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GATE Exam 2020 Civil Engineering (CE-2) Question Paper With Answer Key

June 8, 2023April 22, 2022 by suresh84

GATE-2020

CE2: Civil Engineering

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Rescue team deployed _____ disaster hit areas combat _____ a lot of difficulties to save the people.

(A) with, at

(B) in, with

(D) to, to

Answer: (B)

2. Select the most appropriate word that can replace the underlined word without changing the meaning of the sentence:

Now-a-days, most children have a tendency to belittle the legitimate concerns of their parents.

(A) disparage

(B) applaud

(D) begrudge

Answer: (A)

3. Select the word that fits the analogy:

Partial : Impartial : : Popular : _____

(A) Impopular

(B) Dispopular

(D) Unpopular

Answer: (D)

4. After the inauguration of the new building, the Head of the Department (HoD) collated faculty preferences for office space. P wanted a room adjacent to the lab. Q wanted to be close to the lift. R wanted a view of the playground and S wanted a corner office.

Assuming that everyone was satisfied, which among the following shows a possible allocation?

Answer: (C)

5. If f(x) = x² for each x ∈ (−∞, ∞),then is equal to ______.

(A) f(x)

(B) (f(x))²

(D) (f(x))⁴

Answer: (C)

Q6 – Q10 carry two marks each.

6. Nominal interest rate is defined as the amount paid by the borrower to the lender for using the borrowed amount for a specific period of time. Real interest rate calculated on the basis of actual value (inflation-adjusted), is approximately equal to the difference between nominal rate and expected rate of inflation in the economy.

Which of the following assertions is best supported by the above information?

(A) Under high inflation, real interest rate is low and borrowers get benefited.

(B) Under low inflation, real interest rate is high and borrowers get benefited.

(D) Under low inflation, real interest rate is low and borrowers get benefited.

Answer: (A)

7. For the year 2019, which of the previous year’s calendar can be used?

(A) 2011

(B) 2012

(D) 2014

Answer: (C)

8. The ratio of ‘the sum of the odd positive integers from 1 to 100’ to ‘the sum of the even positive integers from 150 to 200’ is ______.

(A) 45 : 95

(B) 1 : 2

(D) 1 : 1

Answer: (C)

9. In a school of 1000 students, 300 students play chess and 600 students play football. If 50 students play both chess and football, the number of students who play neither is ______.

(A) 200

(B) 150

(D) 50

Answer: (B)

10. The monthly distribution of 9 Watt LED bulbs sold by two firm X and Y from January to June 2018 is shown in the pie-chart and the corresponding table. If the total number of LED bulbs sold by two firms during April-June 2018 is 50000, then the number of LED bulbs sold by the firm Y during April-June 2018 is ______.

(A) 11250

(B) 9750

(D) 8250

Answer: (MTA)

CE2: Civil Engineering

Q1 – Q25 Carry one mark each.

1. The ordinary differential equation is

(A) linear and homogeneous

(B) linear and nonhomogeneous

(D) nonlinear and nonhomogeneous

Answer: (B)

2. The value of is

(A) 7/9

(B) 1

(D) indeterminable

Answer: (C)

3. The integral is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson’s rules with a common step size. In this context, which one of the following statements is TRUE?

(A) Simpson’s rule as well as rectangular rule of estimation will give NON-zero error.

(B) Simpson’s rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.

(D) Only Simpson’s rule of estimation will give zero error.

Answer: (D)

4. The following partial differential equation is defined for u: u (x, y)

The set of auxiliary conditions necessary to solve the equation uniquely, is

(A) three initial conditions

(B) three boundary conditions

(D) one initial and two boundary conditions

Answer: (D)

5. The ratio of the plastic moment capacity of a beam section to its yield moment capacity is termed as

(A) aspect ratio

(B) load factor

(D) slenderness ratio

Answer: (C)

6. The state of stress represented by Mohr’s circle shown in the figure is

(A) uniaxial tension

(B) biaxial tension of equal magnitude

(D) pure shear

Answer: (D)

7. A weightless cantilever beam of span L is loaded as shown in the figure. For the entire span of the beam, the material properties are identical and the cross section is rectangular with constant width.

From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads amongst the options given below, is

Answer: (C)

8. As per IS 456:2000, the pH value of water for concrete mix shall NOT be less than

(A) 4.5

(B) 5.0

(D) 6.0

Answer: (D)

9. The traffic starts discharging from an approach at an intersection with the signal turning green. The constant headway considered from the fourth or fifth headway position is referred to as

(A) discharge headway

(B) effective headway

(D) saturation headway

Answer: (D)

10. Soil deposit formed due to transportation by wind is termed as

(A) aeolian deposit

(B) alluvial deposit

(D) lacustrine deposit

Answer: (A)

11. A sample of 500 g dry sand, when poured into a 2 litre capacity cylinder which is partially filled with water, displaces 188 cm³ of water. The density of water is 1 g/cm³. The specific gravity of the sand is

(A) 2.72

(B) 2.66

(D) 2.52

Answer: (B)

12. Muskingum method is used in

(A) hydrologic reservoir routing

(B) hydrologic channel routing

(D) hydraulic reservoir routing

Answer: (B)

13. Superpassage is a canal cross-drainage structure in which

(A) natural stream water flows with free surface below a canal

(B) natural stream water flows under pressure below a canal

(D) canal water flows under pressure below a natural stream

Answer: (C)

14. A triangular direct runoff hydrograph due to a storm has a time base of 90 hours. The peak flow of 60 m³/s occurs at 20 hours from the start of the storm. The area of catchment is 300 km². The rainfall excess of the storm (in cm), is

(A) 2.00

(B) 3.24

(D) 6.48

Answer: (B)

15. The velocity components in the x and y directions for an incompressible flow are given as u = (−5 + 6x) and v = −(9 + 6y), respectively. The equation of the streamline is

(A) (−5 + 6x) – (9 + 6y) = constant

(B)

(D)

Answer: (C)

16. The relationship between oxygen consumption and equivalent biodegradable organic removal (i.e., BOD) in a closed container with respect to time is shown in the figure

Assume that the rat of oxygen consumption is directly proportional to the amount of degradable organic matter and is expressed as where, L_t (in mg/litre) is the oxygen equivalent of the organics remaining at time t and k(in d⁻¹) is the degradation rate constant. L₀ is the oxygen equivalent of organic matter at time, t = 0.

In the above context, the correct expression is

(A) BOD₅ = L₅

(B) BOD_t = L₀ – L_t

(D) L_t = L₀(1 − e⁻^kt)

Answer: (B)

17. A gas contains two types of suspended particles having average sizes of 2 μm and 50 μ Amongst the options given below, the most suitable pollution control strategy for removal of these particles is

(A) settling chamber followed by bag filter

(B) elstrostatic precipitator followed by venture scrubber

(D) bag filter followed by electrostatic precipitator

Answer: (A)

18. A fair (unabised) coin is tossed 15 times. The probability of getting exactly 8 heads (round off to three decimal places), is _______.

Answer: (0.190 to 0.200)

19. The maximum applied load on a cylindrical concrete specimen of diameter 150 mm and length 300 mm tested as per the split tensile strength test guidelines of IS 5816:1999 is 157 kN. The split tensile strength (in MPa, round off to one decimal place) of the specimen is _______.

Answer: (2.0 to 2.4)

20. For an axle load of 15 tonne on a road, the Vehicle Damage Factor (round off to two decimal places), in terms of the standard axle load of 8 tonne, is _________.

Answer: (12.30 to 12.40)

21. 24-h traffic count at a road section was observed to be 1000 vehicles on a Tuesday in the month of July. If daily adjustment factor for Tuesday is 1.121 and monthly adjustment factor for July is 0.913, the Annual Average Daily Traffic (in veh/day, round off to the nearest integer) is ________.

Answer: (1021 to 1024)

22. A soil has dry unit weight of 15.5 kN/m³, specific gravity of 2.65 and degree of saturation of 72%. Considering the unit weight of water as 10 kN/m³, the water content of the soil (in %, round off to two decimal places) is ________.

Answer: (19.00 to 19.50)

23. A one-dimensional consolidation test is carried out on a standard 19 mm thick clay sample. The oedometer’s deflection gauge indicates a reading of 2.1 mm, just before removal of the load, without allowing any swelling. The void ratio is 0.62 at this stage. The initial void ratio (round of to two decimal places) of the standard specimen is________.

Answer: (0.78 to 0.88)

24. Velocity distribution in a boundary layer is given by where u is the velocity at vertical coordinate y, U_∞ is the free stream velocity and δ is the boundary layer thickness. The values of U_∞ and δ are 0.3 m/s and 1.0 m, respectively. The velocity gradient (in s⁻¹, round off to two decimal places at y = 0, is _________.

Answer: (0.45 to 0.49)

25. Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The Surface Overflow Rate (SOR) maintained in the two tanks are 30 m³/m².d and 15 m³/m².d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m³/m².d. and 15 m³/m².d are designated as d₃₀ and d₁₅, respectively. The ratio d₃₀/d₁₅ (round off two decimal places), is_________.

Answer: (1.40 to 1.42)

Q26 – Q55 carry two marks each.

26. An ordinary differential equation is given below

The general solution of the above equation (with constant C₁ and C₂)

(A) y(x) = C₁e⁻^x/3 + C₂e^x/2

(B) y(x) = C₁e^x/3 + C₂e⁻^x/2

(D) y(x) = C₁e⁻^x/3 + C₂xe^x/2

Answer: (B)

27. A 4 × 4 matrix [P] is given below

The eigenvalues of [P] are

(A) 0, 3, 6, 6

(B) 1, 2, 3, 4

(D) 1, 2, 5, 7

Answer: (D)

28. A prismatic linearly elastic bar of length of L, cross-sectional area A, and made up of a material with Young’s modulus, E, is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces P₁ and P₂, the strain energies stored in the bar are U₁ and U₂, respectively.

If U is the strain energy stored in the same bar when subjected to an axial tensile force (P₁ + P₂), the correct relationship is

(A) U = U₁ + U₂

(B) U = U₁ – U₂

(D) U > U₁ + U₂

Answer: (D)

29. The planar structure RST shown in the figure is roller-supported at S and pin-supported at R. Members RS and ST have uniform flexural rigidity (EI) and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening.

When the structure is subjected to a concentrated horizontal load P at the end, T, the magnitude of rotation at the support R, is

(A) PL³/12EI

(B) PL²/12EI

(D) PL/6EI

Answer: (B)

30. Joints, I, J, K, L, Q and M of the frame shown in the figure (not down to the scale are pins. Continuous members IQ and LJ are connected through a pin at N. Continuous members JM and KQ are connected through a pin at P. the frame has hinge supports at joints R and S. The loads acting at joints I, J and K are along the negative Y direction and the loads acting at joints L and M are along the positive X direction.

The magnitude of the horizontal component of reaction (in kN) at S, is

(A) 5

(B) 10

(D) 20

Answer: (C)

31. The flow-density relationship of traffic on a highway is shown in the figure

The correct representation of speed-density relationship of the traffic on this highway is

Answer: (C)

32. Group-I gives a list of test methods for evaluating properties of aggregates. Group-II gives the list of properties to be evaluated.

The correct match test methods under Group-I to properties under Group-II, is

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

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

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

Answer: (B)

33. For the hottest month of the year at the proposed airport site, the monthly mean of the average daily temperature is 39° The monthly mean of the maximum daily temperature is 48°C for the same month of the year. From the given information, the calculated Airport Reference Temperature (in °C), is

(A) 36

(B) 39

(D) 48

Answer: (C)

34. Permeability tests were carried out on the samples collected from two different layers as shown in the figure (not drawn to the scale). The relevant horizontal (k_h) and vertical (k_v) coefficients of permeability are indicated for each layer.

The ratio of the equivalent horizontal to vertical coefficients of permeability, is

(A) 37.29

(B) 80.20

(D) 0.03

Answer: (A)

35. A 10 m high slope of dry clay soil (unit weight = 20 kN/m³), with a slope angle of 45° and the circular slip surface, is shown in the figure (not drawn to the scale). The weight of the slip wedge is denoted by W. The undrained unit cohesion (c_u) is 60 kPa.

The factor of safety of the slope against slip failure, is

(A) 1.84

(B) 1.57

(D) 1.67

Answer: (MTA)

36. Crops are grown in a field having soil, which has field capacity of 30% and permanent wilting point of 13%. The effective depth of root zone is 80 cm. Irrigation water is supplied when the average soil moisture drops to 20%. Consider density of the soil as 1500 kg/m³ and density of water as 1000 kg/m³. If the daily consumptive use of water for the crops is 2 mm, the frequency of irrigating the crops (in days), is

(A) 7

(B) 10

(D) 13

Answer: (MTA)

37. Alkalinity of water, in equivalent/litre (eq/litre), is given by

{HCO₃⁻} + 2 {CO₃²⁻} + {OH⁻] – {H⁺}

Where, {} represents concentration in mol/litre. For a water sample, the concentrations of HCO₃⁻ = 2 × 10⁻³ mol/litre, CO₃²⁻ = 3.04 × 10⁻⁴ mol/litre and the pH of water = 9.0. The atomic weights are: Ca = 40; C = 12; and O = 16. If the concentration of OH⁻ and H⁺ are NEGLECTED, the alkalinity of the water sample (in mg/litre as CaCO₃), is

(A) 130.4

(B) 100.0

(D) 65.2

Answer: (A)

38. A theodolite was set up at a station P. The angle of depression to a vane 2 m above the foot of a staff held at another station Q was 45°. The horizontal distance between stations P and Q is 20 m. The staff reading at a benchmark S or RL 433.050 m is 2.905 m. Neglecting the errors due to curvature and refraction, the RL o the station Q (in m), is

(A) 413.050

(B) 413.955

(D) 435.955

Answer: (B)

39. The Fourier series to represent x – x² for –π ≤ x ≤ π is given by

The value of a₀ (round off to two decimal places), is _________.

Answer: (-6.61 to -6.55)

40. The diameter and height of a right circular cylinder are 3 cm and 4 cm, respectively. The absolute error in each of these two measurements is 0.2 cm. The absolute error in the computed volume (in cm³, round off to three decimal places), is ________.

Answer: (5.180 to 5.200)

41. A concrete beam of span 15 m, 150 mm wide and 350 mm deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of friction for the cable is 0.35, and coefficient of wave effect is 0.0015 per meter.

If the cable is tensioned from one end only, the percentage loss (round off to one decimal place) in the cable force due to friction, is _______.

Answer: (3.8 to 4.7)

42. The plane truss has hinge supports at P and W and is subjected to the horizontal forces as shown in the figure (not drawn to the scale)

Representing the tensile force with ‘+’ sign and the compressive force with ‘−’ sign, the fore in member XW (in kN, round off to the nearest integer), is ________.

Answer: (-31 to -29)

43. The cross-section of the reinforced concrete beam having an effective depth of 500 mm is shown in the figure (not drawn to the scale). The grades of concrete and steel used are M35 and Fe550, respectively. The area of tension reinforcement is 400 mm². It is given that corresponding to 0.2% proof stress, the material safety factor is 1.15 and the yield strain of Fe550 steel is 0.0044.

As per IS 456:2000, the limiting depth (in mm, round off to the nearest integer) of the neutral axis measured from the extreme compression fiber, is_______.

Answer: (220 to 224)

44. Two steel plates are lap jointed in a workshop using 6 mm thick fillet weld as shown in the figure (not drawn to the scale). The ultimate strength of the weld is 410 MPa.

As per limit State Design of IS 800:2007, the design capacity (in kN, round off to three decimal places) of the welded connection, is ______.

Answer: (400 to 420)

45. The design speed of a two-plane two-way road is 60 km/h and the longitudinal coefficient of friction is 0.36. The reaction time of a driver is 2.5 seconds. Consider acceleration due to gravity as 9.8 m/s². The intermediate sight distance (in m, round off to the nearest integer) required for the road is _______.

Answer: (154 to 178)

46. A footing of size 2 m × 2 m transferring a pressure of 200 kN/m², is placed at a depth of 1.5 m below the ground as shown in the figure (not drawn to the scale). The clay stratum is normally consolidated. The clay has specific gravity of 2.65 and compression index of 0.3.

Considering 2:1 (vertical to horizontal) method of load distribution and γ_w = 10 kN/m³, the primary consolidation settlement (in mm, round off to two decimal places) of the clay stratum is _______.

Answer: (74.00 to 76.00)

47. A constant-head permeability test was conducted on a soil specimen under a hydraulic gradient of 2.5. The soil specimen has specific gravity of 2.65 and saturated water content of 20%. If the coefficient of permeability of the soil is 0.1 cm/s, the seepage velocity (in cm/s, round off to two decimal places) through the soil specimen is ______.

Answer: (0.70 to 0.73)

48. A 5 m high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are 18 kN/m³ and 20 kPa, respectively. The angle of internal friction of clay is zero. In order to prevent development of tension zone, the height of the wall is required to be increased. Dry sand is used as backfill above the clay for the increased portion of the wall. The unit weight and angle of internal friction of sand are 16 kN/m³ and 30°, respectively. Assume that the back of the wall is smooth and top of the backfill is horizontal. To prevent the development of tension zone, the minimum height (in m, round off to one decimal place) by which the wall has to be raised, is _______.

Answer: (2.4 to 2.6)

49. A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s². The velocity of the flow in pipe (in m/s, round off to two decimal places) is ________.

Answer: (2.40 to 2.70)

50. A hydraulic jump occurs in a triangular (V-shaped) channel with side slopes 1:1 (vertical to horizontal). The sequent depths are 0.5 m and 1.5 m. The flow rate (in m³/s, round off to two decimal places) in the channel is ________.

Answer: (1.70 to 1.76)

51. A concrete dam holds 10 m of static water as shown in the figure (not drawn to the scale). The uplift is assumed to vary linearly from full hydrostatic head at the heel, to zero at the toe of dam. The coefficient of friction between the dam and foundation soil is 0.45. Specific weights of concrete and water are 24 kN/m³ and 9.81 kN/m³, respectively.

For NO sliding condition, the required minimum base width B (in m, round off to two decimal places) is ________.

Answer: (15.00 to 16.00)

52. The ion product of water (pK_w) is 14. If a rain water sample has a pH of 5.6, the concentration of OH⁻ in the sample (in 10⁻⁹ mol/litre, round off to one decimal place), is _________.

Answer: (3.8 to 4.1)

53. A waste to energy plant burns dry solid waste of composition: Carbon = 35%. Oxygen = 26%, Hydrogen = 10%, Sulphur = 6%, Nitrogen = 3% and Inerts = 20%. Burning rate is 1000 tonnes/d. Oxygen in air by weight is 23%. Assume complete conversion of Carbon to CO₂, Hydrogen to H₂O Sulphur to SO₂ and Nitrogen to NO₂.

Given Atomic weights: H = 1, C = 12, N = 14, O = 16, S = 32

The stoichiometric (theoretical) amount of air (in tones/d, round off to the nearest integer) required for complete burning of this waste, is________.

Answer: (6963 to 6967)

54. A sample of water contains an organic compound C₈H₁₆O₈ at a concentration of 10⁻³ mol/litre. Given that the atomic weight of C = 12 g/mol, H = 1 g/mol, and O = 16 g/mol, the theoretical oxygen demand of water (in g of O₂ per litre, round off to two decimal places), is _______.

Answer: (0.24 to 0.27)

55. A theodolite is set up at station A. The RL of instrument axis is 212.250 m. The angle of elevation to the top of a 4 m long staff, held vertical at station B, is 7°. The horizontal distance between stations A and B is 400 m. Neglecting the errors due to curvature of earth and refraction, the RL (in m, round off to three decimal places) of station B is_________.

Answer: (257.200 to 257.600)

GATE Exam 2020 Civil Engineering (CE-1) Question Paper With Answer Key

June 8, 2023April 22, 2022 by suresh84

GATE-2020

CE1: Civil Engineering

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. It is a common criticism that most o the academicians live in their ______, so, they are not aware of the real life challenges.

(A) homes

(B) ivory towers

(D) big flats

Answer: (B)

2. His hunger for reading is insatiable. He reads indiscriminately. He is most certainly a/an _____ reader.

(A) all-round

(B) precocious

(D) wise

Answer: (C)

3. Select the word that fits the analogy:

Fuse : Fusion :: Use : ______

(A) Usage

(B) User

(D) Usion

Answer: (A)

4. If, 0, 1, 2, …….. 7, 8, 9 are coded as O, P, Q, …., V, W, X, then 45 will be coded as _______.

(A) TS

(B) ST

(D) SU

Answer: (B)

5. The sum of two positive numbers is 100. After subtracting 5 from each number, t he product of the resulting numbers is 0. One of the original numbers is ______.

(A) 80

(B) 85

(D) 95

Answer: (D)

Q6 – Q10 carry two marks each.

6. The American psychologist Howard Gardner expounds that human intelligence can be subcategorized into multiple kinds, in such a way that individuals differ with respect to their relative competence in each kind. Based on this theory, modern educationists insist on prescribing multi-dimensional curriculum and evaluation parameters that enable development and assessment of multiple intelligences.

Which of the following statements can be inferred from the given text?

(A) Howard Gardner insists that the teaching curriculum and evaluation needs to be multidimensional.

(B) Howard Gardner wants to develop and assess the theory of multiple intelligences.

(D) Modern educationists insist that the teaching curriculum and evaluation needs to be multi-dimensional.

Answer: (D)

7. Five friends P, Q, R, S and T went camping. At night, they had to sleep in a row inside the tent. P, Q and T refused to sleep next to R since he snored loudly. P and S wanted to avoid Q as he usually hugged people in sleep.

Assuming everyone was satisfied with the sleeping arrangements, what is the order in which they slept?

(A) RSPTQ

(B) SPRTQ

(D) QTSPR

Answer: (A)

8. Insert seven numbers between 2 and 34, such that resulting sequence including 2 and 34 is an arithmetic progression. The um of these inserted seven numbers is ______.

(A) 120

(B) 124

(D) 130

Answer: (C)

9. The unit’s place in 26591749¹¹⁰⁰¹⁶is ______.

(A) 1

(B) 3

(D) 9

Answer: (A)

10. The total expenditure of a family, on different activities in a month, is shown in the pie-chart. The extra money spent on education as compared to transport (in percent) is _____.

(A) 5

(B) 33.3

(D) 100

Answer: (C)

CE1: Civil Engineering

Q1 – Q25 carry one mark each.

1. In the following partial differential equation, θ is a function of t and z, and D and K are functions of θ

The above equation is

(A) a second order linear equation

(B) a second degree linear equation

(D) a second degree non-linear equation

Answer: (C)

2. The value of is

(A) 0

(B) 1/4

(D) 1

Answer: (B)

3. The true value of ln(2) is 0.69. If the value of ln(2) is obtained by linear interpolation between ln(1) and ln(6), the percentage of absolute error (round of to the nearest integer), is

(A) 35

(B) 48

(D) 84

Answer: (B)

4. The area of an ellipse represented by an equation is

(A) πab/4

(B) πab/2

(D) 4πab/3

Answer: (C)

5. Consider the planar truss shown in the figure (not drawn to the scale)

Neglecting self-weight of the members, the number of zero-force members in the truss under the action of the load P, is

(A) 6

(B) 7

(D) 9

Answer: (C)

6. A reinforcing steel bar, partially embedded in concrete, is subjected to a tensile force P. The figure that appropriately represents the distribution of the magnitude of bond stress (represented as hatched region), along the embedded length of the bar, is

Answer: (C)

7. In a two-dimensional stress analysis, the state of stress at a point P is

The necessary and sufficient condition for existence of the state of pure shear at the point P, is

(A)

(B) τ_xy = 0

(D)

Answer: (C)

8. During the process of hydration of cement, due to increase in Dicalcium Silicate (C₂S) content in cement clinker, the heat of hydration

(A) increases

(B) decreases

(D) does not change

Answer: (B)

9. The Los Angeles test for stone aggregates is used to examine

(A) abrasion resistance

(B) crushing strength

(D) specific gravity

Answer: (A)

10. Which one of the following statements is NOT correct?

(A) A clay deposit with a liquidity index greater than unity is in a state of plastic consistency.

(B) The cohesion of normally consolidated clay is zero when triaxial test is conducted under consolidated undrained condition.

(C) The ultimate bearing capacity of a strip foundation supported on the surface of sandy soil increases in direct proportion to the width of footing.

(D) In case of a point load, Boussinesq’s equations predicts higher value of vertical stress at a point directly beneath the load as compared to Westergaard’s equation.

Answer: (A)

11. In a soil investigation work at a site, Standard Penetration Test (SPT) was conducted at every 1.5 m interval up to 30 m depth. At 3 m depth, the observed number of hammer blows for three successive 150 mm penetrations were 8, 6 and 9 respectively. The SPT N-value at 3 m depth, is

(A) 23

(B) 17

(D) 14

Answer: (C)

12. Velocity of flow is proportional to the first power of hydraulic gradient in Darcy’s law. This law is applicable to

(A) laminar flow in porous media

(B) transitional flow in porous media

(D) laminar as well as turbulent flow in porous media

Answer: (A)

13. A body floating in a liquid is in a stable state of equilibrium if its

(A) metacentre lies above its centre of gravity

(B) metacentre lies below its centre of gravity

(D) centre of gravity is below its centre of bouyancy

Answer: (A)

14. Uniform flow with velocity U makes an angle θ with the y-axis, as shown in the figure

The velocity potential (ϕ), is

(A) ±U(x sin θ + y cos θ)

(B) ±U(y sin θ − x cos θ)

(D) ±U(y sin θ + x cos θ)

Answer: (A)

15. The data an agricultural field for a specific month are given below:

Pan Evaporation = 100 mm

Effective Rainfall = 20 mm (after deducting losses due to runoff and deep percolation)

Crop Coefficient = 0.4

Irrigation Efficiency = 0.5

The amount of irrigation water (in mm) to be applied to the field in that month, is

(A) 0

(B) 20

(D) 80

Answer: (C)

16. During chlorination process, aqueous (aq) chlorine reacts rapidly with water to form Cl⁻, HOCl, and H⁺ as shown below

Cl₂ (aq) + H₂O ⇌ HOCl + Cl⁻ + H⁺

The most active disinfectant in the chlorination process from amongst the following, is

(A) H⁺

(B) HOCl

(D) H₂O

Answer: (B)

17. An amount of 35.67 mg HCl is added to distilled water and the total solution volume is made to one litre. The atomic weights of H and Cl are 1 and 35.5, respectively. Neglecting the dissociation of water, the pH of the solution, is

(A) 3.50

(B) 3.01

(D) 2.01

Answer: (B)

18. The probability that a 50 year flood may NOT occur at all during 25 years life of a project (round of to two decimal places), is ______.

Answer: (0.59 to 0.61)

19. A planar elastic structure is subjected to uniformly distributed load, as shown in the figure (not drawn to the scale)

Neglecting self-weight, the maximum bending moment generated in the structure (in kN.m round off to the nearest integer), is _________.

Answer: (95 to 97)

20. In an urban area, a median is provided to separate the opposing streams of traffic. As per IRC:86-1983, the desirable minimum width (in m, expressed as integer) of the median, is _______.

Answer: (5 to 5)

21. A road in a hilly terrain is to be laid at a gradient of 4.5%. A horizontal curve of radius 100 mm is laid at a location on this road. Gradient needs to be eased due to combination of curved horizontal and vertical profiles of the road. As per IRC, the compensated gradient (in %, round off to one decimal place), is _______.

Answer: (4.0 to 4.0)

22. In a drained triaxial compression test, a sample of sand fails at deviator stress of 150 kPa under confining pressure of 50 kPa. The angle of internal friction (in degree, round of to the nearest integer) of the sample, is _______.

Answer: (36 to 38)

23. A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m³ and 38°, respectively. The unit weight of water is 10 kN/m³. Assume that seepage is parallel to the slope. Against shear failure of the slope. the factor of safety (round off to two decimal places) is _______.

Answer: (0.59 to 0.61)

24. A 4 m wide rectangular channel carries 6 m³/s of water. The Manning’s ‘n’ of the open channel is 0.02. Considering g = 9.81 m/s², the critical velocity of flow (in m/s, round off to two decimal places) in the channel, is _________.

Answer: (2.35 to 2.55)

25. A river has a flow of 1000 million litres per day (MLD), BOD₅ of 5 mg/litre and Dissolved Oxygen (DO) level of 8 mg/litre before receiving the wastewater discharge at a location. For the existing environmental conditions, the saturation DO level is 10 mg/litre in the river. Wastewater discharge of 100 MLD with the BOD₅ of 200 mg/litre and DO level of 2 mg/litre falls at that location. Assuming complete mixing of wastewater and river water, the immediate DO deficit (in mg/litre round off to two decimal places), is ________.

Answer: (2.45 to 2.65)

Q26 – Q55 carry two marks each.

26. For the Ordinary Differential Equation with initial conditions x(0) = 0 and the solution is

(A) −5e^2t + 6e^3t

(B) 5e^2t + 6e^3t

(D) 10e^2t + 10e^3t

Answer: (C)

27. A continuous function f(x) is defined. If the third derivative at x_i is to be computed by using the fourth order central finite-divided-difference scheme (with step length = h), the correct formula is

Answer: (A)

28. Distributed load(s) of 50 kN/m may occupy any position(s) (either continuously or in patches) in the girder PQRST as shown in the figure (not drawn to the scale)

The maximum negative (hogging) bending moment (in kN.m) that occurs at point R is

(A) 22.50

(B) 56.25

(D) 150.00

Answer: (B)

29. A rigid weightless platform PQRS shown in the figure (not drawn to the scale) can slide freely in the vertical direction. The platform is held in position by the weightless member OJ and four weightless, frictionless rollers. Points O and J are pin connections. A block of 90 kN rests on the platform as shown in the figure

The magnitude of horizontal component of the reaction (in kN) at pin O, is

(A) 90

(B) 120

(D) 180

Answer: (B)

30. A cantilever beam PQ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at R as shown in the figure

The deflection at the free end Q is

(A) ML²/6EI

(B) ML²/4EI

(D) 3ML²/4EI

Answer: (C)

31. A dowel bar is placed at a contraction joint. When contraction occurs, the concrete slab cracks at predetermined location(s). Identify the arrangement, which shows the correct placement of dowel bar and the place of occurrence of the contraction crack(s).

Answer: (B)

32. The relationship between traffic flow rate (q) and density (D) is shown in the figure

The shock wave condition is depicted by

(A) flow with respect to point 1 (q₁ = q_max)

(B) flow changing from point 2 to point 6 (q₂ > q₆)

(D) flow with respect to point 4 and point 5 (q₄ = q₅)

Answer: (MTA)

33. The appropriate design length of a clearway is calculated on the basis of ‘Normal Take-off’ condition. Which one of the following options correctly depicts the length of t he clearway? (Note : None of the options are drawn to scale)

Answer: (C)

34. The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below

The correct match between the stress paths and the listed loading conditions, is

(A) OP – I, OQ – II, OR – IV, OS – III

(B) OP – IV, OQ – III, OR – I, OS – II

(D) OP – I, OQ – III, OR – II, OS – IV

Answer: (B)

35. The soil profile at a suite up to a depth of 10 m is shown in the figure (not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of 70 kN/m² at the ground level. The water table is at a depth of 3 m below ground level. The soil unit weight of the respective layers is shown in the figure. Consider unit weight of water as 9.81 kN/m³ and assume that the surcharge (q) is applied instantaneously.

Immediately after preloading, the effective stresses (in kPa) a points P and Q, respectively, are

(A) 124 and 204

(B) 36 and 90

(D) 54 and 95

Answer: (D)

36. Water flows at the rate of 12 m³/s in a 6 m wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is 30 cm (just before the jump). Considering acceleration due to gravity as 9.81 m/s² and density of water as 1000 kg/m³, the energy loss in the jump is

(A) 114.2 kW

(B) 114.2 MW

(D) 141.2 J/s

Answer: (A)

37. A water supply scheme transports 10 MLD (Million Litres per Day) water through a 450 mm diameter pipeline for a distance of 2.5 km. A chlorine dose of 3.50 mg/litre is applied at the starting point of the pipeline to attain a certain level disinfection at the downstream end. It is decided to increase the flow rate from 10 MLD 13 MLD in the pipeline. Assume exponent for concentration, n = 0.86. With this increased flow, in order to attain the same level of disinfection, the chlorine dose (in mg/litre) to be applied at the starting point should be

(A) 3.95

(B) 4.40

(D) 5.55

Answer: (C)

38. An open traverse PQRST is surveyed using theodolite and the consecutive coordinates obtained are given in the table

If the independent coordinates (Northing, Easting) of station P are (400 m, 200 m), the independent coordinates (in m) of station T, are

(A) 194.7, 370.1

(B) 205.3, 429.9

(D) 405.3, 229.9

Answer: (C)

39. If C represents a line segment between (0, 0, 0) and (1,1, 1) in Cartesian coordinate system, the value (expressed as integer) of the line integral ∫_c[(y + z)dx + (x + z)dy + (x + y)dz] is _______.

Answer: (3 to 3)

40. Consider the system of equations

The value of x₃ (round off to the nearest integer), is ______.

Answer: (3 to 3)

41. A rigid, uniform, weightless, horizontal bar is connected to three vertical members P, Q and R as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of 10 kN/mm. The lower ends of bars P and R rest on a rigid horizontal surface. When NO load is applied, a gap of 2 mm exists between the lower end of the bar Q and the rigid horizontal surface. When a vertical load W is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displaced by 5 mm in the vertically downward direction.

The magnitude of the load W (in kN, round off to the nearest integer), is ________.

Answer: (129 to 131)

42. The flange and web plates of the doubly symmetric built-up section are connected by continuous 10 mm thick fillet welds as shown in the figure (not drawn to the scale). The moment of inertial of the section about its principal axis X-X is 7.73 × 10⁶ mm⁴. The permissible shear stress in the fillet welds is 100 N/mm². The design shear strength of the section is governed by the capacity of the fillet welds.

The maximum shear force (in kN, round off to one decimal place) that can be carried by the section, is_______.

Answer: (393.5 to 399.1)

43. The singly reinforced concrete beam section shown in the figure ( not drawn to the scale) is made of M25 grade concrete and Fe500 grade reinforcing steel. The total cross-sectional area of the tension steel is 942 mm².

As per Limit State Design of IS 456:2000, the design moment capacity (in kN.m, round of to two decimal places) of the beam section, is ________.

Answer: (158.00 to 158.80)

44. A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zeo at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.

Answer: (39 to 41)

45. Traffic volume count has been collected on a 2-lane road section which needs upgradation due to severe traffic flow condition. Maximum service flow rate per lane is observed as 1280 veh/h at level of service ‘C’. The Peak Hour Factor is reported as 0.78125. Historical traffic volume count provides Annual Average Daily Traffic as 12270 veh/day. Directional spilt of the traffic flow is observed to be 60:40. Assuming that traffic stream consists of ‘All Cars’ and all drivers are ‘Regular Commuters’, the number of extra lane(s) (round off to the next higher integer) to be provided, is _______.

Answer: (MTA)

46. A vertical retaining wall of 5 m height has to support soil having unit weight of 18 kN/m³, effective cohesion of 12 kN/m², and effective friction angle of 30°. As per Rankine’s earth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in kN/m, round off to two decimal places), is_______.

Answer: (21.00 to 23.00)

47. Water flows in the upward direction in a tank through 2.5 m thick sand layer as shown in the figure. The void ratio and specific gravity of sand are 0.58 and 2.7, respectively. The sand is fully saturated. Unit weight of water is 10 kN/m³.

The effective stress (in kPa, round off to two decimal places) at point A, located I am above the base of tank, is _______.

Answer: (8.70 to 9.30)

48. A 10 m thick clay layer is resting over a 3 m thick sand layer and is submerged. A fill of 2 m thick sand with unit weight of 20 kN/m³ is placed above the clay layer to accelerate the rate of consolidation of the clay layer. Coefficient of consolidation of clay is 9 × 10⁻² m²/year and coefficient of volume compressibility of clay is 2.2 × 10⁻⁴ m²/kN. Assume Taylor’s relation between time factor and average degree of consolidation.

The settlement (in mm, round off to two decimal places) of the clay layer, 10 years after the construction of the fill, is ______.

Answer: (18.40 to 19.50)

49. Three reservoirs P, Q and R are interconnected by pipes as shown in the figure (not drawn to the scale). Piezometric head at the junction S of the pipes is 100 m. Assume acceleration due to gravity as 9.81 m/s² and density of water as 1000 kg/m³. The length of the pipe from junction S to the inlet of reservoir R is 180 m.

Considering head loss only due to friction (with friction factor of 0.03 for all the pipes), the height of water level in the lowermost reservoir R (in m, round off to one decimal place) with respect to the datum, is ________.

Answer: (97.2 to 97.8)

50. In a homogenous unconfined aquifer of area 3.00 km², the water table was at an elevation of 102.00 m. After a natural recharge of volume of 0.90 million cubic meter (Mm³), the water table rose to 103.20 m. After this recharge, ground water pumping took place and the water table dropped down to 101.20 m. The volume of ground water pumped after the natural recharge, expressed (in Mm³ and round of to two decimal places), is ________.

Answer: (1.40 to 1.60)

51. A circular water tank of 2 m diameter has circular orifice of diameter 0.1 m at the bottom. Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice. The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s² and neglect frictional losses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ________.

Answer: (0.50 to 0.54)

52. Surface overflow Rate (SOR) of a primary settling tank (discrete settling) is 20000 litre/m² per day. Kinematic viscosity of water in the tank is 1.01 × 10⁻² cm²/s. Specific gravity of the settling particles is 2.64. Acceleration due to gravity is 9.81 m/s². The minimum diameter (in μm, round off to one decimal place) of the particles that will be removed with 80% efficiency in the tank, is ______.

Answer: (14.0 to 15.0)

53. A gaseous chemical has a concentration of 41.6 μmol/m³ in air at 1 atm pressure and temperature 293 K. The universal gas constant R is 82.05 × 10⁻⁶ (m³ atm)/(mol K). Assuming that ideal gas law is valid, the concentration of the gaseous chemical (in ppm, round off to one decimal place), is _______.

Answer: (0.9 to 1.1)

54. A steam with a flow rate of 5 m³/s is having an ultimate BOD of 0 mg/litre. A wastewater discharge of 0.20 m³/s having BOD₅ of 500 mg/litre joins the stream at a location and instantaneously gets mixed up completely. The cross-sectional area of the stream is 40 m² which remains constant. BOD exertion rate constant is 0.3 per day (logarithm base to e). The BOD (in mg/litre, round off to two decimal places) remaining at 3 km downstream from the mixing location, is _______.

Answer: (49.00 to 50.00)

55. The lengths and bearings of a traverse PQRS are:

The length of line segment SP (in m, round off to two decimal places), is _________.

Answer: (44.00 to 45.00)

GATE Exam 2020 Biotechnology (BT) Question Paper With Answer Key

June 8, 2023April 22, 2022 by suresh84

GATE-2020

BT-Biotechnology

GA-General Aptitude

Q1-Q5 carry one mark each.

1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.

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

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6-Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

BT: Biotechnology

Q1 – Q25 carry one mark each.

1. Protein P becomes functional upon phosphorylation of a serine residue. Replacing this serine with _____ will result in a phophomimic mutant of P.

(A) alanine

(B) aspartic acid

(D) lysine

Answer: (B)

2. Ras protein is a

(A) trimeric GTPase involved in relaying signal from cell surface to nucleus.

(B) monomeric GTPase involved in relaying signal from cell surface to nucleus.

(D) monomeric GTPase involved in regulation of cytoskeleton.

Answer: (B OR D)

3. Which of the following statements are CORRECT?

[P] Viruses can play a role in causing human cancer

[Q] A tumor suppressor gene can be turned off without any change in its DNA sequence

[R] Alteration in miRNA expression levels contributes to the development of cancer

(A) P and Q only

(B) Q and R only

(D) P, Q and R

Answer: (D)

4. Which class of antibody is first made by developing B cells inside bone marrow?

(A) IgG

(B) IgE

(D) IgM

Answer: (D)

5. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r] regarding mammalian cells.

Assertion [a]: Cells use Ca²⁺, and not Na⁺, for cell-to-cell signaling

Reason [r]: In the cytosol, concentration of Na⁺ is lower than that of Ca²⁺

(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)

6. Vincristine and vinblastine, two commercially important secondary metabolites from Catharanthus roseus, are examples of

(A) alkaloids.

(B) flavonoids.

(D) steroids.

Answer: (A)

7. DNA synthesized from and RNA template is called

(A) recombinant DNA.

(B) transcript.

(D) complementary DNA.

Answer: (D)

8. Two monomeric His-tagged proteins of identical molecular weight are present in a solution.pIs of these two proteins are 5.6 and 6.8. Which one of the following techniques can be used to separate them?

(A) Denaturing polyacrylaminde gel electrophoresis

(B) Size-exclusion chromatography

(D) Nickel affinity chromatography

Answer: (C)

9. During a positive-negative selection process, transformed animal cells expressing ________ are killed in presence of ganciclovir in the medium.

(A) pyruvate kinase

(B) viral thymidine kinase

(D) viral tyrosine kinase

Answer: (B)

10. A vector derived from which one of the following viruses is used to high-frequency genomic integration of a transgene in animal cells?

(A) Adenovirus

(B) Adeno-associated virus

(D) Herpes simplex virus

Answer: (C)

11. Which one of the following statements about Agrobacterium Ti plasmid is CORRECT?

(A) Vir genes are located within the T-DNA segment

(B) Phytohormone biosynthesis genes are located outside the T-DNA segment

(D) Opine biosynthesis genes are located within the T-DNA segment

Answer: (D)

12. Which of the following types of molecules act as biological catalysts?

[P] Protein

[Q] RNA

[R] Phospholipid

(A) P and Q only

(B) P and R only

(D) P, Q and R

Answer: (A)

13. Which one of the following media components is used to maintain pH in mammalian cell culture?

(A) CaCl₂

(B) MgSO₄

(D) NaHCO₃

Answer: (D)

14. Which of the following are energy transducing membranes?

[P] Plasma membrane of bacteria

[Q] Inner membrane of chloroplasts

[R] Inner membrane of mitochondria

(A) P and Q only

(B) P and R only

(D) P, Q and R

Answer: (B)

15. Amino acid sequences of cytochrome c and ribulose 5-phosphate epimerase from 40 organsims were chosen and phylogenetic trees were obtained for each of these two protein families.

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

Assertion [a]: The two trees will not be identical

Reason [r]: The nature and frequency of mutations in the two families are different

(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: (A)

16. A microorganism isolated from a salt-rich (salt concentration~2 M) lake was found to posses diglycerol tetraethers, with polyisoprenoid alcohol side chains, as the major lipid component of its cell membrane. The isolated organism is

(A) a planctomycete.

(B) a cyanobacteria.

(D) an archaea.

Answer: (D)

17. A function f is as follows:

The function f is continuous function when c is equal to ______ (answer is an integer).

Answer: (15 to 15)

18. Given that Z= X² + Y², the value of and Y = 0 is _______(answer is an integer).

Answer: (2 to 2)

19. The elemental composition of dry biomass of a yeast species is CH₆O_0.4N_0.2S_0.0024P_0.017, The contribution of carbon to the dry biomass is _________% (round off to 2 decimal places).

[Given: atomic weights of H, C, N, O P and S are 1, 12, 14, 16, 31 and 32, respectively]

Answer: (51.01 to 52.99)

20. Solvents A and B are completely immiscible. Solute S is soluble in both these solvents. 100 g of S was added to a container which has 2 kg each of A and B. The solute is 1.5 times more soluble in solvent A than in solvent B. The mixture was agitated thoroughly and allowed to reach equilibrium. Assuming that the solute has completely dissolved, the amount of solute in solvent A phase is ______g.

Answer: (60 to 60)

21. The number of molecules of a nucleotide of molecular weight 300 g/mol present in 10 picomoles is ______ × 10² (round off to 2 decimal places).

Answer: (5.99 to 6.05)

22. To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius r is introduced into the liquid. The gas bubble then breaks into 8 bubbles of equal radius. Upon this change, the ratio of the interfacial surface area to the gas phase volume for the system changes form 3/r to 3n/r. The value of n is ________.

Answer: (2 to 2)

23. The largest eigenvalue of the matrix is _______.

Answer: (3 to 3)

24. A normal random variable has mean equal to 0, and standard deviation equal to 3. The probability that on a random draw the value of this random variable is greater than 0 is _________ (round off 2 decimal places).

Answer: (0.49 to 0.51)

25. A variable Y is a function of t. Given that Y (t = 0) = 1 and Y(t = 1) = 2, in the interval t = [0, 1] can be approximated as ______.

Answer: (1 to 1)

Q26 – Q55 carry two marks each.

26. A block of ice at 0°C is supplied heat at a constant rate to convert ice to superheated steam. Which one of the following trajectories correctly represents the trend of the temperature of the system with time? Assume that the specific heat of H₂O is not a function of temperature.

Answer: (A)

27. The DNA sequence shown below is to be amplified by PCR:

Which one of the following pair of primers can be used for this amplification?

Answer: (B)

28. Which of the following statements about immune response are CORRECT?

[P] T cells are activated by antigen-presenting cells

[Q] Foreign peptides are not presented to helper T cells by Class II MHC proteins

[R] Dendritic cells are referred to as professional antigen-presenting cells

(A) P and R only

(B) P and Q only

(D) P, Q and R

Answer: (A)

29. Which of the following statements are CORRECT about eukaryotic cells cycle?

[P] CDKs can phosphorylate proteins in the absence of cyclins

[Q] CDKs can be inactivated by phosphorylation

[R] Degradation of cyclins is required for cell cycle progression

[S] CDKs are not involved in chromosome condensation

(A) P and R only

(B) P and S only

(D) Q and R only

Answer: (D)

30. W, X and Y are the intermediates in a biochemical pathway as shown below:

Mutants auxotrophic for Z are found in four different complementation groups, namely Z1, Z2, Z3 and Z4. The growth of these mutants on media supplemented with W, X, Y, or Z is shown below (Yes: growth observed; No: growth not observed):

What is the order of the four complementation groups in terms of the step they block?

Answer: (B)

31. In tomato plant, red (R) is dominant over yellow (r) for fruit color and purple (P) is dominant over green (p) for stem color. Fruit color and stem color assort independently. The number of progeny plants of different fruit/stem colors obtained from a mating are as follows:

Red fruit, purple stem – 145

Red fruit, green stem – 184

Yellow fruit, purple stem – 66

Yellow fruit, green stem – 47

What are the genotypes of the parent plants in this mating?

(A) RrPp × Rrpp

(B) RrPp × RrPp

(D) RrPP × Rrpp

Answer: (A)

32. Some of the cytokinins used in plant tissue culture media are given blow:

[P] BAP

[Q] Zeatin

[R] Kinetin

[S] 2iP

Which of these are synthetic analogs?

(A) P and Q only

(B) Q and S only

(D) P and R only

Answer: (D)

33. Carl Woese used the gene sequence of which one of the following for phylogenetic taxonomy of prokaryotes?

(A) A ribosomal RNA of large ribosomal subunit

(B) A ribosomal RNA of small ribosomal subunit

(D) A ribosomal protein of small ribosomal subunit

Answer: (B)

34. A list of pathogens (Group I) and a list of anti-microbial agents (Group II) used to treat their infections are given below. Match the pathogens with the corresponding anti-microbial agents.

(A) P-4, Q-3, R-2, S-5

(B) P-5, Q-2, R-4, S-1

(D) P-2, Q-3, R-1, S-5

Answer: (C)

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

Assertion [a]: Dam metylase protects E. coli DNA from phage endonucleases

Reason [r]: E. coli dam methylase methylates the adenosine residue in the sequence “GATC”

(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: (D)

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

Assertion [a]: Embryonic stem cells are suitable for developing knockout mice

Reason [r]: Homologous recombination is more frequent in embryonic stem cells than that in somatic cells

(A) Both [a] and [r] are false

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

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

Answer: (B)

37. The schematic of a plasmid with a gap in one of the strands is shown below:

Which of the following enzyme(s) is/are required to fill the gap and generate a covalently closed circular plasmid?

[P] DNA ligase

[Q] Alkaline phosphatase

[R] DNA polymerase

[S] Polynucleotide kinase

(A) P only

(B) P, R and S only

(D) P, Q and R only

Answer: (B)

38. Match sub-cellular organelles listed in Group I with their features listed in Group II:

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

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

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

Answer: (C)

39. Which of the following strategies are used by cells for metabolic regulation?

[P] Phosphorylation-dephosphorylation

[Q] Allostery

[R] Feedback inhibition

(A) P and Q only

(B) P and R only

(D) P, Q and R

Answer: (D)

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

Assertion [a]: A zygote and its immediate descendant cells are unspecialized and are called totipotent

Reason [r]: Totipotent cells retain the capacity to differentiate into only a few cell types

(A) Both [a] and [r] are false

(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)

41. Which of the following statements about gene therapy are CORRECT?

[P] Affected individuals, but not their progeny, can be cured through germline gene therapy

[Q] Affected individuals, as well as their progeny, can be cured through germline gene therapy

[R] Affected individuals, but not their progeny, can be cured through somatic gene therapy

[S] Affected individuals, as well as their progeny, can be cured through somatic gene therapy

(A) P and R only

(B) P and S only

(D) Q and S only

Answer: (C)

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

Assertion [a]: A genetically engineered rice that produces beta-carotene in the rice grain is called Golden rice

Reason [r]: Enabling biosynthesis of provitamin A in the rice endosperm gives a characteristic yellow/orange color

(A) Both [a] and [r] are false

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

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

Answer: (C)

43. The sequence of a 1 Mb long DNA is random. This DNA has all four bases occurring in equal proportion. The number of nucleotides, on average, between two successive EcoRI recognition site GAATTC is______.

Answer: (4096 to 4096)

44. E. Coli was grown in ¹⁵N medium for several generations. Cells were then transferred to ¹⁴N medium, allowed to grow for 4 generations and DNA was isolated immediately. The proportion of total DNA with intermediate density is ________ (round off to 2 decimal places).

Answer: (0.11 to 0.14)

45. A batch reactor is inoculated with 1 g/L biomass. Under these conditions, cells exhibit a lag phase of 30 min. If the specific growth rate in the log phase is 0.00417 min⁻¹, the time taken for the biomass to increase to 8 g/L is _______ min (round off to 2 decimal places).

Answer: (526.01 to 529.99)

46. The system of linear equations

cx + y = 5

3x + 3y = 6

has no solution when c is equal to _______.

Answer: (1 to 1)

47. The amino acid sequence of a peptide is Phe-Leu-Ile-Met-Ser-Leu. The number of codons that encode the amino acids present in this peptide is given below:

Phe: 2 codons

Leu: 6 codons

Ile: 3 codons

Met: 1 codon

Ser: 4 codons

The number of unique DNA sequences that can encode this peptide is________.

Answer: (864 to 864)

48. Assume that a cell culture was started with five human fibroblast cells. Two cells did not divide even once whereas the other three cells completed three rounds of cell division. At this stage, the total number of kinetochores in all the cells put together is _______.

Answer: (1196 to 1196)

49. Growth of an organism on glucose in a chemostat is characterized by Monod model with specific growth rate = 0.45 h⁻¹ and K_s = 0.5 g/L. Biomass from the substrate is generated as Y_XS = 0.4 g/g. The chemostat volume is 0.9 L and media is fed at 1 L/h and contains 20 g/L of glucose. At steady state, the concentration of biomass in t he chemostat is _______ g/L.

Answer: (0 to 0)

50. A function f is given as: f(X) = 4X – X²

The function f is maximized when X is equal to _______.

Answer: (2 to 2)

51. An infinite series S is given as:

S = 1 + 2/3 + 3/9 + 4/27 + 5/81 + ….. (to infinity)

The value of S is ________ (round off to 2 decimal places).

Answer: (2.20 to 2.30)

52. Protein A and protein B form a covalent complex. Gel filtration chromatography of this complex showed a peak corresponding to 200 kDa. SDS-PAGE analysis of this complex, with and without beta-mercaptoethanol, showed a single band corresponding to molecular weight 50 and 25 kDa, respectively. Given that the molecular weight of protein A is 25 kDa, the molecular weight of protein B is ______ kDa.

Answer: (25 to 25)

53. The concentrations of ATP, ADP and inorganic phosphate in a cell are 2.59, 0.73 and 2.72 mM, respectively. Under these conditions, free energy change for the synthesis of ATP at 37°C is _____ kJ/mol (round off to 2 decimal places).

Given: free energy change for ATP hydrolysis under standard condition is −30.5 kJ/mol and R = 8.315 kJ/mol.K

Answer: (48.50 to 49.50 OR 18521.20 to 18521.30)

54. An algorithm was designed to find globins in protein sequence databases. A database which as 78 globin sequences was searched using this algorithm. The algorithm retrieved 72 sequences of which only 65 were globins. The sensitivity of this algorithm is ________% (round off to 2 decimal places).

Answer: (83.30 to 83.40)

55. The mitochondrial electron transfer chain oxidizes NADH with oxygen being the terminal electron acceptor. The redox potentials for the two half-reactions are given below:

The free energy change associated with the transfer of electrons from NADH to O₂ is ______ kJ/mol (round off to 2 decimal places).

Given: F = 96500 C/mol.

Answer: (-219.30 to -219.20)

GATE Exam 2020 Biomedical Engineering (BM) Question Paper With Answer Key

June 8, 2023April 20, 2022 by suresh84

GATE-2020

BM: Biomedical Engineering

GA-General Aptitude

Q1-Q5 carry one mark each.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

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

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6-Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

BM: Biomedical Engineering

Q1 – Q25 carry one mark each.

1. m₁ and m₂ are the roots of the characteristic equation of a linear second order physical system. Match the nature of the roots with the natural response of the system.

(A) P-L, Q-M, R-K

(B) P-M, Q-L, R-K

(D) P-M, Q-K, R-L

Answer: (C)

2. A person is sitting in a chair with feet on the ground. While rising up on his feet, the kinematic motion NOT occurring is

(A) Hip extension

(B) Plantar flexion

(D) Knee extension

Answer: (C)

3. The equipment that measures elasticity of blood vessel in vivo is

(A) Rheometer

(B) Dimension anlayser

(D) Dynamic mechanical analyser

Answer: (B)

4. Biomaterials with shape memory effects are NOT used in

(A) Intracranial aneurysm clips

(B) Arterial blood vessel closure devices

(D) Orthodontic dental arch wires

Answer: (C)

5. The MRI scanner parameter of long T_Rep or short T_Echo will generate a ________contrast image

(A) Proton Density-weighted

(B) T2-weighted

(D) T2^*-weighted

Answer: (MTA)

6. In diagnostic X-ray imaging, the following is NOT a part of primary EM radiation interaction in soft tissue.

(A) Photoelectric effect

(B) Characteristic radiation production

(D) Pair-production

Answer: (B OR D)

7. A 5 MHz ultrasound pulse is used to image a tumor at a depth of 2 cm in a soft tissue. It takes time t for the reflected echo from the tumor to come back to the receiver. Instead, if a 2.5 MHz wave is used, how long will it take for the echo from the same tumor to arrive at the receiver?

(A) t/2

(B) t

(D) 4t

Answer: (B)

8. X(s) is the Laplace transform of a signal x(t).

The Laplace transform of assuming x(0) = 0, is

(A) sX(s)

(B) X(s)/s

(D)

Answer: (A)

9. Which of the following are odd functions?

P: Sin(t)

Q: Cos(t)

R: Sin(t) + Cos(t)

(A) Q and S

(B) P and Q

(D) R and Q

Answer: (C)

10. State-space model of a system is given as:

The conditions for the system to be controllable are

(A) a = 0, b ≠ 0

(B) a ≠, b = 0

(D) a = 0, b = 0

Answer: (C)

11. In microprocessor systems with memory mapped I/O, which of the following is true?

(A) Only I/O devices with internal memory can be interfaced.

(B) I/O devices can be accessed using IN and OUT instructions

(D) Arithmetic and logic operations cannot be directly performed with the I/O data

Answer: (C)

12. The number of electrodes used in recording standard 12-lead Electrocardiogram (ECG)

(A) 13

(B) 12

(D) 10

Answer: (D)

13. Which of the following is NOT a part of knee joint?

(A) Patella

(B) Tibia

(D) Fibula

Answer: (D)

14. During a routine stethoscopic examination at the left midclavicular-5^th intercostals space, murmurs were noted between first and second heart sound. The possible abnormality among the following could be

(A) Aortic stenosis

(B) Mitral regurgitation

(D) Aortic regurgitation

Answer: (B)

15. The thin filament of a muscle fiber is comprised of

(A) Troponin, Tropomyosin, Actin

(B) Troponin, Tropomyosin, Titin

(D) Actin, Mysoin, Troponin

Answer: (A)

16. The value of the integral evaluated over the contour C : |z| = 3/2 is ________

Answer: (-1.1 to -0.9)

17. The eigenvalues of a 3 × 3 non-singular matrix P are 1, 2 and 3. The trace of matrix P⁻¹ (rounded off to two decimal places) is _______

Answer: (1.82 to 1.84)

18. The following recursion relation, when started from a finite positive non-zero value, converges to ______

Answer: (1 to 1)

19. In a nuclear imaging system, Sodium Iodide (NaI) crystals are used to detect gamma rays of 120 keV. The percentage (%) of gamma-rays that will pass through 1 cm of NaI crystal, assuming the Half-Value-Layer (HVL) of NaI as 0.2 cm, is ________ (rounded off to one decimal place).

Answer: (3.0 to 3.2)

20. The distal end of an endoscope is placed at a distance of 1 mm from the gastrointestinal wall. The refractive indices of the fiber core and cladding are 1.5 and 1.45, respectively.

The maximum field of view for the endoscope is _______ degrees (rounded off to one decimal place).

Answer: (44 to 46)

21. Two inductors with the details given below are wound separately on two identical ring type ferromagnetic cores.

The ratio L₂/L₁ is ______.

Answer: (4 to 4)

22. Two days X and Y having concentrations in the ratio 0.25 in identical cuvettes were subjected to absorption measurements in a spectrophotometer. The estimated ratio of their absorbance is 0.5. The ratio of their molar extinction coefficients is ______.

Answer: (2 to 2)

23. Hydrolysis of one ATP molecule provides an energy of _______ kilo calories (correct up to one decimal place).

Answer: (7.25 to 7.35)

24. An 830 nm laser Doppler flow meter probe is oriented at an angle of 60° to the flow axis. If the average flow velocity is 3 cm/s, the magnitude of Doppler shift frequency (kHz) is ________ (rounded off to one decimal place).

Answer: (35.8 to 36.4)

25. A 100 mA single current pulse from a pulse generator is used for artificial pacing of heart at the right ventricle. If the delivered energy does not exceed the fibrillation threshold of 300 μJ, the safe duration of the pulse that could be applied to the tissue mass having an impedance of 500 Ω is ________ μ

Answer: (60 to 60)

Q26 – Q55 carry two marks each.

26. The resting potential of a mammalian nerve cell is −80 mV. A certain drug administered to the body changes the intracellular K⁺ concentration from 150 mmol/L to 55 mmol/L. The nearest value of cell membrane potential after the drug administration, assuming that the external equilibrium of K⁺ does not get changed during the event, is

(Gas constant = 8.315 J/mol/K, core temperature = 37°C and Faraday constant = 96500 C/mol)

(A) −117 mV

(B) −18.71 mV

(D) −141.30 mV

Answer: (C)

27. The arrangement of four resistors of equal value in the diaphragm of a physiological pressure measurement catheter is shown below. The applied pressure is observed to cause an increase in length of resistors R2, R4 and an increase in cross sectional area in R1 and R3. The operation results in an equal change in the values of all four resistors. Which among the configuration given below should be used to connect the resistors to form a Wheatstone bridge so that bridge output voltage is proportional to the change in resistance of individual resistors?

(A) I only

(B) II only

(D) Both I and II

Answer: (A)

28. For the given input voltage, V_in = 10 sin (2πt) to the functional circuit shown below, the output signal will be

Answer: (D)

29. During a non-invasive measurement of blood pressure, mean arterial pressure was observed to be 100 mm Hg. If systolic pressure is 150 mm Hg, the diastolic pressure would be

(A) 110 mm Hg

(B) 75 mm Hg

(D) 50 mm Hg

Answer: (B)

30. Two loads are connected to AC supply mains as depicted in the figure. One load draws 10 kW whereas the other load of 10 kVA is operated at 0.6 pf lagging. To achieve an overall power factor of 0.9544 lagging, the nearest kVAr rating of the capacitor bank needed to be connected across the supply mains is equal to

(A) 3

(B) 5

(D) 9

Answer: (A)

31. The nearest value of power dissipated in the 3Ω resistance in the circuit is

(A) 3 W

(B) 25/3 W

(D) 25/12 W

Answer: (A)

32. A second order low pass filter is being constructed by cascading two first order low pass filters with the following transfer functions

where ω₁ and ω₂ are the respective 3dB cut off frequencies.

The undamped natural frequency ω_c of the resulting second order low pass filter is

(A)

(B)

(C)

(D)

Answer: (A)

33. Match the bridge type with the application given below:

(A) P-L, Q-K, R-N, S-M

(B) P-N, Q-K, R-L, S-M

(D) P-L, Q-M, R-N, S-K

Answer: (A)

34. For a non-unity feedback system with the magnitude of steady-state error to a unit step-input is

(A) 0.50

(B) 0.45

(D) 0.20

Answer: (D)

35. Match the Boolean expression with its minimal realization

(A) P-K, Q-L, R-N, S-M

(B) P-L, Q-K, R-N, S-M

(D) P-M, Q-K, R-L, S-N

Answer: (B)

36. The glomerulus filtration process of kidney is modeled as a flat membrane with pores of radius 1 nm and length of pore 60 nm. The viscosity of the fluid is 0.002 Pa s. The aggregate area of the pores makeup 5% of total surface area of the membrane. The average pressure on the blood side of the membrane is 8000 Pa and on the ultrafiltrate side is 6200 Pa. The total available area of membrane is 1.5 m². The nearest value of resulting filtration rate in cm³/min is

(A) 0.14

(B) 1.40

(D) 84.37

Answer: (C)

37. During resting state, the voltage outside the cell membrane compared to that inside the membrane is _______. Under such conditions, the intracellular and extracellular regions have _______ and ________ concentrations, respectively.

(A) Moe positive, more Potassium [K⁺], more Sodium [Na⁺]

(B) More negative, more Potassium [K⁺], more Sodium [Na⁺]

(D) More positive, more Sodium [Na⁺], more Potassium [K⁺]

Answer: (A)

38. The tensile strength of a degradable suture used for a surgical procedure in the human body is observed to decrease exponentially from its original strength by 40% and 50% after 10 days and 20 days, respectively. The closest approximation of the time taken for the tensile strength to decay to 20% of its original value would be

(A) 35 days

(B) 45 days

(D) 70 days

Answer: (D)

39. A 60 kg person is standing on one foot on force plate. The ground reaction force is found to act 40 mm anterior to the ankle joint. The mass center of a foot is 60 mm from the Trochanter Knee Ankle (TKA) line. If the weight of the foot is 0.8 kg, the closest value of magnitude of moment acting on the ankle joint is

(A) 23 Nm

(B) 48 Nm

(D) 466 Nm

Answer: (A)

40. The temperature of bone cement is increased from 37°C to 87°C during the femoral hip arthroplasty. The cement thickness is noted to be 20 mm. The stress developed due to exothermic reaction of bone cement during the polymerization process and shrinkage of the bone cement, respectively, are

Assume that

(i) bone, cement, and implant are modeled as a set of concentric cylinders

(ii) no direct adhesion takes place between bone and cement

(iii) temperature is uniform

Coefficient of thermal expansion of bone cement = 90 × 10⁻⁶/°C

Young’s modulus of bone cement = 3.5 GPa

(A) 15.75 MPa, 90 μm

(B) 15.75 MPa, 110 μm

(D) 6.85 MPa, 90 μm

Answer: (A)

41. A patient is initially imaged in a 1 Tesla MRI scanner and induced voltage is found to be equal to V₁. The expression for the magnitude of the received voltage in RF coil is given below.

|V| = 2πγ₀V_SM₀ (Sin α) β^r

V_S : MR slice volume, M₀: Magnitude of resultant magnetic vector at equilibrium,

γ₀ : Larmor frequency, α: tip angle, β^r : Magnetic field sensitivity of receive coil.

When the patient is shifted to a 3 Tesla MRI scanner that uses the same RF coil and the slice thickness is halved, the magnitude of the induced voltage was found to be equal to V₂. The ratio V₂/V₁ is

(A) 1.5

(B) 3.0

(D) 6.0

Answer: (C)

42. A 3 MHz ultrasound transducer transmits a 3-cycle long pulse into a soft tissue at normal incidence to fat and liver interface. The axial resolution (mm) and the amplitude reflection coefficient at fat-liver interface, respectively, are

Use C_tissue = 1500 m/s, C_fat = 1450 m/s, C_liver = 1570 m/s, ρ_flat = 920 kg/m³, ρ_liver = 1060 kg/m³

(A) 0.5, 0.22

(B) 0.75, 0.22

(D) 0.75, 0.11

Answer: (D)

43. The forward biased current of a silicon (SI) diode is being calculated from the exponential model of the V-I characteristics. If the diode current I_D = 1 mA at a voltage drop V_D = 0.7 V, the nearest value of I_D when V_D = 0.8 V is

Assume thermal voltage V_T = 25.3 mV for Si diode

(A) 0.133 mA

(B) 2 mA

(D) 90 mA

Answer: (C)

44. A continuous random variable x has a probability density function given by f(x) = e^−α^|x| (−∞ < x < ∞)

where α is a real constant. The variance of x is _______ (correct up to one decimal place).

Answer: (0.5 to 0.5)

45. The magnitude of the gradient of the function f(x, y) = x² + y² at the point (1, 1) is ________ (rounded off to two decimal places).

Answer: (2.8 to 2.9)

46. The value of following double integral is ________ (correct up to three decimal places).

∬_R xy dxdy

where R is the first quadrant of the circle with center at the origin and radius of one unit.

Answer: (0.125 to 0.125)

47. A gynaeocologist recorded the blood pressure (BP) of patients as shown in the Table below. Using Regression processes, the diastolic BP of a 38 year old patient (mm Hg) is ______ (rounded off to two decimal places).

Answer: (86.5 to 87.7)

48. A person in standing position first flexes the hip by 50° from the initial Trochanter knee ankle (TKA) line and then flexes knee by 20°. The distance of ankle joint from the initial TKA line is _____ (rounded off to nearest integer).

(i) the distance between hip joint and knee joint is 400 mm

(ii) the distance between knee joint and ankle joint is 300 mm.

Answer: (456 to 457)

49. A chest radiograph of 36 cm × 48 cm is digitized. If we want to preserve details in the image to a spatial resolution of 6 cycles/mm, the approximate image data size in MB for an 8 bit quantization is _______ (rounded off to two decimal places).

Answer: (23.70 to 23.75)

50. An X-ray radiography scenario is shown in the figure. If the number of incident photons (N_i) is equal to 2 × 10⁶ at 50 keV, the number of photons (N_d) that exit the tissue is ______ × 10⁶ (rounded off to two decimal places).

(use linear attenuation coefficient for soft tissue and blood at 50 keV as 0.4 cm⁻¹ and 0.2 cm⁻¹, respectively)

Answer: (0.5 to 0.6)

51. The wavelength of an electron accelerated to a potential of 1V is ________ nm (rounded off to two decimal places).

Mass of electron = 9.11 × 10⁻³¹ kg

Planck’s constant, h = 6.63 × 10⁻³⁴ Js

Charge of electron = 1.6 × 10⁻¹⁹ C

Answer: (1.20 to 1.25)

52. In a permanent magnetic moving coil (PMMC) instrument having following specifications, the angular deflection of the pointer for a coil current of 100 μA will be _______ degrees (rounded off to one decimal place).

Magnetic flux density = 1.5 Tesla

Torsional spring constant = 2 × 10⁻⁶ Nm/deg

Cross sectional area of the coil = 2.5 cm²

Number of turns of the coil = 500

Answer: (9.0 to 9.6)

53. Arterial blood extracted from a healthy adult showed an oxygen partial pressure value of 40 mm Hg. The total oxygen content in the arterial blood measured in %V/V is ________ (rounded off to one decimal place).

Given : Solubility of oxygen in blood = 0.003 ml/mm Hg/dL

Hemoglobin oxygen saturation = 95%

Oxygen carrying capacity of Hb = 1.34 ml/g

Arterial blood hemoglobin concentration = 15 g/dL

Answer: (19.2 to 19.4)

54. In the process of measure blood flow from an artery using C-clamp magnetic flow probe, the voltage recorded across diametrically opposite sites of the artery is 3.75 nV. The blood flow rate through the artery is _____ cm³/s (rounded off to two decimal places).

The inner diameter of the C-clamp = 0.5 cm,

The magnetic flux density = 1.5 × 10⁻⁵ Wb/m².

Answer: (0.95 to 0.99)

55. A cell is injected with a current i(t) = u(t) to produce a change in the intracellular membrane voltage v(t). The cell-membrane is modeled as a linear system with impulse response h(t) = Ae⁻^t/^τ u(t). The cell membrane voltage output at 5 ms is _______ mV.

Use A = −34 V/s; τ = 3 ms.

Answer: (-84 to -81)

GATE Exam 2020 Architecture and Planning (AR) Question Paper With Answer Key

June 8, 2023April 20, 2022 by suresh84

GATE-2020

AR-Architecture and Planning

GA-General Aptitude

Q1 – Q5 carry one mark each.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

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

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

AR: Architecture and Planning

Q1 – Q25 carry one mark each

1. In the architectural style of ancient North Indian Temples, the term ‘Adhisthana’ refers to

(A) Pinnacle

(B) Base Platform

(D) Transept

Answer: (B)

2. Who among the following architects has NOT won the Pritzker Architecture Prize till 2019>

(A) Arata Isozaki

(B) I. M. Pei

(D) Moshe Safdie

Answer: (A OR D)

3. The stone used in the construction of Kailasa temple at Ellora is

(A) Limestone

(B) Marble

(D) Basalt

Answer: (D)

4. Four vertical lines having same thickness appear to be of the same height in perspective as shown in the figure. Which line actually has the maximum height?

(A) 1

(B) 2

(D) 4

Answer: (B)

5. As per URDPFI Guidelines 2015, Government of India, choose the correct hierarchy of plans higher to lower order.

(A) Perspective plan, Development plan, Regional plan, Zonal plan

(B) Perspective plan, Regional plan, Development plan, Zonal plan

(D) Zonal plan, Development plan, Regional plan, Perspective plan

Answer: (B)

6. Which of the following shapes can be used as an interlocking paver block without adding any other shape?

(A) 1

(B) 2

(D) 4

Answer: (C)

7. In India, the Constitution (Seventy Fourth Amendment) Act, 1992, delegates powers to institutions forming the third tier of government, which are

(A) Municipal Corporation, Municipality and Nagar Panchayat

(B) Development Authority, Municipal Corporation and Municipality

(D) Development Authority, Improvement Trust and Panchayat

Answer: (A)

8. As on 2018, ‘Right to Property’ in India is a

(A) Fundamental Right

(B) Secondary Right

(D) Tertiary Right

Answer: (C)

9. ‘Tendon’ is primarily used

(A) as a compression member

(B) to pre-stress concrete

(D) to prepare a tender document

Answer: (B)

10. Emergency preparedness for risk reduction does NOT include

(A) rescue

(B) relief distribution

(D) revision of code

Answer: (D)

11. If Beam : Column :: Transom : X,

which of the following options can replace ‘X’ ?

(A) Balustrade

(B) Sill

(D) Ceiling

Answer: (C)

12. The correct chronological order of the given architectural movements is

(A) Romanesque; Roman; Baroque; Gothic; Renaissance

(B) Romanesque; Roman; Renaissance; Gothic; Baroque

(D) Roman; Romanesque; Gothic; Baroque; Renaissance

Answer: (C)

13. The decay of sound in a large room is indicated in the following figure. The spike within the dashed zone denotes

(A) Flutter echo

(B) Perfect sound diffusion

(D) Early reflection

Answer: (C)

14. For the same thickness of material layers, relative position of insulation in the wall sections 1 and 2 shown below will have an impact on

(A) Thermal Time Constant

(B) Thermal Conductivity

(D) Thermal Transmittance

Answer: (A)

15. The solar altitude angle on April 16 at 7 : 00 AM in Kochi is 16°. The same solar altitude angle will occur at the same time in the same year at the same location on

(A) July 21

(B) August 27

(D) October 21

Answer: (B)

16. In a perspective drawing, the picture Plane is in between the Object and the Observer. If the Observer comes closer straight towards the Picture Plane, without changing the distance between Object and Picture Plane, the perspective image will be

(A) Bigger than the previous image

(B) Smaller than the previous image

(D) Will become the mirror image of the previous

Answer: (B)

17. Shyam-Rai temple of Bishnupur in West Bengal, is an example of

(A) Nava-ratna terracotta temple

(B) Stone carved Nagara type temple

(D) Stone carved Dravidian type temple

Answer: (C)

18. Which one of the following is NOT a land use zone?

(A) Industrial Zone

(B) Agriculture Zone

(D) Commercial Zone

Answer: (C)

19. ‘Formulation of GIS based master plan’ is a sub-scheme of

(A) Atal Mission for Rejuvenation and Urban Transformation

(B) Smart Cities Mission

(D) Shyama Prasad Mukherji Rurban Mission

Answer: (A)

20. One hectare is equal to

(A) 4000 m²

(B) 4048 m²

(D) 10000 m²

Answer: (D)

21. One of the sites added to the list of UNESCO World Heritage Sites in 2019 is

(A) Walled City, Ahmedabad

(B) Walled City, Jaipur

(D) Fatehpur Sikri

Answer: (B)

22. In the given contour map, the angle at ‘A’ (in degrees, rounded off to two decimal places) is ________

Answer: (18.2 to 18.5)

23. A 1.2 m high window is located on a south facing wall. The solar azimuth angle is equal to the wall azimuth angle and the solar altitude angle is 60°. The minimum depth (in metres, rounded off to two decimal places) of overhand required to completely shade the window is_______

(Assume that the overhang is located at the lintel level of the window)

Answer: (0.68 to 0.70)

24. In the given figure, the area of the shaded portion is_________

Answer: (8 to 8)

25. Average density of a highway is 25 vehicles per km. Average volume of the vehicles on the highway is 520 vehicles per hour. The mean speed (in km/hour, rounded off to one decimal place) is _________

Answer: (20.8 to 20.8)

Q26 – Q55 Carry two marks each.

26. Match the terminologies of Munsell colour wheel in Group I with their corresponding descriptions in Group II

(A) P-2, Q-4, R-5, S-1

(B) P-4, Q-2, R-5, S-3

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

Answer: (B)

27. Match the plant forms in Group I with the botanical names in Group II, as per ‘A Handbook of Landscape’, CPWD 2013, Government of India

(A) P-1, Q-5, R-2, S-3

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

(D) P-1, Q-3, R-4, S-5

Answer: (C)

28. Match the images of gardens in Group I with their names in Group II

(A) P-5, Q-3, R-1, S-4

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

(D) P-3, Q-2, R-4, S-5

Answer: (B)

29. Match the Architects in Group I with their projects in Group II

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

(B) P-2, Q-5, R-4, S-1

(D) P-3, Q-4, R-5, S-2

Answer: (A)

30. Match the graphical representations in Group I with corresponding elements in Group II

(A) P-1, Q-2, R-3, S-5

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

(D) P-2, Q-1, R-4, S-5

Answer: (D)

31. Based on the psychrometric chart given below, match the vector in Group I with the respective process in Group II

(A) P-4, Q-1, R-5, S-2

(B) P-4, Q-3, R-1, S-5

(D) P-3, Q-1, R-5, S-2

Answer: (A)

32. Match the software tools in Group I with their primary applications in Group II

(A) P-2, Q-5, R-4, S-3

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

(D) P-2, Q-4, R-5, S-1

Answer: (A)

33. Match the structural form in Group I with their corresponding illustration in Group II

(A) P-2, Q-4, R-5, S-1

(B) P-2, Q-4, R-1, S-5

(D) P-4, Q-1, R-5, S-2

Answer: (A)

34. Match the books in Group I with the corresponding authors in Group II

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

(B) P-4, Q-1, R-5, S-3

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

Answer: (B)

35. Match the name of tactile paving in Group I with their patterns in Group II

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

(B) P-3, Q-5, R-4, S-1

(D) P-2, Q-5, R-1, S-4

Answer: (C)

36. Match the name of architects in Group I with the buildings designed by them in Group II

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

(B) P-2, Q-5, R-1, S-3

(D) P-4, Q-5, R-1, S-3

Answer: (B)

37. Match the terms in Group I with the parameters in Group II

(A) P-2, Q-5, R-4, S-1

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

(D) P-3, Q-4, R-5, S-1

Answer: (A)

38. Match the structural system in Group I with their potential causes of failure in Group II

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

(B) P-1, Q-3, R-5, S-2

(D) P-3, Q-5, R-4, S-1

Answer: (A)

39. Match the brick masonry bond type in Group I with the corresponding illustration in Group II

(A) P-2, Q-1, R-4, S-5

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

(D) P-4, Q-1, R-2, S-5

Answer: (D)

40. Mach the characteristics in Group I with the type of settlements in Group Ii as given in URDPFI Guidelines 2015, Government of India

(A) P-4, Q-3, R-1, S-5

(B) P-3, Q-5, R-1, S-4

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

Answer: (D)

41. A population of 2500 persons requires a minimum area of 3000 m² for primary schools. For the population in four different sectors given in the table below, the Sector having maximum shortage of school area per person is_______

Answer: (3 to 3)

42. Number of married couples in a household along with number of rooms (for a household) are given in the table. Assuming each married couple needs one separate room, the total number of additional rooms required for them is ________

Answer: (5214 to 5214)

43. In a residential complex , the central play area is to be converted as a detention pond for storm water management. For a 24 hour rainfall event of 100 mm, 100% storm water of central play area and 70% storm water run-off from rest of the complex is to be held at detention pond. Area distribution in the residential complex is given in the table.

Answer: (760 to 760)

44. In the plot shown below, ‘S1’ and ‘S2’ are two non-directional point sources, having a sound intensity level of 95 dB and 60 dB, respectively, at a distance of 1 m from each point source. Considering free field conditions, the effective sound intensity level at the receiver location ‘R’ (in dB, rounded off to two decimal places) is _________

Answer: (75.00 to 79.00)

45. A room measures 5m × 10m × 3m (L×B×H). Consider the following conditions,

Total solar radiation incident on the root surface = 800 W/m²

Outdoor air temperature = 40°C

Outside film coefficient of the root surface = 18 W/m²

The outdoor mean radiant temperature is equal to outdoor air temperature

The minimum reduction required in solar absorptance of the roof (rounded off to two decimal places) to achieve a 20° reduction in sol-air temperature is _______

Answer: (0.43 to 0.47)

46. The activity duration, early start, early finish, late start and late finish of the three activities ‘P’, ‘Q’ and ‘R’ are shown in the following figure. The independent float of activity ‘Q’ is ________

Answer: (1 to 1)

47. A square based regular pyramid has all sides equal to 10 units. Its height (in the same units, rounded off to two decimal places) is ________

Answer: (7.00 to 7.10)

48. A parking area measuring 52m ×67 m is approached through a driveway as shown in the given illustration. The parking is designed at an angle of 30° with the parking by of 2.5m × 5m.

The number of cars that can be parked in the designated parking area considering no car overshoots the length of the parking area is _______

Answer: (9 to 10)

49. Plan and section of an isolated foundation is given below. The volume of concrete up to Ground Level (GL) (in m³, rounded off to two decimal places) is ______

Answer: (3.10 to 3.40)

50. Top floor of a 25 story building is using a flush valve system with a minimum fixture pressure of 1.0 kg/cm². If static pressure increases by 0.3 kg/cm² per metre length and friction loss is zero, then height of bottom of the water tank from the top fixture (in metres, rounded off to two decimal places) is ________

Answer: (3.30 to 3.40)

51. In a single phase alternate current circuit, an electric lamp is rated 100 watts. If 220 volts is impressed on it and the power factor is 0.85, the energy (in watt hour, rounded off to one decimal place) delivered in an hour is ______

Answer: (100 to 100)

52. A simply supported RCC beam of cross section 0.4 m ×6 m covers a span of 8 m. It is subjected to a uniformly distributed load of 30 kN/m. If the unit weight of concrete is 24 kN/m³, the tensile stress (in N/mm², rounded off to two decimal places) at the bottom of the beam at mid-span is_______

Answer: (11.80 to 12.00)

53. A basement wall resists lateral pressure exerted by soil and water. The soil pressure amounts to 4.5 kN/m² for every metre of depth below Ground Level (GL). The subsoil water level is 1.0 m below GL and hydrostatic pressure of water is 9.8 kN/m² for every metre of depth below GL. The total lateral pressure (in kN/m², rounded off to one decimal place) exerted on the wall 2 m below GL is _______

Answer: (14.3 to 18.8)

54. Assuming that the population growth trend given in the table will continue, the population (in persons) for the year 2031 will be_________

Answer: (484315 to 484316)

55. A developer would like to select a residential plot of 3000 m² for group housing in a city. Different options with varying development controls are given. In every group housing plot, 15% of the Floor Area Ratio (FAR) over and above the maximum permissible FAR has to be utilized for Economically Weaker Section (EWS) units. The maximum built-up area (in m²) available from the options given below is_________

Answer: (10350 to 10350)

GATE Exam 2020 Agricultural Engineering (AG) Question Paper With Answer Key

June 8, 2023April 20, 2022 by suresh84

GATE-2020

AG : Agricultural Engineering

General Aptitude

Q 1 – Q5 Carry one mark each.

1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.

(A) in, of

(B) from, of

(D) from, from

Answer: (A)

2. He was not only accused of theft ______ of conspiracy.

(A) rather

(B) but also

(D) rather than

Answer: (B)

3. Select the word that fits the analogy:

Explicit : Implicit : : Express: _______

(A) Impress

(B) Repress

(D) Suppress

Answer: (B)

4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.

The French-speaking couple were upset at ______.

(A) the in-flight announcements being made in English.

(B) the English announcements being clearer than the French ones.

(D) equal importance being given to English and French.

Answer: (C)

5. A superadditive function f (∙) satisfies the following property

f(x₁ + x₂) ≥ f(x₁) + f(x₂)

Which of the following functions is a superadditive function for x > 1?

(A) e^x

(B) √x

(D) e⁻^x

Answer: (A)

Q6 – Q10 carry two marks each.

6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.

Which one of the following sequences shows the correct precedence as per the given passage?

(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.

(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.

(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.

Answer: (A)

7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

(A) 0°

(B) 7.5°

(D) 22.5°

Answer: (B)

8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.

(A) πa² – a²

(B) πa² – √2a²

(D) πa² – 3a²

Answer: (C)

9. a, b, c are real numbers. The quadratic equation ax² – bx + c = 0 has equal roots, which is β, then

(A) β = b/a

(B) β² = ac

(D) b² ≠ 4ac

Answer: (C)

10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .

(A) 8 : 23

(B) 23 : 8

(D) 31 : 23

Answer: (B)

AG: Agricultural Engineering

Q1 – Q25 carry one mark each.

1. The function f(x) = x⁴ – 4x³ + 6x² – 4x + 1 has a

(A) Maxima at x = 0

(B) Minima at x = 0

(D) Minima at x = 1

Answer: (D)

2. A linear system of equations has n unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are r₁ and r₂, respectively. The condition for the equations to be consist with a unique solution is

(A) r₁ ≠ r₂ < n

(B) r₁ = r₂ = n

(D) r₁ ≠ r₂ > n

Answer: (B)

3. General solution to the ordinary differential equation, is

(A) C₁e⁻^x + C₂e⁻^2x + C₃e⁻^3x

(B) C₁e⁻^x + C₂e⁻^2x + C₃e^3x

(D) C₁e^x + C₂e^2x + C₃e^3x

Answer: (D)

4. In a tractor steering system, the angle made by the kingpin axis projected on the longitudinal plane of the tractor with the vertical axis is known as

(A) Kingpin inclination

(B) Caster angle

(D) Steering angle

Answer: (B)

5. A tractor operated 9-row precision planter has 16 cells on the metering plates. The speed ratio of the metering plates to the ground rive wheel is 1:2 and the rolling diameter of the ground drive wheel is 40 cm. Assuming no skid, the plant to plant spacing in rows in mm is

(A) 39

(B) 50

(D) 314

Answer: (C)

6. A self-propelled wheel does not have

(A) Wheel torque

(B) Tractive power

(D) Drawbar pull

Answer: (D)

7. Match the following items between Column I and Column II with the most appropriate combinations:

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

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

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

Answer: (C)

8. From the performance evaluation of drippers, the discharge exponent value and the coefficient of variation were obtained as 0.5 and 0.04, respectively. The drippers are categorized as

(A) Pressure compensating drippers of excellent quality

(B) Turbulent flow-tortuous path orifice type drippers of good quality

(D) Laminar flow drippers of excellent quality

Answer: (B)

9. In a basin, rainfall is recorded by five automatic weather stations A, B, C, D and E with respective average annual rainfall of 1020, 810, 675, 940 and 780 mm. In a particular year, the station A was non-operational and the remaining stations B, C, D and E recorded annual rainfall of 890, 725, 980 and 850 mm, respectively. The estimated rainfall at the station A in that particular year in mm is

(A) 758

(B) 878

(D) 1098

Answer: (D)

10. A field crop is irrigated when the available soil water reduces to 60%. The moisture content at field capacity and wilting point are 32% and 12%, respectively. The bulk density of the soil is 1.5 g cm⁻³. The field water application efficiency is 75% and the crop root zone depth is 50 cm. The gross depth of irrigation required to bring soil moisture content to field capacity in cm is

(A) 6

(B) 8

(D) 12

Answer: (B)

11. A cold storage takes 5 hours to bring down the temperature of 100 metric tons of potato from 35°C to 8° The specific heat capacity of potato is 3.1 kJ kg⁻¹ °C⁻¹. The coefficient of performance (COP) and the latent heat of vapourisation of the refrigerant (R-22) at an evaporation temperature of −10°C are 3.66 and 230 kJ kg⁻¹, respectively. Neglecting respiration heat load of potato, and assuming no power loss, the values of refrigerant flow rate and the power input to the compressor are

(A) 121.3 kg min⁻¹ and 127.1 kW

(B) 124.7 kg min⁻¹ and 121.3 kW

(D) 124.7 kg min⁻¹ and 127.1 kW

Answer: (A)

12. Hydrothermal treatment of paddy makes

(A) Shelling more difficult

(B) Polishing of parboiled rice easier

(D) Kernel soft, resulting in faster cooking

Answer: (C)

13. Both particle formation and drying process are carried out by

(A) Flash dryer

(B) Fluidized bed dryer

(D) Spray dryer

Answer: (D)

14. If one of the two Eigenvalues of a matrix is 4.236, then the other Eigenvalu (round off to 3 decimal places) is ________.

Answer: (-0.237 to -0.235)

15.

Answer: (2 to 2)

16. At the maximum power output of a solar panel, the voltage and current are 18 V and 5.56 V, respectively. If the open circuit voltage and short circuit current of the same solar panel are 21.6 V and 6.11 A, respectively, the fill factor of the panel (round off to 2 decimal places) is ________.

Answer: (0.75 to 0.77)

17. The sound pressure level on the operator’s seat of a tractor is 80 dB. If the reference sound pressure is 2 × 10⁻⁵ N m⁻², the root mean square (RMS) sound pressure in N m⁻² (round off to 2 decimal places) is_______.

Answer: (0.19 to 0.21)

18. A towed pneumatic wheel with an unloaded radius of 330 mm covers a distance of 9.9 m in 5 revolutions without any skid. Assuming the rolling radius to be same as the static loaded radius of the wheel, the deflection of the wheel in mm (round off to 1 decimal place) is ________.

Answer: (14.7 to 15.1)

19. The grain to straw ratio of 500 kg feed material is 3.2. The blown grain loss, separation loss and cleaning efficiency of thresher are 0.05%, 0.5% and 99.1%, respectively. Considering 100% threshing efficiency, grain recovery at the main grain outlet in kg (round off to 2 decimal places) is _________.

Answer: (298.30 to 298.40)

20. A tubewell has a discharge of 40 m³ h⁻¹ and operates daily for 20 h during irrigation season. The irrigation interval is 20 days and depth of irrigation is 8 cm. The command area of tubewell in ha is______.

Answer: (20 to 20)

21. The drainage coefficient of a watershed of 720 ha area is 1.2 cm. The design discharge of the drain in m³s⁻¹ is _______.

Answer: (1 to 1)

22. The following data were used for a watershed experiencing soil erosion problem: Rainfall Erosivity Index = 280 MJ mm ha⁻¹ h⁻¹ year⁻¹, Soil Erodibility Index = 0.38 ton ha h MJ⁻¹ mm⁻¹, Slope length = 200 m, Average slope of the land = 8%, Slope steepness factor = 0.85, Cropping management factor = 0.35, and Conservation practice factor = 0.60

If the slope length is reduced to half, percentage reduction in soil loss (round off to 2 decimal places) is _______.

Answer: (29.10 to 29.50)

23. Fresh tomato juice containing 6% (w/w) total solids enters in a single effect evaporator at a feed rate of 500 kg h⁻¹ to concentrate up to 36% (w/w) solids. In this process, the rate of water removal in kg h⁻¹ (round off to 1 decimal place) is ________.

Answer: (416.0 to 418.0)

24. Heat gain is occurring through a composite cold storage wall, made of brick and polyurethane foam insulation (thickness and thermal conductivity values are given below). If the exposed surfaces of brick and insulation are at 45°C and 10°C, respectively, the temperature at the interface of brick and insulation in °C (round off to 1 decimal place) is ________.

Answer: (41.4 to 41.6)

25. A milk processing plant pasteurize a batch of 12500 L whole milk to inactivate the pathogen Coxiella burnetii, (decimal reduction time of 14 seconds at 72°C) prior to packing in 500 milliliter pouches. The initial count of the noted organism is 10 per millimeter. For this batch pasteurization process at 72°C, resulting in no survivor in any of the packages, the process F-value in seconds is ______.

Answer: (126 to 126)

Q26 – Q55 carry two marks each.

26. A particle moves along the curve where t is the time. The velocity component of the particle in the direction at time t = 2 is

(A) 122/√14

(B) 122

(D) 168

Answer: (c)

27. Let a function f(t) = 4 cos 2t + 6 e⁻^8t. The Laplace transform of the given function f(t), is

(A)

(B)

(C)

(D)

Answer: (*)

28. In an irrigation channel of uniform section, water passes through a 90° triangular weir measuring 36 m head over the crest. After traveling certain distance in the same channel, water passes through 1.0 m long rectangular weir. There is no loss of water in between two weirs. Using Francis’ formula, the head over the crest of rectangular weir in cm is

(A) 22.1

(B) 18.4

(D) 11.8

Answer: (C)

29. Two ends of a differential mercury manometer are connected at two points on a pipe carrying oil. The manometer shows difference in mercury level of 20 cm. The specific gravity of oil of mercury are 0.8 and 13.6, respectively. The density of water is 1000 kg m⁻³ at 4 °C and acceleration due to gravity (g) is 9.814 m s⁻². At the same two points in pipe, the difference of pressure in Nm⁻² is

(A) 25.11

(B) 251.14

(D) 251136.00

Answer: (C)

30. Math the following items between Column I and Column II with the most appropriate combinations:

(A) P-4, Q-5, R-6, S-3, T-1, U-2

(B) P-5, Q-4, R-6, S-3, T-2, U-1

(D) P-4, Q-5, R-6, S-3, T-2, U-1

Answer: (D)

31. A retaining wall of 5 m height retains cohesionless dry soil having density 1.9 Mg m⁻³ and angle of internal friction of 28°. The surface of the backfill soil is horizontal. The active and passive earth pressures per meter length of the wall in kN are ________ and _________, respectively. [Take g = 9.81 ms⁻²]

(A) 84.11, 645.38

(B) 645.38, 84.11

(D) 381.63, 142.12

Answer: (A)

32. A 40 cm diameter tubewell is constructed in a 10 m thick confined aquifer having hydraulic conductivity of 25 m day⁻¹. The peizometric surface is observed to be 40 m high from the impervious stratum at the radius of influence of 500 m. The drawdown in the tubewell is 30 m. If the thickness of aquifer is doubled and diameter of tubewell is reduced to half, keeping all other parameters and conditions same, the change in discharge from the well is [Take π = 3.14]

(A) Increased by 83.72%

(B) Decreased by 83.72%

(D) Decreased by 82.28%

Answer: (A)

33. Choose the correct combination of process (Column I) performed by corresponding machine component(s) (Column II)

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

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

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

Answer: (B)

34. Saturated steam at 121°C is used to sterilize pineapple juice by direct steam injection. The initial temperature of the juice is 80°C and after sterilization, the blend of diluted juice exits the sterilizer at 95° The enthalpy values of steam and condensate water are given in Table below. Specific heat capacity of the juice is 3.9 kJ kg⁻¹ °C⁻¹. Assuming no energy loss to the surroundings in the process of sterilization, the ratio of juice sterilized to steam utilized is

(A) 34.79

(B) 37.94

(D) 43.97

Answer: (C)

35. Hot refined oil at 120°C enters a concentric tube-in-tube heat exchanger (HE) at the rate of 20 kg min⁻¹. The oil is cooled by water entering at a temperature of 30°C from the other end of the HE at the rate of 50 kg min⁻¹. Specific heat capacities of oil and water are 1.9 and 4.2 kJ kg⁻¹ °C⁻¹, respectively. The effectiveness of the HE may be taken as 0.7. Assuming no heat loss to the surrounding under steady-state condition, the exit temperature of water for the HE in °C is

(A) 39.9

(B) 41.4

(D) 63.0

Answer: (B)

36. Taking six intervals, each of π/12 and using Simpson’s one-third rule, the value of the definite integral (round off to 3 decimal places) is ________.

Answer: (1.186 to 1.189)

37. Two playing cards are drawn at random, but in succession from a pack of red cards (26 in number) without replacement. The probability of drawing a king first, followed by drawing a queen is P × 10⁻³. The value of P (round off to 3 decimal places) is________.

Answer: (6.100 to 6.200)

38. A hydraulic sprayer when operating at a speed of 10 km h⁻¹ and working pressure of 420 kPa covers a width of 4.5 m. The power requirement and efficiency of the pump are 0.75 kW and 70%, respectively. Out of total pump discharge, 10% is bypassed for agitation purpose. The working pressure is increased to 500 kPa. Assuming no change in the width of coverage, the application rate of the sprayer in L ha⁻¹ (round of to 1 decimal place) is _______.

Answer: (981.5 to 982.5)

39. A tractor PTO operated rotary disc mower has 4 rotating discs and the width of cut of each disc is 60 cm without any overlap. The specific power losses to air stubble and gear-train friction is 2.5 kW per meter of cutting width. The specific cutting energy requirement is 2.0 kJ m⁻². If the machine is operated at a forward speed of 6 km h⁻¹, the PTO power requirement in kW (round off to 2 decimal places) is _________.

Answer: (13.90 to 14.10)

40. A water pumping system is driven by a horizontal axis multi-bladed wind turbine at a power coefficient (C_p) of 0.4. The total pumping head and discharge are 20 m and 15 L s⁻¹, respectively. The mean wind velocity is 8 ms⁻¹ and the pump efficiency is 70%. The density of air and water are 1.2 and 1000 kg m⁻³, respectively. If the transmission efficiency from wind turbine to the pump is 90%, the required diameter of the wind turbine in m (round of to 2 decimal places) is __________.

Answer: (6.92 to 6.98)

41. A two-wheel drive tractor with a total weight of 25 kN has a wheelbase of 2.2 m and its centre of gravity lies 0.7 m ahead of the centre of rear axle. A steady horizontal pull is applied at a drawbar hitch height of 0.5 m on a concrete surface such that the weight on front axle becomes 20% of static weight of the tractor. The coefficient of net traction (round off to 2 decimal places) is _______.

Answer: (0.64 to 0.66)

42. The cooling system of a tractor fitted with diesel engine rejects 0.58 kW of heat per kW of brake power. It requires 0.16 L s⁻¹ of water per kW of heat rejection from the engine to maintain a temperature drop of 6°C of water as it moves from the top of radiator to its bottom. If the engine develops 45 kW brake power, the required water flow rate in the radiator in Ls⁻¹ (round off to 2 decimal place) is ________.

Answer: (4.16 to 4.18)

43. A V-belt drive transmits 10 kW power at a belt velocity of 8 ms⁻¹. The angle of contact on the smaller pulley is 170° and groove angle of the pulley is 38°. The coefficient of friction between the pulley and the belt is 0.28 and the maximum permissible stress of the belt is limited to 4 MPa. Neglecting centrifugal effect of the belt, the minimum cross-sectional area of the V-belt in mm² (round of to 1 decimal place) is ________.

Answer: (337.0 to 340.0)

44. A chaff cutter is operated by an electric motor running at 1140 rpm. The speed reduction from motor to the main shaft of the cutting units is 4:1. The feed rollers of 10 cm diameter each are driven by the main shaft through a suitable gear drive with a speed reduction o 15 : 1. If the chaff cutter has to knives, the theoretical length of cut chaff in mm (round of to 2 decimal places) is _________.

Answer: (10.40 to 10.60)

45. A tractor drawn right-hand offset disk harrow experiences longitudinal and side soil reactions in the front gang as 3.0 kN and 2.5 kN, respectively as compared to 3.5 kN and 4.0 kN in the rear gang. The longitudinal distance of centers of front and rear gangs are located at 2.5 m and 4.0 m, respectively behind the tractor hitch point. The required amount of offset of the disk harrow in m (round off to 2 decimal places) is ________.

Answer: (1.45 to 1.55)

46. A diesel engine when operates with biodiesel blend B20 (20% biodiesel and 80% diesel by volume) develops a brake power of 10 kW with a brake specific fuel consumption of 0.26 kg kW⁻¹ h⁻¹. If the density of biodiesel is 880 kg m⁻³ and that of diesel is 850 kg m⁻³, the amount of biodiesel required to run the engine for 3 hours in L (round off to 2 decimal places) is ________.

Answer: (1.80 to 1.84)

47. Area enclosed by different contours of a pond is given in the following Table. Using trapezoidal formula, the total estimated capacity of pond in m³ is _________.

Answer: (4860 to 4860)

48. At a speed of 1800 rpm, a centrifugal pump discharges 50 Ls⁻¹ at its best point of efficiency for a total head of 25 m. The specific speed of the pump in rpm (round off to 2 decimal places) is ________.

Answer: (35.90 to 36.10)

49. The Curve Number (CN) of a watershed of 40 ha area under given hydrologic soil group, land use and management practices, and Antecedent Moisture Condition (AMC)-II is 80. The initial abstraction is 20% of maximum retention. For the rainfall event of 40 mm, the direct runoff in mm (round off to 2 decimal places) is ________.

Answer: (8.10 to 8.30)

50. The underside beam of a railway bridge, marked as permanent Bench Mark (BM) with Reduced Level (RL) of 85.168 m, is taken as reference for leveling operation. The Back Sight (BS) on the staff held vertically inverted to the BM is 3.645 m. For the Sight (FS) of 1.523 m at a point in the construction site, the RL or elevation in m is _______

Answer: (80 to 80)

51. Air-water vapour mixture at 30°C DBT and 40% RH is heated to 65°C DBT and 30°C WBT and is used as drying medium under the constant rate period drying of spinach leaves. Specific heat capacities of dry air and pure water vapour are 1.005 and 1.88 kJ kg⁻¹ °C⁻¹, respectively. Using the properties given in Table below, the value of absolute humidity in kg water vapour per kg dry air (round off to 3 decimal places) for the dryer exit air at DBT of 45°C is ________.

Answer: (0.017 to 0.020)

52. Tray type paddy separator is employed to separate paddy from a binary mixture of paddy and brown rice at a feed rate of 1200 kg h⁻¹. Mass fractions of paddy in feed, separated paddy and brown rice steams are 0.2, 0.75 and 0.02, respectively. The amount of paddy in separated paddy steam in kg h⁻¹ (round off to 2 decimal places) is ________.

Answer: (221.00 to 223.00)

53. A cylindrical silo with 3.0 diameter and height to diameter ratio of 5 : 1 is filled with 60 metric ton wheat grains having bulk density of 725 kg m⁻³. The coefficient of friction between grain and silo wall is 0.42 and the ratio of lateral pressure to vertical pressure is 0.5. The vertical pressure at the bottom of silo in kPa (round off to 2 decimal places) is _________. [use 1 kgf = 9.81 N]

Answer: (23.50 to 25.50)

54. A bucket elevator for lifting parboiled paddy (bulk density = 840 kg m⁻³) is operated at a linear speed of 2 ms⁻¹. The width of the bucket is 25.4 cm and its cross section is making a subtending angle of 75° at the centre of a circle having 12.7 cm radius. the space between two adjacent buckets on the elevator belt is 40 cm. If the buckets are filled to 80% of their volumetric capacity, the lifting capacity of elevator in kg min⁻¹ (round off to 2 decimal places) is _________.

Answer: (538.00 to 542.00)

55. A contact plate freezer extracts thermal energy from a 24 mm thick slab of boneless meat containing 85% (w/w) water. Initially the slab is at the freezing point of meat, that is 272.5 K and corresponding latent heat of freezing is 335 kJ kg⁻¹ The plate temperature of the freezer is assumed steady at 247.5 K. Bulk density of the slab is 750 kg m⁻³. The thermal conductivity value for frozen meat is 1.5 W m⁻¹ K⁻¹. The minimum duration required for complete freezing of the slab in seconds is __________.

Answer: (409 to 411)

GATE Exam 2020 Aerospace Engineering (AE) Question Paper With Answer Key

June 8, 2023April 20, 2022 by suresh84

GATE-2020

AE : Aerospace Engineering

General Aptitude

Q 1 – Q5 Carry one mark each.

(A) in, of

(B) from, of

(D) from, from

Answer: (A)

2. He was not only accused of theft ______ of conspiracy.

(A) rather

(B) but also

(D) rather than

Answer: (B)

3. Select the word that fits the analogy:

Explicit : Implicit : : Express: _______

(A) Impress

(B) Repress

(D) Suppress

Answer: (B)

The French-speaking couple were upset at ______.

(A) the in-flight announcements being made in English.

(B) the English announcements being clearer than the French ones.

(D) equal importance being given to English and French.

Answer: (C)

5. A superadditive function f (∙) satisfies the following property

f(x₁ + x₂) ≥ f(x₁) + f(x₂)

Which of the following functions is a superadditive function for x > 1?

(A) e^x

(B) √x

(D) e⁻^x

Answer: (A)

Q6 – Q10 carry two marks each.

Which one of the following sequences shows the correct precedence as per the given passage?

(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.

(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.

(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.

Answer: (A)

7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

(A) 0°

(B) 7.5°

(D) 22.5°

Answer: (B)

(A) πa² – a²

(B) πa² – √2a²

(D) πa² – 3a²

Answer: (C)

9. a, b, c are real numbers. The quadratic equation ax² – bx + c = 0 has equal roots, which is β, then

(A) β = b/a

(B) β² = ac

(D) b² ≠ 4ac

Answer: (C)

(A) 8 : 23

(B) 23 : 8

(D) 31 : 23

Answer: (B)

AE : Aerospace Engineering

Q1 – Q25 Carry one mark each.

1. for f(x) = |x|, with df/dx denoting the derivative, the mean value theorem is not applicable because

(A) f(x) is not continuous at x = 0

(B) f(x) = 0 at x = 0

(D) df/dx = 0 at x = 0

Answer: (C)

2. For the function and σ and μ are constants, the maximum occurs at

(A) x = σ

(B) x = σ√2π

(D) x = μ

Answer: (D)

3. y = Ae^mx + Be⁻^mx, where A, B and m are constants, is a solution of

(A)

(B)

(C)

(D)

Answer: (A)

4. Which of the following statements is true about the effect of increase in temperature on dynamic viscosity of water and air, at room temperature?

(A) It increases for both water and air.

(B) It increases for water and decreases for air.

(D) It decreases for both water and air.

Answer: (C)

5. Given access to the complete geometry, surface pressure and shear stress distribution over a body placed in a uniform flow, one can estimate

(A) the moment coefficient, and the force on the body.

(B) the force coefficient, and the force on the body.

(D) the force and the moment on the body.

Answer: (D)

6. A pair of infinitely long, counter-rotating line vortices of the same circulation strength Γ are situated a distance h apart in a fluid, as shown in the figure. The vortices will

(A) rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to

(B) rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to

(D) translate along +y direction with velocity at the line vortex equal to

Answer: (C)

7. The streamlines of a steady two dimensional flow through a channel of height 0.2 m are plotted in the figure, where Ψ is the stream function in m²/s. The volumetric flow rate per unit depth is

(A) 1.0 m²/s

(B) 2.0 m²/s

(D) 0.1 m²/s

Answer: (B)

8. Which of the following options can result in an increase in the Mach number of a supersonic flow in a duct?

(A) Increasing the length of the duct

(B) Adding heat to the flow

(D) Inserting a convergent-divergent section with the same cross-sectional area at its inlet and exit planes

Answer: (C)

9. Which one of the following conditions needs to be satisfied for ϕ = Ax⁴ + By⁴ + Cxy³ to be considered as an Airy’s stress function?

(A) A – B = 0

(B) A + B = 0

(D) A + C = 0

Answer: (B)

10. Consider the plane strain filed given by ε_xx = Ay² + x, ε_yy = Ax² + y, γ_xy = B x y + y . The relation between A and B needed for this strain field to satisfy the compatibility condition is

(A) B = A

(B) B = 2A

(D) B = 4A

Answer: (D)

11. For hyperbolic trajectory of a satellite of mass m having velocity V at a distance r from the center of earth (G: gravitational constant, M: mass of earth), which one of the following relations is true?

(A)

(B)

(C)

(D)

Answer: (A)

12. For conventional airplanes, which one of the following is true regarding roll control derivative and yaw control derivative where δ_r is rudder deflection?

(A)

(B)

(C)

(D)

Answer: (A)

13. The ratio of exit stagnation pressure to inlet stagnation pressure across the rotating impeller of a centrifugal compressor, operating with a closed exit, is

(A) 0

(B) 1

(D) 0.5

Answer: (C)

14. Which one of the following is a hypergolic propellant combination used in rocket engines?

(A) Liquid hydrogen – liquid oxygen

(B) Unsymmetrical dimethyl hydrazine – nitrogen tetroxide

(D) Liquid hydrogen – liquid fluorine

Answer: (B)

15. In aircraft engine thermodynamic cycle analysis, perfectly expanded flow in the nozzle means that the static pressure in the flow at the nozzle exit is equal to

(A) the stagnation pressure at the engine inlet.

(B) the stagnation pressure at the nozzle exit.

(D) the static pressure at the nozzle inlet.

Answer: (C)

16. Three long and slender aluminum bars of identical length are subjected to an axial tensile force. These bars have circular, triangular and rectangular cross sections. with same cross sectional area. If they yield at F_circle, F_triangle and F_rectangle, respectively, which one of the following is true?

(A) F_circle > F_triangle > F_rectangle

(B) F_circle < F_triangle < F_rectangle

(D) F_circle = F_triangle = F_rectangle

Answer: (D)

17. The positive high angle-of-attack condition is obtained in a steady pull-out maneuver at the largest permissible angle-of-attack of the wing. Under this condition, at which of the following regions of the wing does the maximum tension occur?

(A) I

(B) II

(D) IV

Answer: (C)

18. The natural frequency of the first mode of rectangular cross section contilever aluminum beam is ω rad/s. If the material and cross-section remain the same, but the length of the beam is doubled, the first mode frequency will become

(A)

(B) 4ω rad/s

(C)

(D) 16ω rad/s

Answer: (A)

19. Given the sum of squares of eigenvalues of A is

(A) tan²θ

(B) 1

(D) cos²θ

Answer: (B)

20. Burnout velocity of a space vehicle in a circular orbit at an angle 5 degrees above the local horizon around earth is 13.5 km/s. Tangential velocity of the space vehicle in the orbit is ________ km/s (round off to two decimal places).

Answer: (13.42 to 13.47)

21. Velocity of an airplane in the body fixed axes is given as [100 – 10 20]m/s. The sideslip angle is ______ degrees (round off to two decimal places).

Answer: (-5.62 to -5.57)

22. The similarity solution for the diffusion equation, is u(x, t) = u(η), where similarity variable, _______ (round off to one decimal places).

Answer: (1.9 to 2.1)

23. Air enters the rotor of an axial compressor stage with no pre-whirl (C_θ = 0) and exits the rotor with whirl velocity, C_θ = 150 m/s. The velocity of rotor vanes, U is 200 m/s. Assuming C_p = 1005 J/(kg K), the stagnation temperature rise across the rotor is _______ K (round off to one decimal places).

Answer: (29.8 to 30.0)

24. A thin walled beam of constant thickness shown in the figure is subjected to a torque of 3.2 kNm. If the shear modulus is 25 GPa, the angle of twist per unit length is _____rad/m ((round off to three decimal places).

Answer: (0.009 to 0.011)

25. An airplane of mass 5000 kg is flying at a constant speed of 360 km/h at the bottom of a vertical circle with a radius of 400 m, as shown in the figure. Assuming that the acceleration due to gravity is 9.7 m/s², the load factor experienced at the center of gravity of the airplane is _______(round off to two decimal places).

Answer: (3.50 to 3.60)

Q26 – Q55 carry two marks each.

26. The equation where c is a constant, represents a family of

(A) exponential curves

(B) parabolas

(D) hyperbolas

Answer: (C)

27. A wedge shaped airfoil is placed in a supersonic flow as shown in the figure (not to scale). The corners of the wedge are at x = X_A, x = X_B, x = X_C, respectively.

Which one of the following represents the correct static pressure profiles along y = Y_I and y = Y_II ?

Answer: (D)

28. The value of Poisson’s ratio at which the shear modulus of an isotropic material is equal to the bulk modulus is

(A) 1/2

(B) 1/4

(D) 1/8

Answer: (D)

29. A load P is applied to the free end of a stepped cantilever beam as shown in the figure. The Young’s modulus of the material is E, and the moments of inertia of the two sections of length 2 m and 2 m are I and 3I, respectively. Ignoring transverse shear and stress concentration effects, the deflection at the point where the load is applied at the free end of the cantilever is

(A) 23/243EI

(B) I/3EI

(D) 23/3EI

Answer: (C)

30. The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is

A, B and C are compliances which depend on the elastic properties of the material. Which one of the following is correct?

(A)

(B)

(C)

(D)

Answer: (D)

31. For three different airplanes A, B and C, the yawing moment coefficient (C_n) was measured in a wind-tunnel for three settings of sideslip angle β and tabulated as

Which one of the following statements is true regarding directional static stability of the airplanes A, B and C?

(A) All three airplanes A, B and C are stable.

(B) Only airplane C is stable, while both A and B are unstable.

(D) Airplane C is unstable, A and B are both stable with A less stable than B.

Answer: (C)

32. A closed curve is expressed in parametric form as x = a cos θ and y = b sin θ, where a = 7 m and b = 5 m. Approximating π = 22/7, which of the following is the area enclosed by the curve?

(A) 110 m²

(B) 74 m²

(D) 144 m²

Answer: (A)

33. An axial compressor is designed to operate at a rotor speed of 15000 rpm and an inlet stagnation temperature of 300 K. During compressor testing, the inlet stagnation temperature of the compressor measured was 280 K. What should be the rotor speed for the compressor to develop the same performance characteristics during this test as in the design condition?

(A) 14000 rpm

(B) 14491 rpm

(D) 16071 rpm

Answer: (B)

34. For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses?

Answer: (B)

35. In the equation AX = B, where A is an orthogonal matrix, the sum of the unknowns, x + y +z = ______ (round off to one decimal place).

Answer: (0.9 to 1.1)

36. If is evaluated numerically using trapezoidal rule with four intervals, the difference between the numerically evaluated value and the analytical value of the integral is equal to ________ (round off to three decimal places).

Answer: (0.010 to 0.012)

37. The table shows the lift characteristics of an airfoil at low speeds. The maximum lift coefficient occurs at 16 degrees.

Using Prandtl-Glauert rule, the lift coefficient for the airfoil at the angle of attack of 6 degrees free stream Mach number of 0.6 is _______(round off to two decimal places).

Answer: (0.92 to 0.94)

38. A low speed uniform flow U₀ is incident on an airfoil of chord c. In the figure, the velocity profile some distance downstream of the airfoil is idealized as shown for section B. The static pressure at sections A and B is the same. The drag coefficient of the airfoil is ______(round off to three decimal places).

Answer: (0.009 to 0.011)

39. An oblique shock is inclined at an angle of 35 degrees to the upstream flow of velocity 517.56 m/s. The deflection of the flow due to this shock is 5.75 degrees and the temperature downstream is 182.46 K. Assume the gas constant R = 287 J/(Kg K), specific heat ratio γ = 1.4, and specific heat at constant pressure C_p = 1005 J/(Kg K). Using conservation relations, the Mach number of the upstream flow can be obtained as ______(round off to ne decimal place).

Answer: (1.9 to 2.1)

40. The thickness of a laminar boundary layer (δ) over a flat plate is, where x is measured from the leading edge along the length of the plate. The velocity profile within the boundary layer is idealized as varying linearly with y. For freestream velocity of 3 m/s and kinematic viscosity of 1.5 × 10⁻⁵ m²/s, the displacement thickness at 0.5 m fro the leading edge is _______ mm (round off to two decimal places).

Answer: (4.00 to 4.20)

41. A wing of 15 m span with elliptic lift distribution is generating a lift of 80 kN at a speed of 90 m/s. The density of surrounding air is 1.2 kg/m³ . the induced angle of attack at this condition is ______ degrees (round off to two decimal places).

Answer: (1.29 to 1.38)

42. A solid circular shaft, made of ductile material with yield stress σ_Y = 280 MPa, is subjected to a torque of 10 kNm. Using the Tresca failure theory, the smallest radius of the shaft to avoid failure is _______ cm (round off to two decimal places).

Answer: (3.55 to 3.58)

43. The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.0339. Assuming that the planet’s orbit around the sun is planar and elliptic, the value of eccentricity of the orbit is _________(round off to three decimal places).

Answer: (0.016 to 0.018)

44. The eigenvalues for phugoid mode of a general aviation airplane at a stable cruise flight condition at low angle of attack are λ_{1, 2} = −02 ± 0.25. If the acceleration due to gravity is 9.8 m/s², the equilibrium speed of the airplane is ________m/s (round off to two decimal places).

Answer: (55.20 to 55.33)

45. For a general aviation airplane with tail efficiency η = 0.95, horizontal tail volume ratio V_H = 0.453, downwash angle slope dε/dα = 0.35, wing lift curve slope horizontal tail lift curve slope shift in neutral point location as a percentage of mean aerodynamic chord is ______(round off to two decimal places).

Answer: (25.60 to 25.70)

46. A single engine, propeller driven, general aviation airplane is flying in cruise at sea-level condition (density of air at sea-level is 1.225 kg/m³) with speed to cover maximum range. For drag coefficient C_D = 0.025 + 0.049 C_L² and wing loading W/S = 9844 N/m², the speed of the airplane is ______m/s (round off to one decimal place).

Answer: (149.0 to 151.0)

47. The design flight Mach number of an ideal ramjet engine is 2.8. The stagnation temperature of air at the exit of the combustor is 2400 K. Assuming the specific heat ratio of 1.4 and gas constant of 287 J/(kg K), the velocity of air at the exit of the engine is _______ m/s (round off to one decimal place).

Answer: (1712.0 to 1719.0)

48. The operating conditions of an aircraft engine combustor are as follows.

The rat of total enthalpy of air entering the combustor = 28.94 MJ/s

The rate of total enthalpy of air leaving the combustor = 115.42 MJ/s.

Mass flow rate of air = 32 kg/s.

Air to fuel mass ratio = 15.6.

Lower heating value of the fuel = 46 MJ/kg.

The efficiency of the combustor is _______% (round off to two decimal places.)

Answer: (91 to 93)

49. The figure shows the T-S diagram for an axial turbine stage.

Assuming specific heat ratio of 1.33 for the hot gas, the isentropic efficiency of the turbine stage is ______% (round off to two decimal places).

Answer: (87 to 89)

50. A rocket engine has a sea level specific impulse of 210 s and a nozzle throat area of 0.005 m². While testing at sea level conditions, the characteristic velocity and pressure for the thrust chamber are 1900 m/s and 50 bar, respectively. Assume the acceleration due to gravity to be 9.8 m/s². The thrust produced by the rocket engine is _______kN (round off to one decimal place).

Answer: (27.0 to 27.2)

51. A critically damped single degree of freedom spring-mass-damper system used in a door closing mechanism becomes overdamped due to softening of the spring with extended use. If the new damping ratio (ξ_new) for overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness (k_org/k_new), assuming that the other parameters remain unchanged, is _______(round off to two decimal places).

Answer: (1.43 to 1.45)

52. The two masses of the two degree of freedom system shown in the figure are given initial displacement of 2 cm (x₁) and 1.24 cm (x₂). The system starts to vibrate in the first mode. The first mode shape of this system is ϕ₁ = [1 a]^T, where a = _______(round off to two decimal places).

Answer: (0.61 to 0.63)

53. As shown in the figure, a beam of length 1 m is rigidly supported at one end and simply supported at the other. Under the action of a uniformly distributed load of 10 N/m, the magnitude of the normal reaction force at the simply supported end is _______N (round off to two decimal places).

Answer: (3.74 to 3.76)

54. An airplane of mass 4000 kg and wing reference area 25 m² flying at sea level has a maximum lift coefficient of 1.65. Assume density of air as 1.225 kg/m³ and acceleration due to gravity as 9.8 m/s². Using a factor of safety of 1.25 to account for additional unsteady lift during a sudden pull-up, the speed at which the airplane reaches a load factor of 3.2 is _________m/s (round off to two decimal places).

Answer: (62.95 to 63.08)

55. A Pitot tube mounted on the wing tip of an airplane flying at an altitude of 3 k measures a pressure of 0.72 bar, and the outside air temperature is 268.66 K. Take the sea level condition as, pressure = 1.01 bar, temperature = 288.16 K, and density = 1.225 kg/m³. The acceleration due to gravity is 9.8 m/s² and the gas constant is 287 J/(kg K). Assuming standard atmosphere, the equivalent airspeed for this airplane is _____m/s (round off to two decimal place).

Answer: (57.10 to 60.00)