO₂ and H₂O at 10 bar and ambient temperature. Assume that the gas phase in the bottle is pure CO₂ and follows the ideal gas law. The liquid phase in the bottle contains CO₂ dissolved in H₂O and is an ideal solution. The Henry’s constant at the system pressure and temperature is The equilibrium mole fraction of CO₂ dissolved in H₂O is _____ (rounded off to three decimal places).

Answer: (0.009 to 0.011)

Q. 26 – Q. 55 carry two marks each.

26. The solution of the ordinary differential equation subject to the initial condition

Answer: (D)

27. The value of the complex number i^−1/2 (where i = √−1) is

Answer: (A)

28. An incompressible Newtonian fluid flows in a pipe of diameter D₁ at volumetric flow rate Q . Fluid with same properties flows in another pipe of diameter D₂ =D₁/2 at the same flow rate Q . The transition length required for achieving fully-developed flow is l₁for the tube of diameter D₁, while it is l₂ for the tube of diameter D2 . Assuming steady laminar flow in both cases, the ratio l₁/ l₂ is:

(A) 1/4

(B) 1

(D) 4

Answer: (B)

29. A disk turbine is used to stir a liquid in a baffled tank. To design the agitator, experiments are performed in a lab-scale model with a turbine diameter of 0.05 m and a turbine impeller speed of 600 rpm. The liquid viscosity is 0.001 Pa s while the liquid density is 1000 kg/m³ . The actual application has a turbine diameter of 0.5 m, an impeller speed of 600 rpm, a liquid viscosity of 0.1 Pa s and a liquid density of 1000 kg/m³ . The effect of gravity is negligible. If the power required in the lab-scale model is P1 and the estimated power for the actual application is P₂ , then the ratio P₂/P₁ is

(A) 10³

(B) 10⁴

(D) 10⁶

Answer: (A)

30. Consider two non-interacting tanks-in-series as shown in figure. Water enters TANK 1 at q cm³/s and drains down to TANK 2 by gravity at a rate k √h₁(cm³/s). Similarly, water drains from TANK 2 by gravity at a rate of k√h₂(cm³/s) where h₁ and h₂ represent levels of TANK 1 and TANK 2, respectively (see figure). Drain valve constant k = 4 cm^2.5/s and cross-sectional areas of the two tanks are A₁ = A₂ = 28 cm².

At steady state operation, the water inlet flow rate is qss = 16 cm³/s. The transfer function relating the deviation variables

Answer: (A)

31. Choose the option that correctly matches the step response curves on the left with the appropriate transfer functions on the right. The step input change occurs at time t =0.

(A) P – III, Q – IV; R – II, S – I

(B) P – III, Q – I; R – IV, S – II

(D) P –III, Q – II; R – IV, S – I

Answer: (B)

32. 100 kg of a feed containing 50 wt.% of a solute C is contacted with 80 kg of a solvent containing 0.5 wt.% of C in a mixer-settler unit. From this operation, the resultant extract and raffinate phases contain 40 wt.% and 20 wt.% of C, respectively. If E and R denote the mass of the extract and raffinate phases, respectively, the ratio E/R is

(A) 1/4

(B) 1/2

(D) 1

Answer: (C)

33. The combination that correctly matches the process in Group-1 with the entries in Group-2 is

(A) P-II, Q-IV, R-III, S-I

(B) P-III, Q-IV, R-II, S-I

(D) P-II, Q-I, R-IV, S-III

Answer: (B)

34. If x, y and z are directions in a Cartesian coordinate system and i , j and k are the respective unit vectors, the directional derivative of the function u(x, y, z) = x² − 3yz at the point (2, 0, −4) in the direction (i + j – 2k)/√6 is _________(rounded off to two decimal places).

Answer: (6.52 to 6.54)

35. Two unbiased dice are thrown. Each dice can show any number between 1 and 6. The probability that the sum of the outcomes of the two dice is divisible by 4 is _____ (rounded off to two decimal places).

Answer: (0.24 to 0.26)

36. The Newton-Raphson method is used to determine the root of the equation f (x)= e^−x – x .If the initial guess for the root is 0, the estimate of the root after two iterations is _____ (rounded off to three decimal places).

Answer: (0.565 to 0.567)

37. Carbon monoxide (CO) reacts with hydrogen sulphide (HS) at a constant temperature of 800 K and a constant pressure of 2 bar as:

CO + H₂S ⇋ COS + H₂

The Gibbs free energy of the reaction ∆g°_rxn = 22972.3 J/mol and universal gas constant R =8.314 J/(mol K). Both the reactants and products can be assumed to be ideal gases. If initially only 4 mol of H₂S and 1 mol of CO are present, the extent of the reaction (in mol) at equilibrium is ____ (rounded off to two decimal places).

Answer: (0.27 to 0.30)

38. For a given binary system at constant temperature and pressure, the molar volume (in m³/mol) is given by: υ = 30x_A + 20x_B + x_Ax_B (15x_A – 7x_B), where x_A and x_B are the mol fractions of components A and B, respectively. The volume change of mixing ∆υ_mix (in m³/mol) at x_A = 0.5 is _____ (rounded off to one decimal place).

Answer: (0.9 to 1.1)

39. Consider a vessel containing steam at 180℃. The initial steam quality is 0.5 and the initial volume of the vessel is 1 m³. The vessel loses heat at a constant rate q under isobaric conditions so that the quality of steam reduces to 0.1 after 10 hours. The thermodynamic properties of water at 180 ℃ are (subscript 𝑔: vapor phase; subscript 𝑓: liquid phase):

The rate of heat loss q (in kJ/hour) is ____(rounded off to the nearest integer).

Answer: (810 to 840)

40. A fractionator recovers 95 mol % n-propane as the distillate from an equimolar mixture of n-propane and n-butane. The condensate is a saturated liquid at 55 ℃. The Antoine equation is of the form , and the constants are provided below:

Assuming Raoult’s law, the condenser pressure (in bar) is _____(rounded off to one decimal place).

Answer: (17.5 to 18.5)

41. A centrifugal pump is used to pump water (density 1000 kg/m³) from an inlet pressure of 10⁵ Pa to an exit pressure of 2 ×10⁵ Pa. The exit is at an elevation of 10 m above the pump. The average velocity of the fluid is 10 m/s. The cross-sectional area of the pipes at the pump inlet and outlet is 10⁻³ m² and acceleration due to gravity is g = 10 m/s² . Neglecting losses in the system, the power (in Watts) delivered by the pump is _____ (rounded off to the nearest integer).

Answer: (1990 to 2010)

42. A solid sphere of radius 1 cm and initial temperature of 25 ℃ is exposed to a gas stream at 100 ℃. For the solid sphere, the density is 104 kg/m3 and the specific heat capacity is 500 J/(kg K). The density of the gas is 0.6 kg/m³ and its specific heat capacity is 10³ J/(kg K). The solid sphere is approximated as a lumped system (Biot number ≪ 1) and all specific heats are constant. If the heat transfer coefficient between the solid and gas is 50 W/(m² K), the time (in seconds) needed for the sphere to reach 95 ℃ is _____ (rounded off to the nearest integer)

Answer: (900 to 905)

43. Stream A with specific heat capacity C_PA = 2000 J/(kg K) is cooled from 90℃ to 45℃ in a concentric double pipe counter current heat exchanger having a heat transfer area of 8 m². The cold stream B of specific heat capacity C_PB = 1000 J/(kg K) enters the exchanger at a flow rate 1 kg/s and 40℃. The overall heat transfer coefficient U = 250 W/(m²K). Assume that the mean driving force is based on the arithmetic mean temperature difference, that is, where T_{i, in} and T_{i, out} refer to the temperature of the ith stream (i = A, B) at the inlet and exit, respectively. The mass flow rate of stream A (in kg/s), is _______ (rounded off to two decimal places).

Answer: (0.30 to 0.32)

44. A 20 cm diameter cylindrical solid pellet of a nuclear fuel with density 6000 kg/m3 and conductivity of 300 W/(m K) generates heat by nuclear fission at a spatially uniform rate of 104 W/kg. The heat from the fuel pellet is transferred to the surrounding coolant by convection such that the pellet wall temperature remains constant at 300 ℃. Neglecting the axial and azimuthal dependence, the maximum temperature (in ℃) in the pellet at steady state is _____ (rounded off to the nearest integer).

Answer: (799 to 801)

45. The elementary, irreversible, liquid-phase, parallel reactions, 2A → D and 2A → U, take place in an isothermal non-ideal reactor. The C-curve measured in a tracer experiment is shown in the figure, where C(t) is the concentration of the tracer in g/m3 at the reactor exit at time t (in min).

The rate constants are k₁ = 0.2 Liter/(mol min) and k₂ = 0.3 Liter/(mol min). Pure A is fed to the reactor at a concentration of 2 mol/Liter. Using the segregated model, the percentage conversion in the reactor is ______ (rounded off to the nearest integer).

Answer: (63 to 67)

46. A first-order irreversible liquid phase reaction A → B k = 0.1 min⁻¹ is carried out under isothermal, steady state conditions in the following reactor arrangement comprising an ideal CSTR (Continuous-Stirred Tank Reactor) and two ideal PFRs (Plug Flow Reactors). From the information in the figure, the volume of the CSTR (in Liters) is ______ (rounded off to the nearest integer).

Answer: (850 to 860)

47. The elementary liquid-phase irreversible reactions take place in an isothermal ideal CSTR (Continuous-Stirred Tank Reactor). Pure A is fed to the reactor at a concentration of 2 mol/Liter. For the residence time that maximizes the exit concentration of B, the percentage yield of B, defined as , is _____(rounded off to the nearest integer).

Answer: (65 to 68)

48. The elementary irreversible gas-phase reaction A → B + C is carried out adiabatically in an ideal CSTR (Continuous-Stirred Tank Reactor) operating at 10 atm. Pure A enters the CSTR at a flow rate of 10 mol/s and a temperature of 450 K. Assume A, B and C to be ideal gases. The specific heat capacity at constant pressure ( C_pi) and heat of formation (H⁰_i ) , of component i (i = A,B, C), are:

The reaction rate constant where E = 31.4 kJ/mol and universal gas constant R =0.082 L atm/(mol K) = 8.314 J/(mol K). The shaft work may be neglected in the analysis, and specific heat capacities do not vary with temperature. All heats of formation are referenced to 273 K. The reactor volume (in Liters) for 75% conversion is ______ (rounded off to the nearest integer).

Answer: (131 to 138)

49. For the closed loop system shown in figure, the phase margin (in degrees) is ____ (rounded off to one decimal place).

Answer: (45.3 to 45.5)

50. Two spherical camphor particles of radii 20 cm and 5 cm, far away from each other, are undergoing sublimation in a stream of air. The mass transfer coefficient is proportional to 1√r(t) , where r(t) is the radius of the sphere at time t. Assume that the partial pressure of camphor far away from the surface of the particle is zero. Also, assume quasi-steady state, identical ambient conditions, and negligible heat effects. If t₁ and t₂ are the times required for complete sublimation of the 20 cm and 5 cm camphor particles, respectively, the ratiot₁/t₂ is _____(rounded off to one decimal place).

Answer: (7.9 to 8.1)

51. A countercurrent absorption tower is designed to remove 95% of component A from an incoming binary gas mixture using pure solvent B. The mole ratio of A in the inlet gas is 0.02. The carrier gas flow rate is 50 kmol/h. The equilibrium relation is given by Y = 2X, where Y and X are the mole ratios of A in the gas and liquid phases, respectively. If the tower is operated at twice the minimum solvent flow rate, the mole ratio of A in the exit liquid stream is_______(rounded off to three decimal places).

Answer: (0.004 to 0.006)

52. A binary mixture with components A and B is to be separated in a distillation column to obtain 95 mol% A as the top product. The binary mixture has a constant relative volatility α_AB = 2. The column feed is a saturated liquid containing 50 mol% A. Under the usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays, the minimum reflux ratio for this separation is ______ (rounded off to one decimal place).

Answer: (1.6 to 1.8)

53. Consider the reactor-separator-recycle process operating under steady state conditions as shown in the figure. The reactor is an ideal Continuous-Stirred Tank Reactor (CSTR), where the reaction A + B → C occurs. Assume that there is no impurity in the product and recycle streams. Other relevant information are provided in the figure. The mole fraction of B (x_B) in the reactor that minimizes the recycle rate is ______ (rounded off to two decimal places).

Answer: (0.09 to 0.11)

54. Consider two competing equipment A and B. For a compound interest rate of 10% per annum, in order for equipment B to be the economically cheaper option, its minimum life (in years) is_____ (rounded off to the next higher integer).

Answer: (8 to 8)

55. A taxi-car is bought for Rs 10 lakhs. Its salvage value is zero. The expected yearly income after paying all expenses and applicable taxes is Rs 3 lakhs. The compound interest rate is 9% per annum. The discounted payback period (in years), is ________ (rounded off to the next higher integer).

Answer: (5 to 5)