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GATE Exam 2019 Architecture and Planning (AR) Question Paper With Answer Key

June 7, 2023November 28, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

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

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

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

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

2. No student was involved in the strike.

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

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

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

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

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

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

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

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

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

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

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

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

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

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

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

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

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

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

Answer: (C)

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

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

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

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

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

(A) 9

(B) 10

(D) 11.30

Answer: (B)

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

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

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Architecture and Planning

Q. 1 – Q. 25 carry one mark each.

1. Which of the following commands in AUTOCAD is used to create 3D solid between various cross sections?

(A) LOFT

(B) MESH

(D) PFACE

Answer: (A)

2. Name the architect who criticized ornament in useful objects in his essay ‘Ornament and Crime’.

(A) John Ruskin

(B) H P Berlage

(D) Walter Gropius

Answer: (C)

3. A sanit ground ary landfill is provided with High Density Poly Ethylene (HDPE) lining along the surface. This is provided primarily to prevent

(A) Bleaching

(B) Leaching

(D) Plant growth

Answer: (B)

4. Super-ele vation of a road with pre-determined radius of curvature is primarily dependent on

(A) Altitude

(B) Soil bearing capacity

(D) Design traffic speed

Answer: (D)

5. In a mono-centric urban model, land rent is expected to

(A) diminish as one moves towards the center

(B) diminish as one moves away from the center

(D) be unrelated with distance from center

Answer: (B)

6. Fineness modulus of sand measures its

(A) Compressive strength

(B) Grading according to particle size

(D) Ratio of coarse and fine sand

Answer: (B)

7. The spherical surface of the geodesic dome comprises of

(A) Equilateral triangles of various sizes

(B) Isosceles triangles of various sizes

(D) Isosceles triangles of uniform size

Answer: (C)

8. The abrup t change or junction between two ecological zones is termed as

(A) Ecological niche

(B) Ecosystem

(D) Ecotone

Answer: (D)

9. Complementary colours in a Munsell pigment colour wheel refers to

(A) Colours in alternate positions

(B) Colours opposite to one another

(D) A pair of secondary colours

Answer: (B)

10. The closing syntax, for an executable command line in C or C++ program, is

(A) :

(B) ,

(D) .

Answer: (C)

11. The term ‘Necropolis’ refers to

(A) Orginacally growing Settlment

(B) Origin of settlement

(D) Merging of two settlements

Answer: (C)

12. Which of the following projection types is adopted in the Universal Transeverse Mercator (UTM)?

(A) Spherical Conical

(B) Planar

Answer: (D)

13. The ing redient to be added to produce Aerated Cement Concrete, is

(A) Aluminum

(B) Calcium chloride

(D) Sulphur

Answer: (A)

14. The cause of short column effect, during seismic occurrence, is due to

(A) Centralized rupture of the column

(B) Tearing of reinforcement bars

(D) Stress concentration

Answer: (D)

15. The solar protection system consisting of fixed slats or grids, outside a building façade in front of openings, is known as

(A) Brise–soleil

(B) Solarium

(D) Trombe wall

Answer: (A)

16. The Indian property inscribed by UNESCO on the World Heritage List in the year 2018 is

(A) Mattanchery Palace, Ernakulam

(B) The Victorian Gothic and Art Deco Ensembles of Mumbai

(D) Mughal Gardens in Kashmir

Answer: (B)

17. Typical features of Buddhist architecture are

(A) Mandapa, Chattri, Amalaka, Torana

(B) Stambha, Torana, Vimana , Harmika

(D) Vedika , Stupa, Chaitya, Vimana

Answer: (C)

18. Identify the Queen closure

(A)

(B)

(C)

(D)

Answer: (A)

19. Identify th e role of Vermiculate in vertical landscapes

(A) Fertilizer

(B) Holding material

(D) Water retention element

Answer: (Mark to All)

20. Which of the following parameters is essential to estimate the Envelope Performance Factor (EPF) of a building as per the Energy Conservation Building Code (ECBC), 2011?

(A) Building Type

(B) Maximum humidity

(D) Building occupancy duration

Answer: (D)

21. The illumination level of a room is 300 lux and the efficacy of the lamps is 60. The Light Power Density (LPD) of the room in Watt/m² is _____.

Answer: (5 to 5)

22. The load on a RCC column is 150 kN. The soil bearing capacity is 80 kN/m². Assuming a factor of safety of 1.2, the side of the square column footing is meter (rounded off to one decimal place)________.

Answer: (1.49 to 1.51)

23. A room is separated by a partition wall. The average intensities of sound in the source and
receiving sides across the partition are 10-4 W/m² and 10^-7 W/m² respectively. The transmission loss (TL) of the partition wall is dB______.

Answer: (30 to 30)

24. If the purchase price of 2BHK flat rises by 10 percent, the demand for such flats is observed to decrease by 8 percent. The price elasticity of the housing demand for 2BHK flats is (rounded off to one decimal place)________.

Answer: (0.75 to 0.85)

25. ‘Threshold of enclosure’ created by vertical surfaces or series of vertical elements in an urban plaza, represented by the ratio of height and distance, is given by an angle of degrees (rounded off to one decimal place)_______.

Answer: (260.0 to 30.0)

Q. 26 – Q. 55 carry two marks each.

26. Match the instruments in Column – I with the various types of surveying in Column – II and select the appropriate option.

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

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

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

Answer: (D)

27. Match the characteristics of settlement systems in Column – I with their corresponding theory/rules in Column – II and select the appropriate option.

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

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

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

Answer: (D)

28. Match the architectural projects in Column – I with the architect in Column – II, and select the appropriate option.

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

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

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

Answer: (A)

29. Match the Name of the book provided in Column – I with the corresponding author in Column – II and select the appropriate option.

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

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

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

Answer: (A)

30. Match the thermal properties in the Column – I and their respective units in Column – II and select the appropriate option.

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

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

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

Answer: (B)

31. Match the application in the field of construction in the Column – I and the respective items in Column – II and select the appropriate option.

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

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

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

Answer: (C)

32. Match the following types of masonry joints in Column – I with their corresponding description in Column – II, and select the appropriate option.

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

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

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

Answer: (B OR D)

33. Match the following in Column – I with their suitable description in Column – II, and select the appropriate option.

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

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

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

Answer: (D)

34. Match the units provided in Column – I with their corresponding items in Column – II, and select the appropriate option.

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

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

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

Answer: (D)

35. Match the scientific names of the trees provided in Column – I with the corresponding color of their bloom in Column – II, and select the appropriate option.

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

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

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

Answer: (D)

36. Match the items in Column – I and their respective location in building/site in Column – II, and select the appropriate option.

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

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

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

Answer: (C)

37. As per the Handbook on Barrier Free and Accessibility, CPWD – 2014, match the design guidelines in Column – I with their appropriate standards in Column – II and select the appropriate option.

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

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

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

Answer: (C)

38. Match the contemporary Urban Design Movements listed in Column – I with the corresponding principles listed in Column – II and select the appropriate option.

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

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

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

Answer: (A OR D)

39. Match the figures of vaults in Column – I with their corresponding types in Column – II and select the appropriate option.

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

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

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

Answer: (A)

40. A colony of 50 people is served by a septic tank. The rate of water supply is 90 lpcd in the colony and 40% of it is going to the septic tank. The retention period of the tank is 24 hours. The length of the septic tank is meter (rounded off to two decimal places)__________.

Assume, storage capacity/person = 0.085m³ (3 years)

Space for digestion = 0.0425 m³/person

Depth of tank = 1.4 m Length: Width = 2:1

Answer: (3.40 to 3.45)

41. A cone, with a base of 10 cm diameter and axis of 12 cm, is lying on Horizontal Plane (HP) along its generator. The internal angle which the base of the cone makes with the HP is _____ degrees.

Answer: (67.0 to 68.0)

42. A public utility building of 5000 m² was constructed 5 years before, on a site of 1 hectare. The present value of open land in that location is Rs. 100/m² and present construction cost of such building is Rs. 2500/m². If the value of the building is assumed to be depreciating at a constant rate of 6 percent per annum, then the present value of the property using ‘Valuation by Cost Method’ is___ (in Rs. lakhs) (rounded off to one decimal place).

Answer: (101.0 to 104.0)

43. A residential area of 20 hectares is planned for three different types of plots of 500 m², 300 m² and 200 m² with numbers of plot in each category are 100, 120 and 150 respectively. The rest of the area is allocated for roads and facilities such as schools, shops and parks. Each plot has one dwelling unit and the average household size is 5 persons.

The net residential density of the area in persons per hectare is ______.

Answer: (159 to 160)

44. In a single lane road, traffic volume of 1000 vehicle/h moving at 20 km/h, comes to a halt due to an accident. If jam density is 150 vehicle/km, the velocity of the shock wave generated (in absolute value) is _____ km/h.

Answer: (9.9 to 10.1)

45. In a site map, a rectangular residential plot measures 150 mm × 40 mm, and the width of the front road in the map measures 16 mm. Actual width of the road is 4 m. If the permissible F.A.R. is 1.2, the maximum built-up area for the residential building will be ____ m².

Answer: (450 to 450)

46. The internal dimension of a room is 10m × 10m × 4m (height). The total area of the doors and windows are 16 m2. Keeping the doors and windows closed, the reverberation time of the room becomes 1.2 second. Assume all the interior surfaces including doors and windows have same sound absorption coefficient. If all the doors and windows of the room are kept fully open, the reverberation time will be_____ second (rounded off to two decimal places).

Answer: (0.93 to 0.97)

47. A depressed portion of a land is identified by three closed contours, as shown in the figure below. The area bounded by three contour lines are 6 m2, 24 m² and 96 m² respectively.

The contour interval is 1 m. Using prismoidal method, the volume of the earth needed to fill the land depression is_____ m³.

Answer: (65 to 76)

48. Solar panels are proposed to be installed on a building roof top to generate electricity. The size of each solar panel is 2 m². The efficiency of each panel is 75%. The orientations of the solar panel and related solar data are given in the table below.

As per the above proposal ____ kWh solar power will be generated daily. (rounded off to one decimal place)

Answer: (28.4 to 28.6)

49. A power shovel is having 1.8 m³ excavation output per batch of operation. The average cycle time of the batch operation is 45 seconds. The lost time per hour of the excavation activity is 10 minutes. Assume six working hours of operation per day. The amount of soil excavated by the power shovel per day is _____ m³ (rounded off to two decimal places).

Answer: (719.75 to 720.25)

50. A room having dimension 12 m × 10 m × 3.5 m is required to be mechanically ventilated by air-conditioner. The temperature difference between outdoor ambient air and the supply air is 12°C. Consider three air exchanges per hour. The volumetric specific heat of the air is 1250 J/m³°C. Assume one ton of refrigeration (TR) is equal to 3.5 kW. The capacity of the air-conditioner for the room in TR will be _____.

Answer: (1.49 to 1.51)

51. A simply supported beam AB has a clear span of 7 meter. The bending moment diagram (BMD) of the beam due to a single concentrated load is shown in the figure below.

The magnitude of the concentrated load in kN is _____ .

Answer: (21 to 21)

52. For a symmetrical trapezoidal open drain in a landscape with grass and loose rock surface, the velocity of flow of water is _____ m/sec, (rounded off to two decimal places), given the following data.

Water edge width at the top = 750 mm

Water edge width at the bottom = 450 mm

Water depth = 600 mm

Manning’s coefficient of roughness = 0.05

Slope along the drain = 1 in 250

Answer: (0.40 to 0.50)

53. The stack pressure is created by 10 m height of stack and 15°C temperature difference. The motive force due to the stack pressure over a cross section area of 2.5 m² is ____ N.

Answer: (15.0 to 16.0)

54. An industrial building contains 3000 kg of combustible materials, in dry state, distributed over three rooms of area 100 m², 500 m² and 300 m² each, in a proportion of 30%, 50% and 20% of the contents, respectively. Calorific value of the material is 4400 kCal/kg.

The Total Fire Load of the rooms is equal to _____ kCal/ m².

Answer: (61500 to 61700 OR 14600 to 14700)

55. A simple truss is shown in the figure below. The truss is loaded with horizontal and vertical force 15 kN and 25 kN, respectively. The force in the member AB will be _____ kN.

Answer: (20 to 20)

GATE Exam 2019 Agricultural Engineering (AG) Question Paper With Answer Key

June 7, 2023November 27, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

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

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

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

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

2. No student was involved in the strike.

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

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

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

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

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

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

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

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

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

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

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

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

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

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

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

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

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

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

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

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Agricultural Engineering

Q. 1 – Q. 25 carry one mark each.

1. has the value

(A) 0.785

(B) 0.915

(D) 1.245

Answer: (A)

2. The determinant of the matrix is

(A) 1

(B) 0

(D) 2

Answer: (C)

3. In a relay race there are five teams A, B, C, D and E. Assuming that each team has an equal chance of securing any position (first, second, third, fourth or fifth) in the race, the probability that A, B and C finish first, second and third, respectively is

(A) 1/60

(B) 1/20

(D) 3/10

Answer: (A)

4. The path traced by the material threshed between the cylinder and the concave of an axial flow thresher is

(A) straight single pass and perpendicular to the cylinder shaft

(B) curved and perpendicular to the cylinder shaft

(D) straight and parallel to the cylinder shaft

Answer: (C)

5. The farm machine/implement used only for preparing wetland is

(A) rotavator

(B) disk harrow

(D) cultivator

Answer: (C)

6. The type of typical spray distribution profile of a hollow cone nozzle is

(A) steep sided slo pes

(B) gradual sloping sides

(D) narrow topped with steep sides

Answer: (A)

7. The amount of biogas required to run a diesel engine is 0.65 m3 kW^-1h^-1. The minimum size of the Deenbandhu model biogas plant in m3 required to run a 1 kW (brake power) diesel engine daily for one hour is

(A) 1

(B) 2

(D) 4

Answer: (B)

8. A soil sample has a porosity of 40%. Void ratio of the soil sample is

(A) 0.367

(B) 0.467

(D) 0.667

Answer: (D)

9. In the Muskingum method of channel routing, the routing equation is written as 𝑄₂ = 𝐶𝑜𝐼₂ + 𝐶₁𝐼₁ + 𝐶₂𝑄₁. If the storage-time constant K = 12 h, weighting factor x = 0.15 and the time step for routing ∆𝑡 = 4 h, the coefficient 𝐶_𝑜 is

(A) 0.016

(B) 0.048 .

(D) 0.656

Answer: (A)

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

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

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

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

Answer: (B)

11. Tensiometer installed in the soil measures

(A) osmotic suction of soil moisture

(B) soil permeability

(D) capillary potential of the soil

Answer: (D)

12. Head pulley of a bucket elevator has an effective radius of 150 mm. In order to obtain the most satisfactory discharge from this elevator, the speed of the head pulley in rpm is

(A) 36

(B) 44

(D) 77

Answer: (D)

13. The clean paddy production per annum is 160 million tonnes. Average milling quality analysis indicates the husk content, total yield and degree of polish as 22%, 73.32% and 6%, respectively. For an average bran oil yield of 20%, the annual rice bran oil potential in million tonnes is

(A) 1.268

(B) 1.498

(D) 1.945

Answer: (B)

14. A batch of 10000 L milk is to be sterilized and thereafter packed in 20000 packets of 500 ml each. The mean Standard Plate Count (SPC) of Bacillus subtilis in 100 samples of fresh milk was found to be 50 ml -1. The milk is to be sterilized such that each 500 ml packet is completely devoid of the same organism. Minimum number of log cycle reduction for sterilization of this batch is_______ .

(A) 8

(B) 9

(D) 12

Answer: (B)

15. A tube-in-tube counter-flow heat exchanger is heating oil from 35°C to 77°C by circulating hot water at 100°C. The outlet temperature of water is 70 °C. The log-mean-temperature difference (LMTD) is

(A) exactly equal to the mean arithmetic temperature difference

(B) significantly greater than the mean arithmetic temperature difference

(D) very nearly equal to the mean arithmetic temperature difference

Answer: (D)

16. Using trapezoidal rule, the value of (rounded off to three decimal places)is_______ .

Answer: (1.820 to 1.830)

17. Two cards are drawn at random and without replacement from a pack of 52 playing cards. The probability that both the cards are black (rounded off to three decimal places) is__________.

Answer: (0.244 to 0.246)

18. The total width between the two extreme furrow openers in a tractor drawn 9-row wheat seed drill is 1.6 m. The average mass of wheat seeds dropped per meter of row length in each furrow opener is 2.15 g. Seed rate obtained with the seed drill in kg ha-1 (rounded off to one decimal place) is ________.

Answer: (107.4 to 107.8)

19. The purchase price of a tractor is Rs. 5,50,000. Useful life of the tractor is 10 years and its salvage value is 10% of the purchase price. Following the sum of the years digit method, the depreciation in 3rd year in Rs. is________ .

Answer: (72000 to 72000)

20. A pair of straight teeth spur gears is transmitting power at 500 rpm. The pinion has 16 standard full depth involute teeth of module 8 mm. The pitch line velocity of the pinion in m s-1 (rounded off to two decimal places) is __________.

Answer: (3.30 to 3.40)

21. A soil conservation structure has an expected life of 10 years and is designed for a flood magnitude of return period 50 years. The risk of this hydrologic design in percentage (rounded off to two decimal places) is _________.

Answer: (18.00 to 18.40)

22. A watershed of area 80 ha has a runoff coefficient of 0.3. A storm of intensity 5 cm h-1 occurs for a duration more than the time of concentration of the watershed. The peak discharge in m³ s^-1 (rounded off to two decimal places) is _________.

Answer: (3.30 to 3.35)

23. A lateral has 12 sprinklers spaced 14 m apart in a sprinkler irrigation system. The laterals are spaced 20 m apart on the main line. If the recommended fertilizer dose is 80 kg ha-1, the amount of fertilizer to be applied at each setting in kg (rounded off to two decimal places) is_______.

Answer: (26.87 to 26.89)

24. In a rubber roll sheller, 250 mm diameter rolls are set at a clearance of 1 mm. If the mean thickness of paddy grains being shelled is 2 mm, the length of husking zone in mm (rounded off to two decimal places) is ________.

Answer: (22.20 to 22.35)

25. Air-water vapour mixture at 1 atmosphere pressure has 0.035 kg water vapour (kg dry air)-1 and dry bulb temperature of 37 oC. The value of Universal gas constant is 8.314 kJ (kg mole K)^-1. The humid volume of this air-water vapour mixture in m³ (kg dry air)-1 (rounded off to three decimal places) is _________.

Answer: (0.920 to 0.930)

Q. 26 – Q. 55 carry two marks each.

Q.26 General soluti on to the differential equation y″ + 4y’ + 5y = 0 is

(A) 𝑒^2𝑥(𝑎 𝑐𝑜𝑠 𝑥 + 𝑏 sin 𝑥)

(B) 𝑒^−2𝑥(𝑎 cos 𝑥 + 𝑏 sin 𝑥)

(D) 𝑒^−𝑥(𝑎 cos 2𝑥 + 𝑏 sin 2𝑥)

Answer: (B)

27. For vectors on the curve C (y = 2x²) in the x-y plane from (0, 0) to (1, 2) is

(A) -1.17

(B) 1.50

(D) 2.67

Answer: (A)

28. A 3-cylinder 4-stroke CI engine coupled with a turbocharger has a bore and stroke length of 120 mm and 130 mm, respectively. The engine is running at 1600 rpm with a volumetric efficiency of 150%. The air to fuel ratio for complete combustion on weight basis is 14.9:1 and the density of air entering the cylinder is 1.2 kg m-3. The fuel consumption in kg h^-1 is

(A) 17.05

(B) 25.57

(D) 51.14

Answer: (B)

29. A level field of 1.2 ha (120 m × 100 m) is ploughed using a reversible mould board plough with a total effective cutting width of 0.64 m. The average field overlap is 80 mm between two consecutive laps. The average time taken for each turn is 30 seconds and the mean operating speed is 5.0 km h-1. The maximum effective field capacity in ha h^-1 is

(A) 0.207

(B) 0.236

(D) 0.318

Answer: (A)

30. The thresher ‘A’ has output capacity of 170 kg h^-1 while threshing paddy crop at 14% moisture content (m.c.) with a grain to straw ratio 45:55. The thresher ‘B’ has output capacity of 160 kg h-1 while threshing paddy crop at 13% m.c. with a grain to straw ratio 40:60. Both the threshers have threshing efficiency of 97%. If a farmer has to carry out threshing of paddy crop at 12% m.c. with a grain to straw ratio 40:60 in the least time, the selected thresher and its output in kg when operated for 5 hours will be

(A) A and 738

(B) A and 850

(D) B and 800

Answer: (C)

31. A horizontal axis drag type wind rotor, fitted with 4 thin rectangular blades having drag coefficient 1.29, is used to extract power when the average wind velocity in the rotor plane is 10 km h-1. The maximum power coefficient is

(A) 0.148

(B) 0.191

(D) 0.593

Answer: (B)

32. A two-wheel drive tractor while operating a plough at a forward speed of 5 km h^-1 experiences a wheel slip of 15%. If the angular speed of the rear axle is 2.4 rad s^-1, the rolling radius of the traction wheel in meter will be

(A) 0.49

(B) 0.58

(D) 0.75

Answer: (C)

33. The combined mass of a tractor seat and operator is 75 kg and the undamped natural frequency of the operator seat is 10 rad s^-1. If the seat suspension damping rate is 600 N m^-1 s^-1, the damping ratio is

(A) 0.2

(B) 0.4

(D) 0.8

Answer: (B)

34. A catchment has eight raingauge stations. In a year, the annual rainfall recorded by the gauges (in cm) are 93.8, 106.5, 170.6, 138.7, 87.8, 156.2, 180.9 and 110.3. For a 10% error in the estimation of the mean rainfall, the optimum number of stations in the catchment is

(A) 4

(B) 6

(D) 10

Answer: (C)

35. On a 4% land slope in a medium rainfall zone, the horizontal spacing of bunds in meter and the length of bunds per hectare in meter, respectively are

(A) 25 and 300

(B) 25 and 400

(D) 30 and 400

Answer: (B)

36. In a drainage area of 15 ha, the slope and drainage coefficient are 0.4% and 11 mm/day, respectively. The value of Manning’s roughness coefficient is 0.016. The inside diameter (in mm) of the corrugated plastic tubing used for drainage is

(A) 200.51

(B) 205.52

(D) 215.23

Answer: (C)

37. A 20 cm diameter well fully penetrates a confined aquifer of thickness 20 m. After a long period of pumping at the rate of 1500 L min^-1, the steady drawdowns in the wells at 30 m and 50 m from the pumping well are found to be 2.0 m and 1.5 m, respectively. Assuming π = 3.14, the transmissivity of the aquifer in m² s^-1 is

(A) 0.244

(B) 14.676

(D) 880.560

Answer: (Marks to All)

38. Water is flowing at a velocity of 1.6 m s^-1 in a pipe of diameter 8 cm and length 100 m. Assuming the value of coefficient of friction for pipe, f = 0.005 and acceleration due to gravity, g = 9.81 m s-2, the head loss (in meter) due to friction in the pipe is

(A) 1.28

(B) 2.28

(D) 3.26

Answer: (D)

39. A cream separator has discharge radii of 6 cm and 9 cm and the density of cream and skim milk are 860 and 1035 kg m^-3, respectively. The ideal radius (in meter) for placing the feed inlet is

(A) 0.085

(B) 0.098

(D) 0.174

Answer: (D)

40. Head rice contents in the samples collected at feed inlet, head rice outlet and broken rice outlet of an indented cylinder grader are 82%, 94% and 15%, respectively. If the grader receives the feed at 1200 kg h^-1, the flow rate (in kg h-¹) of head rice in the broken rice stream is

(A) 20.17

(B) 27.34

(D) 1017.72

Answer: (B)

41. A batch of 100 kg grain at 32% moisture content (wet basis) is being dried using hot air at 70 °C and 30% RH. The values of Henderson equation’s constants c and n for the grain are 8.5×10^-6 and 2.07, respectively. Considering the maximum possible drying of the batch, the quantity of moisture removed in kg is

(A) 10.20

(B) 17.05

(D) 25.07

Answer: (D)

42. A chiller used for 3 hours. kW and working on mechanical vapour compression refrigeration system (COP = 4.5) is cooling 12500 kg of fresh cow milk (cp = 3.8 kJ kg^-1 K^-1) from 30°C to 4°C in Assuming ideal compression process, the power consumed by the electric motor in the tonnage of refrigeration (TR), respectively are

(A) 25.4 and 32.5

(B) 25.4 and 114.3

(D) 114.3 and 25.4

Answer: (A)

43. Two streams of air with the following conditions are adiabatically mixed:

Latent heat of vapourization of water at 0°C = 2501 kJ kg^-1 Specific heat capacity of dry air = 1.005 kJ kg^-1 K^-1 Specific heat capacity of water vapour = 1.880 kJ kg^-1 K^-1

Using above values, the dry bulb temperature and the absolute humidity of the mixed air in o°C and g water vapour (kg dry air)^-1, respectively are

(A) 43 and 30

(B) 44 and 31

(D) 46 and 35

Answer: (D)

44. Directional derivative of 𝑓(𝑥, 𝑦, 𝑧) = 𝑥𝑦² + 𝑦𝑧³ at the point (2, -1, 1) in the direction of vector (rounded off to two decimal places) is __________.

Answer: (-3.70 TO -3.60)

45. The mean absolute deviation about the median for the data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21
(rounded off to two decimal places) is ___________.

Answer: (5.26 to 5.28)

46. The application rate of an 18-nozzle hydraulic sprayer is 1120 L ha^-1. The nozzle spacing and forward speed are 400 mm and 3.4 km h^-1, respectively. The operating pressure is 2.1 MPa and the pump efficiency is 60%. If 10% of the pump output power is used for agitating the liquid, the power needed to operate the sprayer in kW (rounded off to three decimal places) is ________.

Answer: (2.900 to 3.000)

47. A two-wheel drive tractor is taking a turn with a radius of curvature 5.0 m. The minimum horizontal distance between the tipping axis and line of action of the CG is 800 mm. The angle between the line of action of centrifugal force and perpendicular direction to the tipping plane is 15o. If the vertical distance of the CG from the ground level is 900 mm, the limiting speed (in km h-1) of the tractor to prevent overturning (rounded off to two decimal places) is __________.

Answer: (24.00 to 24.45)

48. During operation, a two-wheel drive tractor with a total weight of 2000 kg has a weight distribution of 35% and 65% in front and rear axles, respectively. The width and diameter of the tyres fitted to the front axle are 0.18 m and 0.56 m, and those of the rear axle are 0.34 m and 1.10 m, respectively. If tyre deflection is 20%, then rolling resistance (in kN) of the tractor in a soil with average cone index 1000 kPa at a wheel slip of 15% (rounded off to two decimal places) will be __________.

Answer: (1.31 to 1.36)

49. The peak of a flood hydrograph due to a 5-hour storm is 670 m³ s^-1. The total depth of rainfall is 9 cm. Assuming an average infiltration loss of 0.2 cm h^-1 and a constant baseflow of 30 m3 s-1, the peak discharge of the 5-hour unit hydrograph for this catchment in m³ s^-1 is ________.

Answer: (80 to 80)

50. A parabolic grassed water channel 8 m wide at the top and 60 cm deep is laid on a slope of 3%. Assuming the value of ‘n’ in Manning’s formula as 0.04 m^-1/3 s, the discharge capacity (in m3 s-1) of the channel (rounded off to two decimal places) is __________.

Answer: (7.35 to 7.55)

51. Undisturbed soil sample is collected from a field when the soil moisture is at field capacity. The inside diameter of the core sampler is 7.5 cm with a height of 15 cm. Weight of the core sampling cylinder with moist soil is 2.81 kg and that with oven dry soil is 2.61 kg. The weight of the core sampling cylinder is 1.56 kg. Assuming π = 3.14, the water depth in centimeter per meter depth of soil (rounded off to two decimal places) is _________.

Answer: (30.10 to 30.30)

52. An irrigation stream of 27 L s^-1 is diverted to a check basin of size 12 m × 12 m. The water holding capacity of the soil is 15% and the average soil moisture content in the crop root zone prior to applying water is 7.5%. The depth of crop root zone is 1.2 m and apparent specific gravity of the soil is 1.5. Assuming no loss due to deep percolation, irrigation time (in minute) required to replenish the root zone moisture to its field capacity is _______.

Answer: (12 to 12)

53. Angle of internal friction of a certain grain (bulk density = 650 kg m^-3) is 30°. A bin filled with this grain experiences a pressure of 60 kPa at its base. Ignoring the factor of safety, the safe height (in meter) to which water (density = 1000 kg m^-3) can be filled in this bin (rounded off to two decimal places) is ________.

Answer: (2.00 to 2.10)

54. The steady-state mass transfer coefficient (kg) based on water vapour pressure differential (VPD) operating across stagnant, non-diffusing air was estimated to be 0.05 g mole s^-1 m^-2 kPa^-1. If VPD varies from 12 kPa to 7 kPa over a distance of 2 mm, then the mass transfer coefficient (kyˈ) based on equimolar counter-diffusion in g mole s-1 m^-2 (mole fraction)^-1 (rounded off to one decimal place) is __________.

Answer: (4.5 to 4.7)

55. In an air blast freezing operation, a flat tray of 1.0 m×1.0 m×0.02 m dimensions is used to freeze filled depodded peas. Bulk density and moisture content of peas are 550 kg m^-3 and 85% (w.b.), respectively. Latent heat of freezing from water to ice at -1 −°C is 335 kJ kg-1 and heat transfer occurs identically from the top and the bottom surfaces of the tray. Convective film heat transfer coefficient on the heat transfer surfaces of the tray is 30 W m^-2 K^-1 and the thermal conductivity of frozen peas is 0.54 W m^-1 K^-1. Assuming the tray to be a semi-infinite slab, the freezing time (in minutes) to completely freeze the product (rounded off to one decimal place) is ________.

Answer: (Marks to All)

GATE Exam 2019 Aerospace Engineering (AE) Question Paper With Answer Key

June 7, 2023November 27, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

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

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

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

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

2. No student was involved in the strike.

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

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

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

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

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

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

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

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

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

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

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

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

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

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

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

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

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

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

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

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Aerospace Engineering

Q. 1 – Q. 25 carry one mark each.

1. The maximum value of the function 𝑓(𝑥) = 𝑥𝑒^−𝑥 (where x is real) is

(A) 1/𝑒

(B) 2/𝑒²

(D) ∞

Answer: (A)

2. Vector 𝑏⃗ is obtained by rotating 𝑎 = 𝑖̂ + 𝑗̂ by 90° about 𝑘̂, where 𝑖̂, 𝑗̂ and 𝑘̂ are unit vectors along the x, y and z axes, respectively. 𝑏⃗ is given by

(A) 𝑖̂ − 𝑗̂

(B) −𝑖̂ + 𝑗̂

(D) −𝑖̂ − 𝑗̂

Answer: (B)

3. A scalar function is given by 𝑓(𝑥, 𝑦) = 𝑥² + 𝑦². Take 𝑖̂ and 𝑗̂ as unit vectors along the x and y axes, respectively. At (𝑥, 𝑦) = (3, 4), the direction along which 𝑓 increases the fastest is

Answer: (C)

4. The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

(A) LT⁻¹

(B) L²T ⁻¹

(D) L⁻²T

Answer: (B)

5. ϕ(𝑥, 𝑦) represents the velocity potential of a two-dimensional flow with velocity field are unit vectors along the x and y axes, tively. Which of the following is necessarily true?

(A) ∇²ϕ

(D) 𝑢 = −𝜕𝜙/𝜕𝑦, 𝑣 = 𝜕𝜙/𝜕𝑥

Answer: (B)

6. For a quasi-one-dimensional isentropic supersonic flow through a diverging duct, which of the following is true in the direction of the flow?

(A) Both the Mach number and the static temperature increase.

(B) The Mach number increases and the static temperature decreases.

(D) Both the Mach number and the static temperature decrease.

Answer: (B)

7. For a NACA2415 airfoil of chord length c, which of the following is true?

(A) Maximum camber is located at 0.2c from the leading edge.

(B) Maximum thickness is located at 0.15c from the leading edge.

(D) Maximum thickness is 0.05c.

Answer: (C)

8. When a propeller a the following state irplane in ground-roll during take-off experiences headwind, which of ments is FALSE?

(A) The drag on the airplane increases.

(B) The thrust from the propellers decreases.

(D) The ground-roll distance increases.

Answer: (D)

9. Which of the following graphs represents the response of a dynamically unstable airplane?

(A)

(B)

(C)

(D)

Answer: (A)

10. The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine

(A) has larger kinetic energy lost in the exhaust jet.

(B) has lower thrust power.

(D) has higher thrust to weight ratio.

Answer: (A)

11. While flying at order from the l Mach 2.0, 11 km altitude and producing the same thrust, what is the correct owest thrust specific fuel consumption (tsfc) to the highest tsfc?

(A) Turbofan, R amjet, Turbojet

(B) Turbofan, Turbojet, Ramjet

(D) Turbojet, Turbofan, Ramjet

Answer: (B)

12. For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

(A) CPR of an axial compressor > CPR of centrifugal compressor.

(B) CPR of an axial compressor < CPR of centrifugal compressor.

(D) CPR of any value can be attained with either an axial or a centrifugal compressor.

Answer: (B)

13. For a beam subjected to a transverse shear load through its shear center,

(A) the twist per unit length is zero.

(B) the shear stress is uniform throughout the cross-section.

(D) the shear strain is zero at the shear center.

Answer: (A)

14. A function 𝑓(𝑥) is defined by The value of

is (round off to 1 decimal place).

Answer: ()

15. The value of the following limit is______ (round off to 2 decimal places).

Answer: (0.5 to 0.5)

16. To simulate the aerodynamic forces on a cylinder of 1 m diameter due to a uniform air flow of 1 m/s at standard temperature and pressure (STP), low-speed wind tunnel experiments at STP are conducted on a 0.1 m diameter cylinder. The free stream air speed in the wind tunnel experiments should be _____ m/s (round off to the nearest integer).

Answer: (0.16 to 0.17)

17. The power-off glide range for an airplane with a maximum Lift to Drag ratio of 18, when the glide starts at an altitude of 4 km, is _______ km (round off to the nearest integer).

Answer: (10 to 10)

18. For an airplane flying in a vertical plane, the angle of attack is 3°, the horizontal and vertical components of velocity in wind axis are 300 km/h and 15.72 km/h, respectively. The pitch attitude of the airplane is _______ degrees (round off to 2 decimal places).

Answer: (5.98 to 6.00)

19. An airplane is in steady level flight with a true air speed of 50 m/s. The ambient air density and ambient pressure at the flight altitude are 0.91 kg/m³ and 7×10⁴N/m^2, respectively. At sea level, air density is 1.225 kg/m³ and ambient pressure is 1.01×10⁵ N/m². The equivalent or indicated air speed of the airplane is ______ m/s (round off to 2 decimal places).

Answer: (43.05 to 43.15)

20. For the complete combustion of 1 mole of ethanol (C₂H₅OH), the required number of moles of oxygen is _____ .

Answer: (3 to 3)

21. One kg of diatomic gas is heated and its temperature increases from 100 K to 600 K. The energy added at constant pressure during this process is 500 kJ. The specific heat at constant volume for the gas is _____ kJ/kgK. (round off to 2 decimal places).

Answer: (0.70 to 0.72)

22. The number of independent elastic constants for a homogeneous isotropic linear elastic material is______ .

23. A thin plate with Young’s modulus 210 GPa and Poisson’s ratio 0.3 is loaded as shown in the figure. The change in length along the y-direction________ is mm (round off to 1 decimal place).

Answer: (2 to 2)

24. For the state of stress shown in the figure, the normal stress, 𝜎_𝑛 , on a plane inclined at 45 degrees to the x-axis is MPa (round off to the nearest integer).

Answer: (247 to 255)

25. In the spring-mass system, shown in the figure, mass m = 3 kg and the spring stiffness k = 20 kN/m. The natural frequency of the system is _____ Hz (round off to the nearest integer).

Answer: (16 to 16)

Q. 26 – Q. 55 carry two marks each.

26. The following system of equations

2𝑥 − 𝑦 − 𝑧 = 0,

−𝑥 + 2𝑦 − 𝑧 = 0,

−𝑥 − 𝑦 + 2𝑧 = 0

(A) has no solution.

(B) has a unique solution.

(D) has an infinite number of solutions.

Answer: (D)

27. A supersonic flow in a constant area duct at Mach number M₁ encounters a ramp of angle θ₁ (see Figure 1). The resulting oblique shock with shock angle β₁ is then reflected from the top wall. For the reflected shock, the turn angle is θ2 and the shock angle is β₂.

Use the weak shock solution from the θ-β-M plot shown in Figure 2 to choose the correct option from the following.

(A) β₁ > β₂

(B) β₁ < β₂

(D) θ₁ < θ₂

Answer: (B)

28. Which of the following statements about adverse yaw of an airplane is/are correct?

P. It is caused by flow separation resulting from large rudder deflection.

Q. It is caused by dissimilar drag forces acting on the two halves of the wing resulting from aileron deflections of same magnitude.

R. It can be eliminated by ensuring that the upward deflection of one aileron is greater than the downward deflection of the opposite aileron.

(A) P only

(B) Q only

(D) Q and R

Answer: (D)

29. In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine

(A) decreases, as the heat input is lower.

(B) remains unchanged.

(D) decreases, as the thrust produced is higher.

Answer: (C)

30. For a 1 m long simply supported beam with a concentrated vertical load of 200 N and a concentrated bending moment of 100 Nm at the center as shown in the figure, the correct bending moment diagram is :

(A)

(B)

(C)

(D)

Answer: (A)

31. For real x, the number of points of intersection between the curves 𝑦 = 𝑥 and 𝑦 = cos 𝑥 is_________.

Answer: (1 to 1)

32. One of the eigenvalues of the following matrix is 1.

The other eigenvalue is ______ .

Answer: (2 to 2)

33. The curve 𝑦 = 𝑓(𝑥) is such that its slope is equal to 𝑦² for all real x. If the curve passes through (1, -1), the value of y at 𝑥 = −2 is_______ (round off to 1 decimal place).

Answer: (0.5 to 0.5)

34. The inviscid, incompressible flow field resulting from a uniform flow past a circular cylinder of radius R centered at the origin is given by:

where u_r and u_θ are the radial and azimuthal velocity components in polar coordinates, (r, θ), as shown in the figure. U is the free stream speed. Ignore the effects of gravity. The azimuthal location (in the first quadrant) on the cylinder at which the pressure coefficient is zero is ______ degrees (round off to the nearest integer).

Answer: (30 to 30)

35. A cylindrical container of radius R = 50 cm is filled with water up to a height ho. Upon rotating the cylinder about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaced upwards by h₁ = 10 cm at r = R. The magnitude of the downward displacement h₂ of the free surface at r = 0 _____ is cm (round off to the nearest integer).

Answer: (10 to 10)

36. A two-dimensional, incompressible fluid flow is described by the stream function Ψ = xy³ m²/s on the Cartesian x-y plane. If the density and dynamic viscosity of the fluid are 1 kg/m3 and 0.1 kg/m-s, respectively, the magnitude of the pressure gradient in the x direction at x=1 m and y=1 m is _______ N/m³ (round off to 1 decimal place).

Answer: (3.5 to 3.7 or 2.3 to 2.5)

37. The static pressure ratio across a stationary normal shock is given by

where M₁ is the upstream Mach number. For a stationary normal shock in air (γ = 1.4, 𝑅 = 287 J/kg-K) with upstream flow conditions given by: speed 800 m/s, static temperature 300 K and static pressure 1 atm., the static pressure downstream of the shock is ____atm. (round off to 2 decimal places).

Answer: (5.95 to 6.10)

38. For a symmetric airfoil at an angle of attack of 10º, assuming thin airfoil theory, the magnitude of the pitching moment coefficient about the leading edge is ______ (round off to 2 decimal places).

Answer: (0.24 to 0.30)

39. The span-wise distribution of circulation over a finite wing of span b = 10 m is

If Γ₀ = 20 m²/s and the free stream density and speed are 1.2 kg/m³ and 100 m/s, respectively, the total lift is _______ kN (round off to 2 decimal places).

Answer: (18.00 to 19.20)

40. The airplane shown in figure starts executing a symmetric pull-up maneuver from steady level attitude with a constant nose-up pitch acceleration of 20 deg/s². The vertical load factor measured at this instant at the centre of gravity (CG) is 2. Given that the acceleration due to gravity is 9.81 m/s², the vertical load factor measured at point P on the nose of the airplane, which is 2 m ahead of the CG, is _______ (round off to 2 decimal places).

Answer: (2.06 to 2.08)

41. Consider an airplane with a weight of 8000 N, wing area of 16 m², wing zero-lift drag coefficient of 0.02, Oswald’s efficiency factor of 0.8, and wing aspect ratio of 6, in steady level flight with wing lift coefficient of 0.375. Considering the same flight speed and ambient density, the ratio of the induced drag coefficient during steady level flight to that during a 30o climb is ______ (round off to 2 decimal places).

Answer: (1.32 to 1.35)

42. The product of earth’s mass (M) and the universal gravitational constant (G) is GM = 3.986×1014 m³/s². The radius of earth is 6371 km. The minimum increment in the velocity to be imparted to a spacecraft flying in a circular orbit around the earth at an altitude of 4000 km to make it exit earth’s gravitational field is______ km/s (round off to 2 decimal places).

Answer: (2.54 to 2.62)

43. A propeller driven airplane has a gross take-off weight of 4905 N with a wing area of 6.84 m². Assume that the wings are operating at the maximum of 13, the propeller efficiency is 0.9 and the specific fuel consumption of the engine is 0.76 kg/kW-hr. Given that the density of air at sea level is 1.225 kg/m³ and the acceleration due to gravity is 9.81 m/s², the weight of the fuel required for an endurance of 18 hours at sea level is ________ N (round off to the nearest integer).

Answer: (1440 to 1490)

44. The design of an airplane is modified to increase the vertical tail area by 20% and decrease the moment arm from the aerodynamic centre of the vertical tail to the airplane centre of gravity by 20%. Assuming all other factors remain unchanged, the ratio of the modified to the original directional static stability ( due to tail fin) is ______ (round off to 2
decimal places).

Answer: (0.96 to 0.96)

45. For a rocket engine, the velocity ratio r is V_a/V_e, where Va is the vehicle velocity and V_e is the exit velocity of the exhaust gases. Assume the flow to be optimally expanded through the nozzle. For r = 2, if F is the thrust produced and 𝑚̇ is the mass flow rate of exhaust gases, then, 𝐹/(𝑚̇𝑉_𝑒) is__________ .

Answer: (1 to 1)

46. The specific impulse of a rocket engine is 3000 Ns/kg. The mass of the rocket at burnout is 1000 kg. The propellant consumed in the process is 720 kg. Assume all factors contributing to velocity loss to be negligible. The change in vehicle velocity Δu is ____ km/s (round off to 2 decimal places).

Answer: (1.60 to 1.65)

47. The combustion products of a gas turbine engine can be assumed to be a calorically perfect gas with γ = 1.2. The pressure ratio across the turbine stage is 0.14. The measured turbine inlet and exit stagnation temperatures are 1200 K and 900 K, respectively. The total-to- total turbine efficiency is_______ % (round off to the nearest integer).

Answer: (88 to 90)

48. The figure shows the velocity triangles for an axial compressor stage. The specific work input to the compressor stage is kJ/kg_______ (round off to 2 decimal places).

Answer: (2.50 to 2.60)

49. As shown in the figure, a rigid slab CD of weight W (distributed uniformly along its length) is hung from a ceiling using three cables of identical length and cross-sectional area. The central cable is made of steel (Young’s modulus = 3E) and the other two cables are made of aluminium (Young’s modulus = E). The percentage of the total weight taken by the central cable is______ % (round off to the nearest integer).

Answer: (60 to 60)

50. All the bars in the given truss are elastic with Young’s modulus 200 GPa, and have identical cross-sections with moment of inertia 0.1 cm⁴. The lowest value of the load P at which the truss fails due to buckling is _____ kN (round off to the nearest integer).

Answer: (550 to 570)

51. A solid circular shaft is designed to transmit a torque T with a factor of safety of 2. It is proposed to replace the solid shaft by a hollow shaft of the same material and identical outer radius. If the inner radius is half the outer radius, the factor of safety for the hollow shaft is (round off to 1 decimal place).

Answer: (1.8 to 1.9)

52. In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load along the z- direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is N (round off to the nearest integer).

Answer: (310 to 320)

53. A thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of T = 1 kN-m. The walls have uniform thickness t = 1 mm and shear modulus G = 26 GPa. Assume that the curved portion is semi-circular. The shear stress in the wall is_____ MPa (round off to 1 decimal place).

Answer: (17.0 to 17.5)

54. For a damped spring-mass system, mass m = 10 kg, stiffness k = 103 N/m, and damping coefficient c = 20 kg/s. The ratio of the amplitude of oscillation of the first cycle to that of the fifth cycle is______ (round off to 1 decimal place).

Answer: (12.3 to 12.6)

55. For the system of springs and masses shown below, k = 1250 N/m and m = 10 kg. The highest natural frequency, ω, of the system is _____ radians/s (round off to the nearest integer).

Answer: (25 to 25)

GATE Exam 2018 Life Sciences (XL) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

4. A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m² of area. What is the area of the original rectangle in square meters?

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

8. From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

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

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Life Sciences (XL)

Chemistry (COMPULSORY) – XL-P

XL-P: Q. 1 – Q. 5 carry one mark each & Q. 6 – Q. 15 carry two marks each

1. F or the complete combustion of graphite and diamond in oxygen individually, the standard
enthalpy change (ΔH°₂₉₈) values are –393.5 kJ mol–1 and –395.4 kJ mol–1, respectively. Then, the ΔH° ₂₉₈ for the conversion of graphite into diamond is

(A) +1.9 kJ mol^–1

(B) –1.9 kJ mol^–1

(D) –3.8 kJ mol^–1

Answer: (A)

2. F or a 4s orbital of hydrogen atom, the magnetic quantum number (m_l) is

(A) 4

(B) 3

(D) 0

Answer: (D)

3. Hybridization of xenon in XeF₂ is

(A) sp

(B) sp²

(D) sp³d

Answer: (D)

4. Two equivalents of P react with one equivalent of Q to produce a major product R.

The number of double bonds present in the major product R is _______.

Answer: (11 to 11)

5. T he total number of possible stereoisomers for the compound with the structural formula CH₃CH(OH)CH=CHCH₂CH₃ is _______.

Answer: (4 to 4)

6. Among B—H, C—H, N—H and Si—H bonds in BH₃, CH₄, NH₃ and SiH₄, respectively, the polarity of the bond which is shown INCORRECTLY is

(A) B^δ+– H^δ–

(B) C^δ–– H^δ–

(D) Si^δ–– H^δ+

Answer: (D)

7. Among the following statements,

(i) [NiCl₄]^2– (atomic number of Ni = 28) is diamagnetic

(ii) Ethylamine is a weaker Lewis base compared to pyridine

(iii) [NiCl₂{P(C₆H₅)₃}₂] has two geometrical isomers

(iv) Bond angle in H₂O is greater than that in H₂S,

the CORRECT one is

(A) (i)

(B) (ii)

(D) (iv)

Answer: (D)

8. In [Mn(H₂O)₆]²⁺ (atomic number of Mn = 25), the d-d transitions according to crystal field theory (CFT) are

(A) Laporte forbidden and spin forbidden

(B) Laporte allowed and spin allowed

(D) Laporte allowed and spin forbidden

Answer: (A)

9. The major product M in the reaction

Answer: (D)

10. The two major products of the reaction

are

Answer: (A)

11. The compound, which upon mono-nitration using a mixture of HNO₃ and H₂SO₄, does NOT give the meta-isomer as the major product, is

Answer: (C)

12. The standard reduction potential (E°) for the conversion of CrO₇^2– to Cr³⁺ at 25°C in an aqueous solution of pH 3.0 is 1.33 V. The concentrations of CrO₇^2–to Cr³⁺ are 1.0 × 10^–4 M and 1.0 × 10^–3 M, respectively. Then the potential of this half-cell reaction is (Given: Faraday constant = 96500 C mol^–1, Gas constant R = 8.314 J K^–1 mol^–1)

(A) 1.04 V

(B) 0.94 V

(D) 0.74 V

Answer: (B)

13. The solubility product (Ksp) of Mg(OH)₂ at 25 °C is 5.6 × 10^–11. Its solubility in water is S × 10^–2 g/L, where the value of S is _______ (up to two decimal places). (Given: Molecular weight of Mg(OH)₂ = 58.3 g mol^–1)

Answer: (1.39 to 1.43)

14. The activation energy (Ea) values for two reactions carried out at 25°C differ by 5.0 kJ mol^–1. If the pre-exponential factors (A₁ and A₂) for these two reactions are of the same magnitude, the ratio of rate constants (k₁/k₂) is _______ (up to two decimal places). (Given: Gas constant R = 8.314 J K^–1 mol^–1)

Answer: (7.39 to 7.54)

15. One mole of helium gas in an isolated system undergoes a reversible isothermal expansion at 25 °C from an initial volume of 2.0 liters to a final volume of 10.0 liters. The change in entropy (ΔS) of the surroundings is ______ J K^–1 (up to two decimal places). (Given: Gas constant R = 8.314 J K^–1 mol^–1)

Answer: (-13.40 to -13.36)

Biochemistry-XL(Q)

Q. 1 – Q. 10 carry one mark each & Q.11 – Q.20 carry two marks each.

1. To which one of the following classes of enzymes does chymotrypsin belong?

(A) Oxidoreductase

(B) Hydrolase

(D) Isomerase

Answer: (B)

2. The substrate saturation profile of an enzyme that follows Michaelis-Menten kinetics is depicted in the figure. What is the order of the reaction in the concentration range between 0.8 to 1.4 M?

(A) Zero

(B) Fraction

(D) Second

Answer: (A)

3. Which one of the following conformations of glucose is most stable?

(A) Boat

(B) Half Chair

(D) Planar

Answer: (C)

4. Which one of the following profiles represent the phenomenon of cooperativity?

Answer: (C)

5. Which one of the following amino acids is responsible for the intrinsic fluorescence of proteins?

(A) Pro

(B) Met

(D) Trp

Answer: (D)

6. The glycosylation of the proteins occurs in_____.

(A) glyoxysomes

(B) lysosomes

(D) plasma membrane

Answer: (C)

7. Which one of the following properties of the myeloma cells is used in the hybridoma technology to generate monoclonal antibody?

(A) lack of thymidylate synthase

(B) over-expression of hypoxanthine-guanine phosphoribosyl transferase

(D) lack of hypoxanthine-guanine phosphoribosyl transferase

Answer: (D)

8. The movement of protons through the FoF1-ATPase during mitochondrial respiration is required for ____

(A) the increase in pH of mitochondrial matrix.

(B) changing the conformation of FoF1-ATPase to expel the ATP.

(D) decreasing the affinity of ADP to FoF1-ATPase.

Answer: (B)

9. The number of NADP⁺ molecules required to completely oxidize one molecule of glucose to CO2 through pentose phosphate pathway is ____ (correct to integer number).

Answer: (12 to 12)

10. Measurement of the absorbance of a solution containing NADH in a path length of 1cm cuvette at 340 nm shows the value of 0.31. The molar extinction coefficient of NADH is 6200 M-1 cm-1. The concentration of NADH in the solution is ___ μM (correct to integer number).

Answer: (50 to 50)

Q. 11 – Q. 20 carry two marks each.

11. Among the reagents given below which one of the combination of reagents will NOT break the disulphide bonds in the immunoglobulin molecules?

(P) Reduced glutathione

(Q) Dithiothritol

(R) Sodium dodecyl sulphate

(S) Methionine

(A) R&S

(B) P&R

(D) Q&R

Answer: (A)

12. Match the protein elution condition given in Group I with the appropriate chromatography matrices from Group II.

(A) P-iii; Q-iv; R-i; S-ii

(B) P-ii; Q-iv; R-i; S-iii

(D) P- iv; Q-ii; R-iii; S-i

Answer: (A)

13. Which one of the following is NOT a neurotransmitter?

(A) Adrenaline

(B) Glutamate

(D) Histidine

Answer: (D)

14. The type-II hypersensitivity reaction is mainly mediated by____.

(A) IgE

(B) IgM

(D) T cells

Answer: (B)

15. Which one the following reaction mechanisms drives the conversion of low energy 3-phosphoglyceraldehyde to high energy 1,3-bisphosphoglycerate?

(A) Oxidation without anhydride bond formation

(B) Oxidation coupled with anhydride bond formation

(D) Formation of carboxylate

Answer: (B)

16. A polymerase reaction is carried out for 10 cycles in a volume of 1 ml with 5 molecules of template DNA. Assuming that the efficiency of the reaction is 100 %, the number of molecules of DNA present in 100 μl at the end of the reaction is ___ (correct to integer number).

Answer: (512 to 512)

17. The secondary structure topology diagram of 400 amino acid long “Protein-X” is depicted in the figure. The start and end amino acid residue numbers of each α-helix are marked. The percentage (correct to integer number) of residues forming α-helix is____.

Answer: (20 to 20)

18. An enzyme follows Michaelis-Menten kinetics with substrate S. The fraction of the maximum velocity (V_max) will be observed with the substrate concentration [S] = 4K_m is _____ (correct to one decimal place). (K_m is Michaelis-Menten constant)

Answer: (0.8 to 0.8)

19. The mass spectrum of benzoic acid will generate the fragment as a base peak (100% relative abundance) of m/z (mass to charge ratio) at ____ (correct to integer number).

Answer: (77 to 77)

20. The standard free energy(ΔG´) values of reactions catalyzed by citrate lyase and citrate synthetase are -670 and -8192 cal/mol, respectively.

The standard free energy (in cal/mol) of acetyl-CoA hydrolysis is ___ (correct to integer number).

Answer: (-8862 to -8862)

Botany (XL-R)

XL-R: Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. Which of the following genera produces dimorphic seeds that help to broaden the time of germination in a variable habitat?

(A) Xanthium

(B) Pisum

(D) Linum

Answer: (A)

2. The genes for microRNA (miRNA) in plants are usually transcribed by

(A) RNA polymerase I

(B) RNA polymerase II

(D) RNA polymerase IV

Answer: (B)

3. Which of the statements is TRUE for transposable elements Ac and Ds?

(A) Both Ac and Ds are autonomous because they encode their own transposase

(B) Both Ac and Ds are non-autonomous because they do not encode their own transposase

(D) Only Ds is autonomous because it encodes its own transposase

Answer: (C)

4. Identify the CORRECT statement.

(A) Receptor-like kinases play role in gametophytic self-incompatibility in Brassicaceae

(B) Receptor-like kinases play role in sporophytic self-incompatibility in Solanaceae

(D) Ribonucleases play role in gametophytic self-incompatibility in Solanaceae

Answer: (D)

5. Which of the following statements is TRUE for an ecotone?

(A) An ecotone is the synonym of an ecosystem

(B) An ecotone is an interface zone of two or more ecosystems

(D) An ecotone is exclusively characterized by decreased biodiversity

Answer: (B)

6. Acid rain with a pH of 4.0 is more acidic than the rain with a pH of 6.0 by

(A) 2 times

(B) 10 times

(D) 1000 times

Answer: (C)

7. Which of the following plants produces Ylang-ylang oil?

(A) Cananga odorata

(B) Carcum copticum

(D) Pimenta racemosa

Answer: (A)

8. Identify the INCORRECT statement in connection with polar transport of auxin.

(A) The putative influx carrier AUX1 is a cytosolic protein

(B) Polar auxin transport in root tends to be both acropetal and basipetal in direction

(D) AUX1 and PIN1 proteins are located in the opposite ends of a cell for polar transport

Answer: (A)

9. Which of the following stains is used to visualize callose under the microscope?

(A) Alcian blue

(B) Aniline blue

(D) Thymol blue

Answer: (B)

10. The coding sequence of a gene XLR18 has the single ORF of 783 bp. The pproximate molecular weight of the XLR18 protein in kDa is ______.

Answer: (28.00 to 31.00)

11. Statements given below are either TRUE (T) or FALSE (F). Select the CORRECT combination.

P. Mitosis occurs exclusively in diploid mother cell

Q. Mitosis occurs both in diploid and haploid mother cells

R. Meiosis occurs exclusively in diploid mother cell

S. Meiosis occurs both in diploid and haploid mother cells

(A) P-T, Q-F, R-T, S-F

(B) P-F, Q-T, R-F, S-T

(D) P-F, Q-T, R-T, S-F

Answer: (D)

12. You are asked to design a genetic construct for high-level expression of a gene encoding the therapeutic protein 18 (TP18) via plastid transformation. Select the CORRECT set ofgenetic elements for this construct.

(A) Actin1 promoter → TP18 coding sequence → Actin1 transcription terminator

(B) Ubiquitin1 promoter → TP18 coding sequence → Ubiquitin1 transcription terminator

(D) rbcL promoter → TP18 coding sequence → rbcL transcription terminator

Answer: (D)

13. Select the CORRECT combination of the following statements.

P. The cyclic electron transport chain involving PSI results in net production of both ATP and NADPH

Q. The cyclic electron transport chain involving PSI results in net production of ATP

R. Rubisco enzyme usually converts RuBP and CO2 into 2-phosphoglycolate and 3-phosphoglycerate

S. Rubisco enzyme usually converts RuBP and O2 into 2-phosphoglycolate and 3-phosphoglycerate

(A) P, Q

(B) R, S

(D) P, R

Answer: (C)

14. Match the fruit characters with their families and representative plant species.

(A) P-2-iv, Q-3-ii, R-1-vi, S-4-v

(B) P-1-iii, Q-3-iv, R-2-i, S-4-ii

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

Answer: (B)

15. Select the CORRECT combination by matching the disease, affected plant and the causal organism.

(A) P-2-v, Q-1-iv, R-3-iii, S-4-vi

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

(D) P-4-vi, Q-1-iii, R-3-ii, S-2-v

Answer: (C)

16. Select the CORRECT combination by matching Group-I with Group-II.

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

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

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

Answer: (D)

17. Match the plant alkaloids with their uses and source species.

(A) P-2-iv, Q-1-iii, R-4-i, S-3-ii

(B) P-4-iii, Q-2-v, R-1-vi, S-3-i

(D) P-3-ii, Q-4-iii, R-1-iv, S-2-i

Answer: (A)

18. Identify the CORRECT combination of statements with respect to chemical defense in plants.

P. Pisatin, a phytoalexin produced by Ricinus communis is a constitutive defense compound

Q. Phaseolus vulgaris produces Phaseolus agglutinin I, which is toxic to the cowpea weevil

R. A single step non-enzymatic hydrolysis of cyanogenic glycoside releases the toxic hydrocyanic acid (HCN) to protect plant against herbivores and pathogens

S. Avenacin, a triterpenoid saponin from oat prevents infection by Gaeumannomyces graminis, a major pathogen of cereal roots

(A) P, Q

(B) Q, S

(D) P, S

Answer: (B)

19. In garden pea, dwarf plants with terminal flowers are recessive to tall plants with axial flowers. A true-breeding tall plant with axial flowers was crossed with a true-breeding dwarf plant with terminal flowers. The resulting F1 plants were testcrossed, and the following progeny were obtained:

Tall plants with axial flowers = 320

Dwarf plants with terminal flowers = 318

Tall plants with terminal flowers = 79

Dwarf plants with axial flowers = 83

The map distance between the genes for plant height and flower position is______cM.

Answer: (20.25 to 20.25)

20. Two true-breeding snapdragon (Antirrhinum majus) plants, one with red flowers and another with white flowers were crossed. The F1 plants were all with pink flowers. When the F1 plants were selfed, they produced three kinds of F2 plants with red, pink and white flowers in a 1:2:1 ratio. The probability that out of the five plants picked up randomly, two would be with pink flowers, two with white flowers and one with red flowers is _____%.

Answer: (11.00 to 12.00)

Microbiology (XL-S)

XL (S): Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. David Baltimore’s classification of viruses is based on differences in

(A) host cell receptors used by viruses

(B) the pathways required to synthesize virus mRNA

(D) the envelope proteins on the surface of viruses

Answer: (B)

2. Which of the following immune system components can function as an opsonin?

(A) Antibodies

(B) T-cell receptors

(D) Interferons

Answer: (A)

3. The oral polio vaccine (OPV) consists of

(A) live attenuated virus

(B) killed virus

(D) viral capsid subunit

Answer: (A)

4. Which of the following eukaryotic cellular components carries out intracellular degradation during autophagy?

(A) Nucleus

(B) Golgi bodies

(D) Lysosomes

Answer: (D)

5. A nalysis of DNA sequences suggest that eukaryotic mitochondrial genomes primarily originated from

(A) fungi

(B) protozoa

(D) bacteria

Answer: (D)

6. Binomial nomenclature has NOT yet been adopted for

(A) bacteria

(B) fungi

(D) protozoa

Answer: (C)

7. Which of the following is NOT an accepted method for sterilization?

(A) Autoclaving

(B) X-rays

(D) UV rays

Answer: (D)

8. The primary product of nitrogen fixation is

(A) N₂

(B) NH₄⁺

(D) NO₃

Answer: (B)

9. In humans, the key stages in the life cycle of malarial parasites occur in

(A) red blood cells and the liver

(B) red blood cells and platelets

(D) red blood cells and the gut

Answer: (A)

10. You have a 50 mg/mL stock solution of arginine. To prepare 1 liter of growth medium for an arginine auxotroph that requires 70 μg/mL of arginine, the volume of this stock solution that should be added is _____________ mL (up to 1 decimal point) .

Answer: (1.38 to 1.42)

11. Accumulating evidence suggest that Domain Archaea is more closely related to Domain Eukarya than to Domain Bacteria. Which of the following properties are shared between eukaryotes and archaea ?

(i) Protein biogenesis

(ii) Presence of sterol containing membranes

(iii) Ribosomal subunit structures

(iv) Adaptation to extreme environmental conditions

(v) Fatty acids with ester linkages in the cell membrane

(A) (ii), (iii) and (v)

(B) (i), (ii), (iv), and (v)

(D) (iii) and (iv)

Answer: (C)

12. Match the antimicrobial agents in group I with their category/mode of action in group II.

(A) (i)-(q), (ii)-(s), (iii)-(r), (iv)-(p)

(B) (i)-(s), (ii)-(r), (iii)-(p), (iv)-(q)

(D) (i)-(s), (ii)-(r), (iii)-(q), (iv)-(p)

Answer: (C)

13. Match the microorganisms to their predominant modes of transmission.

(A) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

(B) (i)-(s), (ii)-(q), (iii)-(p), (iv)-(r)

(D) (i)-(s), (ii)-(r), (iii)-(p), (iv)-(q)

Answer: (A)

14. Match the precursors/intermediates with the corresponding metabolic pathways.

(A) (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)

(B) (i)-(p), (ii)-(r), (iii)-(s), (iv)-(q)

(D) (i)-(r), (ii)-(s), (iii)-(q), (iv)-(p)

Answer: (D)

15. Match the scientists to their area of major contribution

(A) (i)-(s), (ii)-(q), (iii)-(p), (iv)-(r)

(B) (i)-(s), (ii)-(p), (iii)-(q), (iv)-(r)

(D) (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s)

Answer: (B)

16. Which of the following combinations would improve the resolution of a microscope?

(i) Increasing the half aperture angle of the objective lens

(ii) Decreasing the wavelength of the illumination source

(iii) Decreasing the numerical aperture of the objective lens

(iv) Decreasing the refractive index of immersion medium

(A) (i) and (ii)

(B) (ii) and (iii)

(D) (i) and (iii)

Answer: (A)

17. Active transport involves the movement of a biomolecule against a concentration gradient across the cell membrane using metabolic energy. If the extracellular concentration of a biomolecule is 0.005M and its intracellular concentration is 0.5M, the least amount of energy that the cell would need to spend to transport this biomolecule from the outside to the inside of the cell is ________ kcal/mol (up to 2 decimal points). (Temperature T = 298K and universal gas constant R= 1.98 cal/mol·K)

Answer: (2.60 to 2.80)

18. A continuous cell culture being carried out in a stirred tank reactor is described in terms of its cell mass concentration X and substrate concentration S. The concentration of the substrate in the sterile feed stream is SF = 10 g/L and yield coefficient Y_x/s = 0.5. The flow rates of the feed stream and the exit stream are equal (F=5 mL/min) and constant. If the
specific growth rate the steady state concentration of S is _____ g/L (up to 1 decimal point).

Answer: (0.5 to 0.5)

19. The initial concentration of cells (N₀) growing unrestricted in a culture is 1.0×10⁶cells/mL. If the specific growth rate (μ) of the cells is 0.1 h^-1, the time required for the cell concentration to become 1.0×10⁸ cells/mL is _________ hours (up to 2 decimal points).

Answer: (45.50 to 46.50)

20. The following stoichiometric equation represents the conversion of glucose to lactic acid in a cell:

Glucose + 2Pi + 2ADP → 2Lactate + 2ATP +2H₂O

If the free energy of conversion of glucose to lactic acid only is ΔG⁰ = –47000 cal/mol, the efficiency of energy transfer is _______ % (up to 1 decimal point). (ΔG⁰ for ATP hydrolysis is –7.3 kcal/mol)

Answer: (30.5 to 31.5)

Zoology (XL-T)

XL (T): Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. Animals belonging to phylum Echinodermata are closer to chordates than other invertebrate phyla. Which ONE of the following reasons can account for this relatedness?

(A) Highly evolved nervous system

(B) Radially symmetric body plan

(D) Well-developed muscles

Answer: (C)

2. A zoologist recovered some tissue from preserved skin of a woolly mammoth. Further genetic analysis requires DNA isolation and increasing its amount. Which ONE of the following techniques would be most useful for increasing the amount of DNA?

(A) RFLP analysis

(B) Polymerase chain reaction (PCR)

(D) Chromatography

Answer: (B)

3. In a chemical reaction where the substrate and product are in equilibrium in solution, what will occur if an enzyme is added?

(A) The equilibrium of the reaction will not change.

(B) There will be a decrease in product formed.

(D) The free energy of the system will change.

Answer: (A)

4. Tay-Sachs disease is a human genetic disorder that is associated with defects in which ONE of the following cellular organelles?

(A) Endoplasmic reticulum

(B) Mitochondria

(D) Lysosome

Answer: (D)

5. Increase in the existent population of grey peppered moth, Biston betularia, during industrial revolution in Britain is an example of which ONE of the following evolutionary processes?

(A) Neutral selection

(B) Disruptive selection

(D) Stabilizing selection

Answer: (C)

6. Which ONE of the following is NOT a characteristic of a cancer cell?

(A) Increase in cell motility

(B) Loss of contact inhibition

(D) Uncontrolled meiosis

Answer: (D)

7. Cardiac and cerebral tissues are derived from the following germ layers respectively

(A) Ectoderm and mesoderm

(B) Mesoderm and ectoderm

(D) Endoderm and ectoderm

Answer: (B)

8. An animal’s ability to escape from a predator by using the explored knowledge of home area is an example of

(A) Latent learning

(B) Insight learning

(D) Imprinting

Answer: (A)

9. Bowman’s capsules are present in which ONE of the following organs/ tissues?

(A) Renal cortex

(B) Urinary bladder

(D) Ureter

Answer: (A)

10. Which ONE of the following is the primary function of lung surfactants?

(A) Remove dust particles from bronchi

(B) Provide immunity to respiratory tract

(D) Aid in carbon dioxide exchange

Answer: (B)

11. Match the disorders/diseases listed in Column I to their respective causative agents listed in Column II.

(A) I-iv, II-iii, III-ii, IV-i

(B) I-iii, II-iv, III-ii, IV-i

(D) I-iii, II-i, III-iv, IV-ii

Answer: (B)

12. Glucose monomers are joined together by glycosidic linkages to form a cellulose polymer. During this process, changes in the free energy, total energy, and entropy respectively are represented correctly by which ONE of the following options?

(A) +ΔG, +ΔH, +ΔS.

(B) +ΔG, -ΔH, -ΔS.

(D) +ΔG, +ΔH, -ΔS.

Answer: (D)

13. In Drosophila melanogaster, a mutation in Ultrabithorax which defines the third segment of the thorax or T3 leads to development of four winged flies, as the halteres develop into a second pair of wings. Which ONE of the following phenotypes in fly will result from overexpression of Ultrabithorax in the second thoracic segment?

(A) Four winged flies.

(B) Two wings and two halteres flies.

(D) Flies with two halteres.

Answer: (C)

14. Which ONE of the following is TRUE in case of respiratory acidosis?

(A) Increased rate of ventilation is a cause of respiratory acidosis

(B) Blood pH more than 7

(D) Acidosis can be compensated through reduction of bicarbonate levels in plasma

Answer: (C)

15. Match the proteins / molecules listed in column I with the cellular location mentioned in the column II.

(A) I-ii; II-iii; III-i; IV-iv

(B) I-iii; II-iv; III-i; IV-ii

(D) I-iv; II-iii; III-ii; IV-i

Answer: (B)

16. In an experiment, nucleus from a Drosophila oocyte was transplanted into the anterior part of another oocyte, at a region opposite to the existing nucleus. Which ONE of the following phenotypes will the developing egg show?

(A) A ventralized egg with no dorsal appendages

(B) A dorsalized egg with two dorsal appendages

(D) A dorsalized egg with four dorsal appendages

Answer: (D)

17. Match the organisms listed in Column I with the features listed in Column II

(A) I-iii; II-i; III-iv; IV-ii

(B) I-ii; II-iv; III-i; IV-iii

(D) I-iv; II-iii; III-ii; IV-i

Answer: (C)

18. Which ONE of the following statements is NOT part of the classical Darwinian theory of evolution by natural selection?

(A) A trait which is constantly used will get inherited by next generation.

(B) Phenotypic variations exist among the individuals of a population of a species

(D) Each population can randomly acquire a distinct and separate suite of variations.

Answer: (A)

19. A population of rabbits was determined to have a birth rate of 200 and mortality rate of 50 per year. If the initial population size is 4000 individuals, after 2 years of non-interfered breeding the final population size will be _______________.

Answer: (5270 to 5310)

20. In a population which is in Hardy-Weinberg equilibrium, the frequency of occurrence of a disorder caused by recessive allele (q) is 1 in 1100. The frequency of heterozygotes in the population will be ______________. (Give the answer to three decimal places).

Answer: (0.056 to 0.062)

Food Technology ( XL-U)

Q. 1 – Q. 10 carry one mark each & Q.11 – Q.20 carry two marks each.

1. Which of the following is an oil soluble pigment present in fruits and vegetables?

(A) Flavonoids

(B) Carotenoids

(D) Tannins

Answer: (B)

2. Which of the following represent the group of saturated fatty acids?

(A) Lauric, Myristic, Arachidic

(B) Palmitic, Linoleic, Linolenic

(D) Behenic, Caprylic, Arachidonic

Answer: (A)

3. The anti-nutritional factor present in fava bean is

(A) Gossypol

(B) Curcine

(D) Cyanogen

Answer: (C)

4. Which of the following is a Gram positive bacteria?

(A) Listeria monocytogenes

(B) Proteus vulgaris

(D) Shigella dysenteriae

Answer: (A)

5. Irradiation carried out to reduce viable non-spore forming pathogenic bacteria using a dose between 3 to 10 kGy is

(A) Radurization

(B) Thermoradiation

(D) Radicidation

Answer: (D)

6. Identify the correct statement related to the viscosity of Newtonian fluids from the following.

(A) It is not influenced by temperature

(B) It increases with shearing rate

(D) It is not influenced by shearing rate

Answer: (D)

7. Adult male Wistar rats were fed with a protein based diet. Total 150 g of protein was ingested per animal. If the average weight increased from 110 g to 350 g after the end of experiment, the Protein efficiency ratio of the given protein would be _______. (up to two decimal points).

Answer: (1.55 to 1.65)

8. The initial moisture content of a food on wet basis is 50.76%. Its moisture content (%) on dry basis is _______.(up to two decimal points)

Answer: (103.0 to 103.2)

9. The oxygen transmission rate through a 2.54 × 10^-3cm thick low density polyethylene film with air on one side and inert gas on the other side is 3.5 × 10^-6 mL cm^-2 s^-1. Oxygen partial pressure difference across the film is 0.21 atm. The permeability coefficient of the film to oxygen is _______ × 10^-11 mL (STP) cm cm^-2 s^-1 (cm Hg)^-1.

Answer: (54 to 56)

10. Ambient air at 30°C dry bulb temperature and 80% relative humidity was heated to a dry bulb temperature of 80°C in a heat exchanger by indirect heating. The amount of moisture gain (g kg^-1 dry air) during the process would be _______.

Answer: (0 to 0)

Q. 11 – Q. 20 carry two marks each.

11. Match the commodity in Group I with the bioactive constituent in Group II

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

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

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

Answer: (B)

12. Match the process operation in Group I with the separated constituent in Group II

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

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

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

Answer: (C)

13. Match the spoilage symptom in Group I with the causative microorganism in Group II

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

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

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

Answer: (C)

14. Match the fermented product in Group I with the base material in Group II

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

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

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

Answer: (A)

15. Match the operation in Group I with the process in Group II

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

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

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

Answer: (D)

16. Out of 7 principles of HACCP system, 4 are listed below. Arrange these principles in the order in which they are applied.

(P) Conduct a hazard analysis

(Q) Establish monitoring process

(R) Establish critical limit

(S) Establish record keeping and documentation process

(A) P, R, Q, S

(B) Q, R, P, S

(D) R, S, P, Q

Answer: (A)

17. Identify an example of a classical diffusional mass transfer process without involving heat, among the following.

(A) Drying of food grains

(B) Carbonation of beverages

(D) Concentration of fruit juice

Answer: (B)

18. For an enzyme catalyzed reaction S → P the kinetic parameters are:

[S] = 40 μM, V₀ = 9.6 μM s-1 and V_max = 12.0 μM s^-1.

The K_m of the enzyme in μM will be _______.(up to one decimal points)

Answer: (9.8 to 10.2)

19. A microbial sample taken at 10 AM contained 1 × 10⁵ CFU/mL. The count reached to 1 × 10¹⁰ CFU/mL at 8 PM of the same day. The growth rate (h-1) of the microorganism would be _______.(up to two decimal points)

Answer: (1.1 to 1.8)

20. The rate of heat transfer per unit area from a metal plate is 1000 W m^-2. The surface temperature of the plate is 120°C and ambient temperature is 20°C. The convective heat transfer coefficient (W m^-2 °C^-1) using the Newton’s law of cooling will be _______.

Answer: (10 to 10)

GATE Exam 2018 Engineering Sciences (XE) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

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

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Engineering Sciences

Engineering Mathematics (XE-A)

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

1. The largest interval in which the initial value problem

has a unique solution is

(A) (–∞, ∞)

(B) (–5, 5)

(D) (0, 5)

Answer: (D)

2. The sum of the roots of the indicial equation at 0x of the differential equation

(A) 0

(B) 1

(D) –2

Answer: (A)

3. Let f be a three times continuously differentiable real valued function on (0, 5) such that its third derivative for all x ∈ (0, 5). If P(x) is a polynomial of degree ≤ 2 such that P(1) = f(1), P(2) = f(2) and P(3) = f(3) then |f(4) – P(4)| equals _______________

Answer: (0.01 to 0.01)

4. For real numbers α₁ and α₂ if the formula is exact for all polynomials of degree ≤ 1 then 2α₁ + 3α₂ equals _______

Answer: (5 to 5)

5. Raju has four fair coins and one fair dice. At first Raju tosses a coin. If the coin shows head then he rolls the dice and the number that dice shows is taken as his score. If the coin shows tail then he tosses three more coins and the total number of tails shown (including the first one) is taken as his score. If Raju tells that his score is 2 then the probability that he rolled the dice is (up to two decimal places) _______________

Answer: (0.29 to 0.32)

6. Let f be a continuously differentiable real valued function defined by

Then the value of a²b is _______________

Answer: (250 to 250)

7. A rectangular box without top cover having a square base is to be made from a sheet of 108 square meters. Then the largest possible volume of the box in cubic meters is ______________

Answer: (108 to 108)

8. Let Then the trace of A¹⁰⁰⁰ equals

(A) 2¹⁰⁰⁰ – 1

(B) 2¹⁰⁰⁰ + 1

(D) 2¹⁰⁰⁰

Answer: (B)

9. Let ℂ denote the set of complex numbers and i² = –1. Let ϒ be the simple positively oriented circle |z| = 1 and S = {z ∈ ℂ| 0 <|z| < 2}. If f : S → ℂ is analytic in S and is given by

then the value of the contour integral

(A) 0

(B) 1/8

(D) 7/2

Answer: (C)

10. Let ℝ³ denote the three dimensional Euclidean space and for all (x, y, z) ∈ ℝ³. If C is the curve described by the parametric equation then the value of the line integral i is ______________

Answer: (3 to 3)

11. Let u(x, t) satisfy the initial and boundary value problem

Then the value of is __________

Answer: (0.04 to 0.04)

Fluid Mechanics (XE (B))

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

1. Rheological diagram of different types of fluids is shown in figure. Column I represents the nature of the fluid and column II represents the curve showing the variation of shear stress against shear strain rate.

The most appropriate match between columns I and II is,

(A) (i) – O; (ii) – N ; (iii) – P; (iv) – M

(B) (i) – O; (ii) – P ; (iii) – N; (iv) – M

(D) (i) – P; (ii) – O ; (iii) – N; (iv) – M

Answer: (B)

2. In a two-dimensional, incompressible and irrotational flow, stream function (Ψ = Ψ (x, y) ) and velocity potential (Φ = Φ(x, y) exist. The velocities in x and y directions are non-zero. The product of , is

(A) −1

(B) 0

(D) ∞

Answer: (A)

3. The inviscid flow past a rotating circular cylinder can be generated by the superposition of

(A) uniform flow, source and vortex

(B) uniform flow, doublet

(D) uniform flow, doublet and vortex

Answer: (D)

4. The velocity field and the surface normal vector are given by, and respectively. If Euler equations are to be solved, the boundary condition that must be satisfied at the wall is,

Answer: (A)

5. The influence of Froude number is most significant in

(A) capillary flows

(B) creeping flows

(D) compressible flows

Answer: (C)

6. If the stream function (Ψ(x, y)) for a two-dimensional incompressible flow field is given as 2y(x² − y²), the corresponding velocity field is

Answer: (B)

7. Water is flowing in two different tubes of diameters D and 2D, with the same velocity. The ratio of laminar friction factors for the larger diameter tube to the smaller diameter tube is

(A) 0.5

(B) 1.0

(D) 4.0

Answer: (A)

8. If the velocity field is vorticity of the fluid element in the field at (x=1, y=2) in s^-1 is ____.

Answer: (4 to 4)

9. A pitot-static tube is used to measure air velocity in a duct by neglecting losses. The density of air is 1.2 kg/m³. If the difference between the total and static pressures is 1 kPa, the velocity of air at the measuring location, in m/s, is _______.

Answer: (39 to 42)

10. A parallelepiped of (2 m × 2 m) square cross-section and 10 m in length, is partially floating in water upto a depth of 1.2 m, with its longest side being horizontal. The specific gravity of the block is

(A) 0.8

(B) 0.6

(D) 0.4

Answer: (B)

11. The velocity field in a two-dimensional, unsteady flow is given by The magnitude of acceleration of a fluid particle located at x = 1 m, y = 1 m at the time t = 1 s, in m/s², is

(A) 16.0

(B) 18.1

(D) 34.1

Answer: (C)

12. In a two-dimensional, incompressible and irrotational flow, fluid velocity (v) in the ydirection is given by v = 2x−5y . The velocity (u) in the x-direction is

(A) u = 2x−5y

(B) u = 2x − 5y

(D) u = 5x−2y

Answer: (C)

13. A two-dimensional laminar viscous liquid film of constant thickness (h) steadily flows down an incline as shown in figure. Acceleration due to gravity is g. If the velocity profile in the liquid film is given as, u = ky(2h– y); v = 0, the value of constant k is

Answer: (A)

14. A water jet of 100 mm diameter issuing out of a nozzle at a speed of 50 m/s strikes a vane and flows along it as shown in figure. The vane is attached to a cart which is moving at a constant speed of 20 m/s on a frictionless track. The jet is deflected at an angle of 30o. Take the density of water as 1000 kg/m³. Neglecting the friction between the vane and the fluid, the magnitude of the force exerted by water on the cart in the x-direction, in N, is ______.

Answer: (900 to 990)

15. Capillary waves are generated in the sea. The speed of propagation (C) of these waves is known to be a function of density (ρ), wave length (λ), and surface tension (σ). Assume, ρ and λ to be constant. If the surface tension is doubled, in the functional form of the relevant non-dimensional group, the percentage increase in propagation speed (C) is _______

Answer: (40 to 42)

16. Consider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________.

Answer: (2.9 to 3.1)

17. A 2.6 gram smooth table-tennis (ping-pong) ball has a diameter of 38 mm. Density (ρ) of air is 1.2 kg/m3. Neglect the effect of gravity. Take coefficient of drag as 0.5. If the ball is struck with an initial velocity of 30 m/s, the initial deceleration, in m/s², is _________.

Answer: (107 to 127)

18. O n a flat plate, transition from laminar to turbulent boundary layer occurred at a critical Reynolds number (Re_cr). The empirical relations for the laminar and turbulent boundary layer thickness are given by respectively. The ratio of laminar to turbulent boundary layer thickness, at the location of transition, is 0.3. The value of Recr is _______.

Answer: (440000 to 442000)

19. In a capillary tube of radius R = 0.25 mm, a fully developed laminar velocity profile is defined as, MPa/m, μ is the dynamic viscosity of the fluid, and r is the radial position from the centerline of the tube. If the flow rate through the tube is 1000 mm³/s, the viscosity of the fluid, in Pa-s, is ______________.

Answer: (0.001 to 0.002)

20. The skin friction coefficient for a turbulent pipe flow is defined as, where τ_w is the wall shear stress and V is the average flow velocity. The value of f C is empirically given by the relation: C_f = 0.065(2/Re)^0.25where Re is the Reynolds number. If the average flow velocity is 10 m/s, diameter of the pipe is 250 mm, kinematic viscosity of the fluid is 0.25×10^–6 m²/s, and density of the fluid is 700 kg/m³, the skin friction drag induced by the flow over 1 m length of the pipe, in N, is ___________.

Answer: (30 to 45)

21. A (150 mm × 150 mm) square pillar is located in a river with water flowing at a velocity of 2 m/s, as shown in figure. The height of the pillar in water is 8 m. Take density of water as 1000 kg/m³ and kinematic viscosity as 1×10^–6 m/s². The coefficient of drag of the pillar is 2.0. The drag force exerted by water on the pillar in N is _______.

Answer: (4800 to 4800)

22. An orifice plate is used to measure flow rate of air (density = 1.23 kg/m³) in a duct of 250 mm diameter as shown in figure. The volume flow rate is 1 m³/s. Flow at sections 1 and 3 is uniform and section 2 is located at vena contracta. The diameter ratio, D_t/D₁, is 0.66. The flow area at vena contracta, A₂ = 0.65At, where At is area of the orifice. The pressure difference between locations 2 and 3 in N/m² is ____________.

Answer: (1200 to 1350)

Materials Science (XE-C)

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

1. The stress ratio for a completely reversed cyclic loading during a fatigue test is

(A) 0

(B) 1

(D) –1/2

Answer: (C)

2. Minimum symmetry that a cubic crystal must possess is

(A) four 3-fold rotation axes.

(B) three 4-fold rotation axes.

(D) centre of symmetry.

Answer: (A)

3. If a material is repelled in an external magnetic field then it is

(A) Ferromagnetic

(B) Diamagnetic

(D) Antiferromagnetic

Answer: (B)

4. An electron makes a transition from the valence band to the conduction band in an indirect band gap semiconductor. Which one of the following is true?

(A) Energy of the electron decreases.

(B) A photon is emitted in the process.

(D) A photon is created in the process.

Answer: (C)

5. Which one of the following is the characteristic of a screw dislocation?

(A) Dislocation line and Burgers vector are parallel.

(B) Direction of motion of dislocation is parallel to the Burgers vector.

(C) Atomic displacement due to the movement of the dislocation is in the direction of the motion of the dislocation line.

(D) It has a unique slip plane.

Answer: (A)

6. The number of vibrational degrees of freedom for a non-linear triatomic molecule are

(A) 9

(B) 6

(D) 3

Answer: (D)

7. An atom is restricted to move in one dimension by making unit jumps either to the left or right, as shown in the figure. Assuming that a jump to the left or right is equally probable, the probability of the atom returning back to the starting point after four jumps is

(A) 0.250

(B) 0.333

(D) 0.500

Answer: (C)

8. For a two-dimensional solid, the variation of lattice specific heat as a function of temperature T (in K, at low temperatures) is given as: 𝐶_𝑝=𝑏𝑇^𝑛, where b is a constant. The value of n is ____________.

Answer: (2 to 2)

9. If the cation (C) to anion (A) radius ratio,r_C/r_Ais 0.6, then the coordination number (i.e., number of A ions surrounding a C ion) is likely to be ____________.

Answer: (6 to 6)

10. Match the invariant reactions in Column I with the names in Column II (L is liquid phase, and α, β, γ are solid phases). All reactions proceed to the right on cooling.

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

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

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

Answer: (B)

11. Consider the following anodic (oxidation) reaction in an acidic solution:

Mg → Mg⁺² + 2e^–

If 48250 Coulomb charge is produced during this anodic reaction then the amount of Mg (in g) dissolved into the solution is
(Given: Faraday Constant =96500 C/mole of electrons, Atomic weight of Mg = 24)

(A) 6

(B) 12

(D) 48

Answer: (A)

12. An intrinsic semiconductor has conduction electron concentration, n = 10¹² cm^–3. The mobility of both electrons and holes are identical = 4 × 10⁴ cm² V^–1 s^–1. If a voltage of 100 V is applied on two parallel end faces of the cube (edge length 1 cm) through Ohmic contacts, the current through the cube would be (in mA)
(Given: charge of electron = 1.6 × 10^–19 C)

(A) 640

(B) 1280

(D) 12800

Answer: (B)

13. An infinite plate with a through-thickness crack of length 2 mm is subjected to a tensile stress (as shown in the figure). Assuming the plate to be linear elastic, the fracture stress is ____________ MPa (round off to the nearest whole number)

(Given: Fracture toughness, 𝐾_𝐼𝐶=25 𝑀𝑃𝑎 √m)

Answer: (430 to 500)

14. A unidirectionally aligned carbon fibre reinforced epoxy composite is loaded as shown in the figure. The volume fraction of the fibre is 0.6. The Young’s modulus of the composite is ____________ GPa.

(Given: Young’s Modulus of the fibre and the matrix are 200 GPa and 10 GPa, respectively)

Answer: (124 to 124)

15. A sintered sample was weighed in air and water using an analytical balance. The mass of the sample in air is 2.67 g and its apparent mass in water is 1.67 g. The density of the sample is __________ g cm^–3 (give answer up to 2 decimal places)
(Given: Density of water = 1.00 g cm^–3)

Answer: (2.60 to 2.70)

16. The atoms in a gas laser have two energy levels such that a transition from the higher to the lower level releases a photon of wavelength 500 nm. If 7 × 10²⁰ atoms are pumped into the upper level with 4 × 10²⁰ atoms in the lower level, the amount of energy released in a single pulse is ____________ Joules (give answer up to 2 decimal places)
(Given: Planck’s constant, h = 6.6 × 10^–34 J s; speed of light, c = 3 × 10⁸ m s^–1)

Answer: (59.00 to 60.00)

17. The speed of an electron is measured to be 300 m s^–1 with an uncertainty of 0.01%. The fundamental accuracy with which the position of the electron can be determined simultaneously with the speed in the same experiment is _________ mm (give answer up to 2 decimal places)
(Given: Planck’s constant, h = 6.6 × 10^–34 J s; mass of electron = 9.1 × 10^–31 J kg)

Answer: (1.85 to 2.00)

18. When 3 identical non-interacting spin ½ particles are put in an infinite potential well, the ground state energy of the system is 18 meV. If instead, seven particles are put inside the potential well, the new ground state energy is ________ meV.

Answer: (132 to 132)

19. If the value of the integral (I) is 4, the value of the constant b is ___________ (give answer up to 2 decimal places).

Answer: (5.01 to 5.17)

20. X-ray diffraction pattern is obtained from FCC polycrystalline aluminium (lattice parameter = 0.405 nm) using Cr-K radiation of wavelength 0.229 nm. The maximum number of peaks that can be observed in the pattern is ____________.

Answer: (5 to 5)

21. The planar atomic density in the (110) plane of a BCC iron crystal is ____________ nm^–2 (give answer up to 2 decimal places)
(Given: lattice parameter of iron is 0.287 nm)

Answer: (15.5 to 18.5)

22. Mild steel is carburized at 1300 K for 1 hour to obtain a certain case depth. Keeping the time as 1 hour, the case depth can be doubled by increasing the temperature to ______________K (round off to the nearest whole number)

(Given: Activation energy Q = 148 kJ mol^–1, Gas constant, R = 8.314 J mol^–1 K^–1)

Answer: (1420 to 1480)

SOLID MECHANICS (XE-D)

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

1. A thin cylinder (thickness, t and diameter, d) with closed ends is subjected to an internal pressure, p. The ratio of hoop stress to longitudinal stress developed in the wall of the cylinder is

(A) 1:4

(B) 1:2

(D) 2:1

Answer: (D)

2. A steel rod is fixed at one end and free at the other end. The coefficient of thermal expansion of the steel is α, and modulus of elasticity is E. If the temperature of the rod is increased by ΔT then the stress and strain developed in the rod are respectively

(A) zero, αΔT

(B) EαΔT, αΔT

(D) zero, zero

Answer: (A)

3. The effective lengths of the columns with ideal boundary conditions shown in Case-I, Case-II, and Case-III are respectively

(A) L, 4L, 2L

(B) L, 2L, L/4

(D) L, 2L, L/2

Answer: (D)

4. At a point in a stressed body, sum of the normal stresses acting on perpendicular faces of an arbitrarily oriented plane stress element is always

(A) dependent on the angle of orientation of the element

(B) constant and independent of angle of orientation of the element

(D) zero

Answer: (B)

5. The principal stresses on a plane stress element are shown in the figure. The maximum shear stress (in MPa) is

(A) 200

(B) 100

(D) 0

Answer: (B)

6. A rigid and thin L-shaped bracket is fixed to the wall at point B, and a force F is applied at point A as shown. For a given force F, the point B experiences the maximum clockwise moment when the inclination θ (in degrees) with the x-axis is……….[up to two decimal places].

Answer: (52.50 to 53.50)

7. A cantilever beam with length, L = 1 m, modulus of elasticity, E = 210 GPa, and area moment of inertia, I = 1.2 × 10^–7m⁴ carries a concentrated mass m = 100 kg at its freeend. By idealizing it as a single degree-of-freedom system and neglecting the mass of the cantilever beam, the natural frequency (in rad/s) of small transverse oscillations of the mass m is …….. [up to two decimal places]

Answer: (27.00 to 28.00)

8. For a typical grade of steel, the value of modulus of elasticity (E) and Poisson’s ratio (ν) are 208 GPa and 0.3 respectively. The value of shear modulus (G) of the steel (in GPa) is ……..

Answer: (80 to 80)

9. A tensile test is performed on a metallic specimen of diameter 8 mm and gauge length 50 mm. When the tensile load P reaches a value of 20 kN, the distance between the gauge marks increases by 0.09 mm. If the sample remains within the elastic limit, the modulus of elasticity (in GPa) of the test metal is………..[up to two decimal places]

Answer: (220.00 to 222.00)

10. A beam ABC is subjected to load P at its free end C as shown in the figure. The flexural rigidity of the beam is EI. The vertical support reaction at point B is

(A) 5P/4

(B) 5P/2

(D) 2P/5

Answer: (B)

11. A horizontal effort P is applied to raise a block of weight W on a rough surface inclined at an angle θ with the horizontal. If μ_s is the coefficient of static friction between the block and the surface, the minimum effort P required to impend the upward motion of the block along the surface is

Answer: (B)

12. Three round bars of same material, equal lengths, and different cross-sectional dimensions are shown in the figures as Case-I, Case-II and Case-III. All the bars are clamped at the upper end, and a concentrated load P is applied at the lower end of each bar. If the elastic strain energy stored in the bar shown in Case-I is U₁ then the elastic strain energy stored in Case-II and Case-III respectively is

(A) (8/5)U₁, (5/8)U₁

(B) (5/16)U₁, (5/16)U₁

(D) (5/8)U₁, (5/8)U₁

Answer: (D)

13. A rigid uniform rod with mass m, length L and center of gravity G is freely suspended from a hinge as shown in the figure. The rod is given a small angular displacement θ in the counter-clockwise direction from the position in which it hangs vertically (θ = 0). If g is the acceleration due to gravity, the natural frequency of oscillations (in rad/s) is

Answer: (C)

14. A cylindrical member, made up of ductile material, is subjected to pure torsion as shown in the figure. The failure plane (from Option-I to Option-IV) for ductile material as per maximum shear stress theory is represented by

(A) Option I

(B) Option II

(D) Option IV

Answer: (C)

15. A simply supported beam of span L is subjected to a couple Mo at a distance a from support A. Among the four options (Option-I to Option-IV) shown, the correct shear force diagram of the beam is

(A) Option-I

(B) Option-II

(D) Option-IV

Answer: (A)

16. A circular shaft ABC of diameter, L and length, A is fixed at end A. It is subjected to the torsional moments at point B and point C as shown in the figure. The ratio of angle of twists at point B to point C is

(A) 1.5 : 1

(B) 1 : 3

(D) 1 : 1.5

Answer: (D)

17. A circular steel bar of diameter 10 mm is bent into the shape as shown in figure, and lies in x-z plane. A horizontal force P is applied along the positive z-direction as shown. The yield strength of the steel is 200 MPa. Neglecting the effect of transverse shear, the load P (in Newton) required to initiate yielding as per maximum shear stress theory of failure is…………[up to two decimal places]

Answer: (195.00 to 197.00)

18. Two sliders A and B, connected by a rigid link of length L, slide in two mutually perpendicular and frictionless guide-ways. At a particular instance, the slider A is moving in the downward direction with a speed of 0.05 m/s. At this instance, the magnitude of the velocity of slider B (in m/s) is ……[up to two decimal places]

Answer: (0.01 to 0.02)

19. A simply supported beam ABC is subjected to load as shown in the figure. The 20 kN load is applied at point B with the help of a welded bracket as shown. The beam has a rectangular cross-section of 15 mm width and 100 mm depth as shown. The maximum transverse shear stress developed in the beam (in MPa) is ……..[up to one decimal place]

Answer: (14.5 to 15.5)

20. A rigid rod ABC, in the form of a quarter-circular arc of radius R, is hinged at C and supported by a roller at B. A vertical force P is applied at the end A of the bar. For the reactions at B and C to be equal in magnitude, the value of the angle θ (in degrees) is ………. [up to two decimal places].

Answer: (26.00 to 27.00)

21. A marble of mass m slides along a frictionless linear slide AB kept in a vertical plane. The marble is released from point A with zero initial velocity, and it reaches point B under the action of gravity. Assuming the acceleration due to gravity to be 9.81 m/s², the speed (in m/s) of the marble when it just reaches point B is………[up to two decimal places].

Answer: (3.10 to 3.20)

22. A horizontal force 10 N is applied at support B on the frame as shown in figure. Considering only bending deformation, the vertical reaction (in N) at support B is ………. [up to one decimal place]

Answer: (13.5 to 14.5)

Thermodynamics (XE-E)

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

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, C_p : molar heat capacity at constant pressure, C_v : molar heat capacity at constant volume, R : universal gas constant

1. When a fixed mass of air-water vapour mixture is heated at constant pressure,

(A) both relative and specific humidity decrease.

(B) relative humidity decreases, but specific humidity remains unchanged.

(D) both relative and specific humidity increase.

Answer: (B)

2. For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the magnitude of work done is

Answer: (A)

3. The statement which is NOT a consequence of the first law of thermodynamics is

(A)Heat is a path function

(B) Energy is a property of a system

(D)A perpetual motion machine of the first kind is not possible

Answer: (C)

4. For a refrigerator absorbing heat Q_L from a cold region and rejecting heat Q_H to a hot region, the coefficient of performance is written as

Answer: (A)

5. The value of the compressibility factor at the critical point evaluated using the van der Waals equation of state is

(A) 2/7

(B) 5/8

(D) 1/7

Answer: (C)

6. The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour pressure of 13.5 kPa is

(A) 58.7

(B) 51.4

(D) 35.2

Answer: (D)

7. One kmol of an ideal gas (C_p = 21 kJ/kmol.K) undergoes a constant pressure process from 300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy (in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.

Answer: (160.0 t0 161.0)

8. A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.

Answer: (14.5 to 15.0)

9. An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of 2 bar and a temperature of 300 K, the volume (in m³) of 1 kg of this gas (up to 2 decimal places) is ________.

Answer: (0.30 to 0.32)

10. Consider the following statements for an ideal gas undergoing a reversible non-flow process:

P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero.

Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero.

R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero.

S. If the process is isothermal, the change in entropy of the gas is necessarily zero.

Which one of the following options is valid?

(A) Only P is correct

(B) Only S is correct

(D) Only P and S are correct

Answer: (C)

11. An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature and reject equal amount of heat. Also, the working fluid enters at the same state before compression. One of the following statements always true about their efficiencies (𝜂) is

(A) 𝜂_O > 𝜂_D

(B) 𝜂_O= 𝜂_D

(D) 𝜂_O= 1−𝜂_D

Answer: (C)

12. A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection (in kJ/s) to the reservoir at 650 K is

(A) 11

(B) 31

(D) 52

Answer: (D)

13. A gas obeys the following equation of state:

where is molar volume, and a, b are constants with values a = 10^–5 J.K/Pa² and b = 8 × 10^–2 m³/mol. Take C_p = 30 kJ/kmol.K. At 10 bar and 500 K, the value of the Joule-Thomson coefficient (in K/Pa) is

(A) –2 × 10^–6

(B) –4 × 10^–6

(D) 4 × 10^–6

Answer: (B)

14. In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (ℎ = 3375.1 kJ/kg, 𝑠 = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa, ℎ_𝑓 = 191.81 kJ/kg, 𝑠_𝑓 = 0.6492 kJ/kg.K, ℎ_𝑔 = 2583.9 kJ/kg and 𝑠_𝑔 = 8.1488 kJ/kg.K. The heat rejected in the condenser (in kJ/kg) is

(A) 1898

(B) 3796

(D) 2847

Answer: (A)

15. Methane has compressibility factor value of 0.9 at reduced pressure of 1.0 and reduced temperature of 1.5. For propane, the critical temperature and pressure are 369.8 K and 42.48 bar, respectively. Take R = 8.314 kJ/kmol.K. Applying the principle of corresponding states, the molar volume of propane (in m3/kmol) at the same reduced pressure and temperature is

(A) 0.355

(B) 0.526

(D) 0.977

Answer: (D)

16. A rigid insulated vessel is divided into two compartments by a partition. One compartment contains 12 kg of oxygen at 200 kPa and 280 K. The other compartment contains 26 kg of carbon dioxide at 400 kPa and 360 K. The specific heats at constant volume in kJ/kg.K for oxygen and carbon dioxide are 0.662 and 0.653, respectively. The partition is removed and the gases are allowed to mix. Considering both gases are ideal, the final temperature (in K) of the mixture (up to 1 decimal place) is ________.

Answer: (332.5 to 336.5)

17. Moist air having 60% relative humidity, enters a steady-flow air-conditioning unit at 102 kPa and 30 °C. The volume flow rate of the moist air entering the unit is 0.1 m³/s. The moist air leaves the unit at 95 kPa and 15 °C with a relative humidity of 100%. Liquid condensate leaves the unit at 15 °C.

For water: at 15 °C, ℎ_𝑓 = 62.982 kJ/kg, ℎ_𝑔 = 2528.3 kJ/kg, 𝑃_𝑠𝑎𝑡 = 1.7057 kPa. at 30 °C, ℎ_𝑓 = 125.74 kJ/kg, ℎ_𝑔 = 2555.6 kJ/kg, 𝑃_𝑠𝑎𝑡 = 4.2469 kPa.

For air, specific heat at constant pressure is 1.004 kJ/kg.K and the specific gas constant is 0.287 kJ/kg.K.

Neglecting heat leakage to the surrounding, the magnitude of heat extracted (in kW) from the air stream (up to 2 decimal places) is __________.

Answer: (3.01 to 3.07)

18. Air at 150 kPa and 323 K is filled in a rigid vessel of 0.05 m³ capacity. For air, assumed as an ideal gas, specific heat at constant volume is 0.7163 kJ/kg.K and the specific gas constant is 0.287 kJ/kg.K. Neglect kinetic and potential energy changes. If 30 kJ of heat is added, the final temperature (in K) of air (up to 1 decimal place) is __________.

Answer: (838.0 to 844.0)

19. Superheated steam at 2 bar and 300 °C, with an enthalpy of 3072.1 kJ/kg, enters a horizontal adiabatic nozzle with negligible velocity and leaves at 0.2 bar as saturated vapour with an enthalpy of 2609.9 kJ/kg. Assuming steady flow and neglecting the potential energy changes, the exit velocity (in m/s) of the steam (up to 1 decimal place) is __________.

Answer: (961.0 to 962.0)

20. A given mass of a simple compressible substance undergoes a reversible cycle, as shown in the P-V diagram. The magnitude of the net work done during the cycle is 3 kJ. The pressure (in bar) at point C (up to 1 decimal place) is ________.

Answer: (5.7 to 6.1)

21. One kmol of an ideal gas at 300 K and 10 bar is reversibly heated in a constant volume process to 500 K. It is then reversibly and isothermally expanded to 2 bar. Take C_v = 20.8 kJ/kmol.K and R = 8.314 kJ/kmol.K. The total heat supplied (in kJ) to the gas (up to 1 decimal place) is ________.

Answer: (12950.0 to 13000.0)

22. A rigid container is completely filled with a liquid having a constant isothermal compressibility of 1.09 × 10^–4 bar^–1 and a constant coefficient of volume expansion of 1.12 × 10^–3 K^–1 . The liquid is initially at 300 K and 1 bar. Heat is supplied to the liquid to raise its temperature to 350 K. Assuming that no phase change occurs, the final pressure (in bar) of the liquid (up to 1 decimal place) is ________.

Answer: (513.0 to 517.0)

Polymer Science & Engineering (XE – F)

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

1. Which one of the following polymers occurs naturally?

(A) Bakelite

(B) Teflon

(D) Perspex

Answer: (C)

2. The order of average molecular weights of a polymer is

Answer: (A)

3. Rubbers are a class of polymer known for

(A) High intermolecular forces

(B) High T_g polymers

(D) Low intermolecular forces

Answer: (D)

4. Nylon 6 is manufactured from

(A) Sebacic acid and hexamethylene diamine

(B) Caprolactam

(D) Caprolactone

Answer: (B)

5. S torage modulus and tan δ of a polymer are experimentally measured by

(A) Differential scanning calorimetry

(B) Thermogravimetric analysis

(D) Dynamic mechanical thermal analysis

Answer: (D)

6. A plastic bucket is manufactured by

(A) Compression moulding

(B) Injection moulding

(D) Blow moulding

Answer: (B)

7. T he monomers, A and B with reactivity ratios rA and rB, form alternate copolymers when,

(A) r_A = r_B = 0

(B) r_A = r_B = 1

(D) r_A < 1, r_B < 1

Answer: (A)

8. The degree of polymerization of a poly(methyl methacrylate) sample having number average molecular weight of 1,50,000 g/mol is___________.

(C = 12, H = 1, O = 16 g/mol).

Answer: (1500.00 to 1500.00)

9. If the heat of fusion of 100 % crystalline polyethylene is 290 mJ/mg, a sample of polyethylene with heat of fusion of 141 mJ/mg will have_______ % crystallinity.

Answer: (48.52 to 48.72)

10. Match the following:

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

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

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

Answer: (D)

11. Match the following:

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

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

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

Answer: (A)

12. Flexible PVC tubes are used for watering. If some organic solvents are passed through this tube, it becomes stiff. This is due to the fact that the organic solvents

(A) plasticize PVC and raise Tg.

(B) remove plasticizer and raise Tg.

(D) react with PVC and increase Tg

Answer: (B)

13. Match the following:

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

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

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

Answer: (D)

14. Match the following:

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

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

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

Answer: (B)

15. A plot of strain (%) versus time of a polymer is given below. Based on this plot and the properties as mentioned below, find out the correct combination.

1 = Viscoelastic deformation; 2 = Elastic deformation

3 = Viscoelastic recovery; 4 = Elastic recovery

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

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

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

Answer: (D)

16. T he plot shows apparent viscosity versus shear rate of Newtonian, Dilatent and Pseudoplastic fluids. Based on this plot and the fluid behaviour as mentioned below, find out the correct combination.

1 = Dilatent fluid; 2 = Newtonian fluid, 3 = Pseudoplastic fluid

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

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

(D) P-2; Q-3; Q-1

Answer: (C)

17. Plot of the modulus versus temperature of different types of polymers is given below. Based on this plot and the nature of the polymers as mentioned below, find out the correct combination.

1 = An amorphous polymer of high molecular weight having entanglements

2 = An amorphous polymer of moderate molecular weight

3 = Highly crosslinked polymer

4 = Semi-crystalline polymer

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

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

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

Answer: (C)

18. The T_g of homopolymers of A and B are +100°C and -70°C respectively. The T_g of a random copolymer of A and B having 40 wt% A and 60 wt% B is _________°C.

Answer: (-25.00 to -24.50)

19. The number average molecular weight of a polymer prepared from HO(CH₂)₁₄COOH is 24,000 g/mol. The conversion of the monomer required to reach the above molecular weight is__________%. (C = 12, H = 1, O = 16 g/mol).

Answer: (98.80 to 99.10)

20. Glass fibers in nylon provide reinforcement. The modulus of elasticity for each component of the composite is; E_glass = 10.5 x 10⁶ psi; E_nylon = 0.4 x 10⁶ psi. If the nylon contains 30 vol % E-glass, the fraction of the applied force is carried by the glass fiber is__________. (Assume that both glass fiber and nylon have equal strain).

Answer: (0.90 to 0.93)

21. The solubility parameter of a polymer having cohesive energy density (E_coh) 43870 J/mol and molar volume (V) 136 cm³/mol is _________ (J/cm³)^1/2.

Answer: (17.91 to 18.00)

22. T he heat of polymerization of styrene is 20 Kcal/mol. Heat of 5 x10⁵ Kcal will be released on polymerization of __________ Kg of styrene (C = 12 and H = 1 g/mol).

Answer: (2600 to 2600)

Food Technology – XE-G

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

1. Which of the following is oil soluble pigment present in fruits and vegetables?

(A) Flavonoids

(B) Carotenoids

(D) Tannins

Answer: (B)

2. Which of the following represent the group of saturated fatty acids?

(A) Lauric, Myristic, Arachidic

(B) Palmitic, Linoleic, Linolenic

(D) Behenic, Caprylic, Arachidonic

Answer: (A)

3. The anti-nutritional factor present in fava bean is

(A) Gossypol

(B) Curcine

(D) Cyanogen

Answer: (C)

4. Irradiation carried out to reduce viable non-spore forming pathogenic bacteria using a dose between 3 to 10 kGy is called

(A) Radurization

(B) Thermoradiation

(D) Radicidation

Answer: (D)

5. Identify the correct statement related to the viscosity of Newtonian fluids from the following

(A) It is not influenced by temperature

(B) It increases with shearing rate

(D) It is not influenced by shearing rate

Answer: (D)

6. Adult male Wistar rats were fed with a protein based diet. Total 150 g of protein was ingested per animal. If the average weight increased from 110 g to 350 g after the end of the experiment, the Protein efficiency ratio of the given protein would be _______. (up to two decimal points)

Answer: (1.55 to 1.65)

7. The initial moisture content of a food on wet basis is 50.76%. Its moisture content (%) on dry basis is _______.(up to two decimal points)

Answer: (103.0 to 103.2)

8. The oxygen transmission rate through a 2.54 x 10^-3 cm thick low density polyethylene film with air on one side and inert gas on the other side is 3.5 x 10^-6 mL cm^-2 s^-1. Oxygen partial pressure difference across the film is 0.21 atm. The permeability coefficient of the film to oxygen is _______ x 10^-11 mL (STP) cm cm^-2 s^-1 (cm Hg)^-1.

Answer: (54 to 56)

9. A mbient air at 30°C dry bulb temperature and 80% relative humidity was heated to a dry bulb temperature of 80°C in a heat exchanger by indirect heating. The amount of moisture gain (g kg^-1 dry air) during the process would be _______.

Answer: (0 to 0)

10. Match the commodity in Group I with the bioactive constituent in Group II

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

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

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

Answer: (B)

11. Match the process operation in Group I with the separated constituent in Group II

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

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

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

Answer: (C)

12. Match the spoilage symptom in Group I with the causative microorganism in Group II

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

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

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

Answer: (C)

13. Match the fermented product in Group I with the base material in Group II

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

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

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

Answer: (A)

14. Match the operation in Group I with the process in Group II

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

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

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

Answer: (D)

15. Out of 7 principles of HACCP system, 4 are listed below. Arrange these principles in the order in which they are applied.

(P) Conduct a hazard analysis

(Q) Establish monitoring process

(R) Establish critical limit

(S) Establish record keeping and documentation process

(A) P, R, Q, S

(B) Q, R, P, S

(D) R, S, P, Q

Answer: (A)

16. Apple juice of 10% total solids (TS) is being concentrated in a single effect evaporator working with a surface condenser to 40% TS under a vacuum of 20 kPa. After some time the vacuum pump stops but the evaporation process continued. Choose the combination of possible implications from the following.

(P) Product quality is affected

(Q) Substantial increase in thermal energy requirement

(R) Decrease in the rate of evaporation

(A) P & Q

(B) Q & R

(D) P,Q & R

Answer: (C)

17. Identify an example of a classical diffusional mass transfer process without involving heat, among the following.

(A) Drying of food grains

(B) Carbonation of beverages

(D) Concentration of fruit juice

Answer: (B)

18. For an enzyme catalyzed reaction S → P, the kinetic parameters are:

[S] = 40 μM, V₀ = 9.6 μM s^-1 and V_max = 12.0 μM s^-1.

The K_m of the enzyme in μM will be _______.(up to one decimal points)

Answer: (9.8 to 10.2)

19. A microbial sample taken at 10 AM contained 1 × 10⁵ CFU/mL. The count reached to 1 × 10¹⁰ CFU/mL at 8 PM of the same day. The growth rate (h^-1) of the microorganism would be _______.(up to two decimal points)

Answer: (1.1 to 1.8)

20. Black pepper is ground from an equivalent particle size of 6 mm to 0.12 mm using a 10 hp motor. Assuming Rittinger’s equation and that 1 hp = 745.7 W, the power (hp) of motor required to fine grind black pepper to 0.08 mm would be _______.(up to two decimal points)

Answer: (14.5 to 15.5)

21. Green pea (average diameter 0.8 cm) is frozen in a blast freezer operating at -40°C and with a surface heat transfer coefficient of 30 W m^-2 K^-1. The thermal conductivity of pea is 2.5 W m^-1K^-1, and latent heat of crystallization is 2.74 × 10² kJ kg^-1. If the freezing point of pea is -1°C and the density is 1160 kg m^-3, the freezing time in minutes will be _______.(up to two decimal points)

Answer: (6.0 to 6.4)

22. The rate of heat transfer from a metal plate is 1000 W m^-2. The surface temperature of the plate is 120°C and ambient temperature is 20°C. The convective heat transfer coefficient (W m^-2°C^-1) using the Newton’s law of cooling will be _______.

Answer: (10 to 10)

Atmospheric and Oceanic Sciences (XE-H)

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

1. The most abundant gas in the atmosphere among inert gases is

(A) Helium

(B) Argon

(D) Krypton

Answer: (B)

2. The pair of variables that always exhibit monotonic decrease with height in the atmosphere is

(A) Pressure, Temperature

(B) Pressure, Ozone concentration

(D) Temperature, Water Vapour

Answer: (C)

3. Correct order of the maximum vertical extent of atmospheric circulation cells is

(A) Hadley > Ferrel > Polar

(B) Polar > Hadley > Ferrel

(D) Ferrel > Hadley > Polar

Answer: (A)

4. Analysis of an atmospheric variable shows prominent modes at 5, 40 and 1460 days. These modes correspond respectively to

(A) Tidal, MJO and ENSO

(B) Synoptic, MJO and ENSO

(D) Tidal, Milankhovich and ENSO

Answer: (B)

5. Atmospheric vertical profile of temperature is measured by radiosonde. Equivalent instruments for measuring ocean temperature profile among the following are:

(P) drifting buoy (Q) ARGO float (R) current mooring (S) XBT

(A) Q, R, S

(B) Q, S

(D) P, R, S

Answer: (B)

6. When deep water sinks in the North Atlantic and moves away from where it formed, it gets

(A) richer in oxygen and nutrients

(B) less acidic and richer in metals

(D) richer in CO₂ and O₂

Answer: (C)

7. The speed of sound in the ocean depends on

(A) temperature alone

(B) temperature and pressure

(D) temperature, salinity and pressure

Answer: (D)

8. In a numerical weather prediction model with a horizontal grid resolution of 50 km, convective cloud processes are parameterized, because

(A) Cloud physics is not known for modelling

(B) Models cannot handle phase change

(D) Cloud size is much smaller than the grid size

Answer: (D)

9. Figure below shows SST anomaly (in °C). It is associated with the phenomenon known as

(A) El Nino

(B) Indian Ocean dipole

(D) MJO

Answer: (B)

10. For an inviscid and barotropic ocean of constant depth (D), a water parcel with initial vorticity 2Ω is displaced from the equator to the north pole. Latitudinal variation of the parcel vorticity (ζ ) is well represented by the curve

(A) S

(B) Q

(D) R

Answer: (A)

11. A wave progresses up an estuary of decreasing water depth. If friction is neglected, then

(A) wave amplitude decreases and wave length increases

(B) wave amplitude increases and wave length decreases

(D) wave amplitude increases and wave length increases

Answer: (B)

12. In the Ekman flow limit, directions of ocean surface current and the geostrophic wind are

(A) the same

(B) surface current is 45° to the left of the geostrophic wind

(D) exactly opposite to each other

Answer: (A)

13.

P and Q respectively describe flow fields corresponding to

(A) Mid latitude Rossby and Polar gravity waves

(B) Equatorial Rossby and Equatorial Kelvin waves

(D) Equatorial Kelvin and Equatorial Rossby waves

Answer: (B)

14. On the summer solstice day, the maximum incident shortwave radiation at the top of the atmosphere over the equator (up to one decimal place) is __________ W m^–2. (Take solar constant as 1368 W m^–2).

Answer: (1254 to 1256)

15. In an isothermal atmosphere having a temperature of 15°C, the height at which pressure decreases to 1/10 of its value at the surface is __________ km. (Give the answer to two decimal places.) Take g = 9.8 m s^–2, gas constant R = 287 J kg^–1 K^–1

Answer: (19.42 to 19.44)

16. At 30°N and 700 hPa pressure level, wind field is in gradient balance. If the gradient wind speed is 50 m s–1 and radius of curvature of the flow is 50 km, the corresponding geostrophic wind speed is __________ m s^–1. (Give the answer to one decimal place.) Take the angular velocity of the Earth as 7.3 × 10^–5 s^–1

Answer: (734.8 to 735.0)

17. In a tropical cyclone over the Pacific Ocean, surface pressure at 500 km from the cyclone centre is 1000 hPa. Surface pressure at the centre is 900 hPa. Sea surface temperature and surface air temperature remain constant at 28°C and 27°C, respectively. Difference in potential temperature between 500 km and cyclone centre is __________ K. (Give the answer to two decimal places.) Take g = 9.8 m s^–2, Cp = 1005 J kg^–1 K^–1, gas constant R = 287 J kg^–1 K^–1

Answer: (9.16 to 9.18)

18. A cloud forms by the lifting of moist air from the surface with the initial conditions T_o = 30°C, RH = 80% and P_o = 1005 hPa. If the vapour pressure of this parcel at 500 hPa is 6.5 hPa, the liquid water content of the parcel if no precipitation takes place is __________ gm kg^–1. (Give the answer to one decimal place.) Saturation vapour pressure of water at 30°C is 42.43 hPa.

Answer: (12.8 to 13.2)

19. A numerical model of the atmosphere uses sigma (𝜎) coordinate system in vertical. At locations P and Q, surface pressures are 1005 hPa and 500 hPa, respectively. Absolute difference in the heights of 𝜎 = 0.9 level between these locations is __________ meters. (Give the answer to one decimal place.) Layer mean temperatures at P and Q are 300 K and 270 K, respectively. (Take g = 9.8 m s^–2 gas constant R = 287 J kg^–1 K^–1)

Answer: (92.4 to 92.8)

20. If difference in sea surface elevation is 1 m in 100 km at 30°N latitude, the corresponding geostrophic current is __________ m s^–1. (Give the answer to one decimal place.) Take g = 9.8 m s^–2 and angular velocity of the Earth = 7.3 × 10^–5s^–1.

Answer: (1.3 to 1.4)

21. If wind speed over ocean surface is 10 m s^–1, air-sea interface momentum flux is __________ N m^–2. (Give the answer to two decimal places.) Surface air temperatureand pressure are 27°C and 1000 hPa, respectively. Take drag coefficient as 0.001 and gas constant R = 287 J kg^–1K^–1.

Answer: (0.11 to 0.12)

22. Let L_x, L_y be length scales in x- and y-directions and corresponding mass transports are Mx and My. The ratio of M_x and M_y (to nearest integer) is __________ , if the ratio of L_xand L_y is 10 and vertical velocity is zero.

Answer: (9.99 to 10.01)

GATE Exam 2018 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

6. An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

8. To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

10. In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another unrelated study, it was found that the revenue from cracker sales in India which remained fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. The solid line in the graph below refers to annual sale of crackers and the dashed line refers to the annual crow births in India. Choose the most appropriate inference from the above data.

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Textile Engineering and Fibre Science

Q. 1 – Q. 25 carry one mark each.

1. Let then |𝐴| is equal to

(A) 2

(B) −2

(D) 6

Answer: (D)

2. If 𝐴 and 𝐵 are two independent events such that then 𝑃(𝐴 ∪ 𝐵) is equal to

(A) 11/12

(B) 1/12

(D) 5/6

Answer: (C)

3. Which one of the following is a leaf fibre?

(A) Coir

(B) Sisal

(D) Hemp

Answer: (B)

4. The pair of fibres most prone to accumulation of static charge is

(A) Cotton and Polyester

(B) Silk and Polyester

(D) Silk and Polypropylene

Answer: (C)

5. H eat-setting of melt-spun and drawn Nylon 6 filament yarn under slack condition leads to increase in its

(A) Tenacity

(B) Molecular orientation

(D) Dimensional stability

Answer: (D)

6. Which one of the fibres, having stress-strain curves as shown in the figure, is the most suitable for making mountaineering ropes?

(A) P

(B) Q

(D) S

Answer: (C)

7. The technology that produces yarn with the maximum fibre migration is

(A) Rotor spinning

(B) Friction spinning

(D) Ring spinning

Answer: (A (or) D)

8. The cleaning machine, located in the fine cleaning zone of blowroom, uses the following as the opening element

(A) Roller with saw tooth wire points

(B) Drum with large spikes

(D) Drum with large bladed discs

Answer: (A)

9. The purpose of having grooves or notches in modern flyer tops in speed frames is to

(A) Increase real twist in roving

(B) Insert false twist in roving

(D) Increase fineness of roving

Answer: (B)

10. With time, wind per double traverse in a drum-driven winder

(A) Increases

(B) Decreases

(D) First increases and then decreases

Answer: (B)

11. In a loom, seven-wheel take-up motion is

(A) Negative and intermittent

(B) Negative and continuous

(D) Positive and continuous

Answer: (C)

12. The relative humidity (in %) and temperature (in °C) of standard testing atmosphere are respectively

(A) 65 and 25

(B) 65 and 20

(D) 60 and 20

Answer: (B)

13. In Stelometer, if F is the force acting on a fibre bundle and θ is the angle through which the pendulum is moved, then F is directly proportional to

(A) sin θ

(B) cos θ

(D) cot θ

Answer: (A)

14. Yarn diameter varies

(A) Directly with yarn packing density

(B) Inversely with yarn packing density

(D) Inversely with square root of yarn packing density

Answer: (D)

15. The constant-rate-of-extension type tensile tester is NOT used for

(A) Tongue tear test

(B) Wing rip tear test

(D) Trapezoid tear test

Answer: (C)

16. During bleaching of cotton with hydrogen peroxide, addition of sodium silicate

(A) Reduces the viscosity of bath

(B) Controls the rate of decomposition of perhydroxyl ions (HO₂⁻)

(D) Enhances swelling of cotton

Answer: (B)

17. In dyeing of wool with levelling acid dyes, with time, the pH of dye bath

(A) Increases

(B) Decreases

(D) First increases and then decreases

Answer: (A)

18. The discharging agent used in discharge printing of cotton with reactive dyes is

(A) Citric acid

(B) Sodium dithionite

(D) Sodium formaldehyde sulphoxylate

Answer: (D)

19. A pplication of a fluorochemical based finish on a textile fabric imparts

P. Water repellency
Q. Oil repellency
R. Soil repellency
S. Soil release property

(A) P, Q & R only

(B) Q, R & S only

(D) P, Q & S only

Answer: (Marks to All)

20. If are three vectors such that is perpendicular to then the value of 𝜆 is ______________

Answer: (-1 to -1)

21. If 𝑦(𝑥) is the solution of the differential equation 𝑦 𝑦′ = 8 𝑥 , 𝑦(0) = 2 , then the absolute value of 𝑦(2) is _______________

Answer: (6 to 6)

22. If is a continuous function for all real values of 𝑥 , then 𝑓(8) is equal to _______________

Answer: (20 to 20)

23. A twistless polyester yarn has 90 filaments, each of 2 denier. The metric count of the yarn is ______________

Answer: (49.8 to 50.2)

24. Bottom shaft of a shuttle loom, weaving 2 up 1 down twill weave, is rotating at 90 rpm. The speed of cam shaft (in rpm) is ____________

Answer: (60 to 60)

25. If wale constant and course constant for knitted fabrics are 4.2 and 5.46, respectively, then the value of the loop shape factor, accurate to one decimal place, is ______________

Answer: (1.3 to 1.3)

Q. 26 – Q. 55 carry two marks each.

26. The cross-sectional shape of a fibre affects the following properties of yarn

P. Lustre
Q. Torsional rigidity
R. Flexural rigidity
S. Packing density

(A) P & Q only

(B) P & R only

(D) P, Q, R & S

Answer: (D)

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

[a]: The reaction temperature and rate of agitation during polymerization of polyethylene terephthalate have an important effect on molecular weight of the polymer produced.

[r]: Polymerization of polyester by melt polycondensation is a predominantly diffusion controlled process.

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

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

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

Answer: (A)

28. Group I gives a list of fibres and Group II contains their applications. Match the fibre with its application.

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

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

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

Answer: (B)

29. Techniques used to determine the glass transition temperature of textile fibres are

P. X-ray diffraction (XRD)
Q. Differential scanning calorimetry (DSC)
R. Thermogravimetric analysis (TGA)
S. Dynamic mechanical analysis (DMA)

(A) P & Q only

(B) Q & R only

(D) R & S only

Answer: (C)

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

[a]: In a carding machine, carding type of wire point configuration is used between cylinder and doffer.

[r]: Carding type of wire point configuration gives the best fibre transfer without disturbing the fibre alignment.

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

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

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

Answer: (D)

31. Match the spinning technology listed in Group I with the machine component / function listed in Group II.

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

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

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

Answer: (C)

32. Compared to filaments in spunbonded nonwovens, those in meltblown nonwovens have

P. Lower orientation of molecular chains
Q. Higher orientation of molecular chains
R. Lower variability in diameter
S. Higher variability in diameter

(A) P & R only

(B) P & S only

(D) Q & S only

Answer: (B)

33. Match the weave in Group I with fabric attribute in Group II.

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

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

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

Answer: (A)

34. Match the test in Group I with fabric property in Group II.

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

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

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

Answer: (D)

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

[a]: The work factor of silk fibre is greater than 0.5.

[r]: The work factor is calculated by assuming the following as the stress-strain curve of silk fibre.

(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)

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

[a]: As the concentration of a surfactant in water increases, the surface tension of water initially decreases and then becomes constant.

[r]: After reaching the Critical Micelle Concentration, additional surfactant molecules do not further reduce the surface tension.

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

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

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

Answer: (A)

37. A dye is applied on a fibre using Na2S2O4 as an auxiliary. Washing fastness of the dye on fibre is good. The correct combination of the dye and the fibre is

(A) Cationic dye, acrylic fibre

(B) Vat dye, cotton fibre

(D) Reactive dye, cotton fibre

Answer: (B)

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

[a]: Emulsion thickener is used in pigment printing of textiles.

[r]: Emulsion thickener has high solid content.

(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)

39. Match the dye-fibre in Group I with the interactions in Group II.

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

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

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

Answer: (C)

40. Let 𝑋 be a random variable following the binomial distribution. If 𝐸(𝑋) = 2 and 𝑉𝑎𝑟(𝑋) = 1.2 , then 𝑃(𝑋 = 2) , accurate to three decimal places, is equal to ____________

Answer: (0.325 to 0.365)

41. The value of the integral is ____________

Answer: (64 to 64)

42. Starting from the initial point 𝑥0 = 10, if the sequence {𝑥_𝑛} is generated using Newton Raphson method to compute the root of the equation 𝑥⁴ − 600 = 0, then 𝑥², accurate to two decimal places, is equal to _____________

Answer: (5.95 to 6.25)

43. If then the sum of all eigenvalues of the matrix 𝑀 = 𝐴² − 4 𝐴⁻¹ is equal to _____________

Answer: (17 to 17)

44. If the density of 100% crystalline polyethylene is 1000 kg·m^-3 and that of 100% amorphous polyethylene is 865 kg·m^-3, then the mass fractional crystallinity of a polyethylene fibre with density 970 kg·m^-3, accurate to two decimal places, is ___________

Answer: (0.79 to 0.81)

45. In winding zone of ring spinning, the permissible minimum angle of lead is 30°. For a ring of 40 mm diameter, the minimum diameter (in mm) of bobbin required is _________

Answer: (20 to 20)

46. A sliver of 4.2 kilotex is fed in a rotor spinning machine with opening zone draft of 1400. The draft in the transport duct is 5 and the sliding draft on the rotor wall till the rotor groove is 2. If the total back doubling within the rotor is 120, then the linear density (in tex) of the output yarn is ___________

Answer: (35.0 to 38.0)

47. An eight head comber is running at 400 nips/min. The lap fed is 60 kilotex and noil extracted is 20%. If the feed/nip is 7 mm, then with machine utilization of 80%, the production rate (in kg/h), accurate to one decimal place, is ____________

Answer: (51.0 to 52.0)

48. A shuttle loom having 1.75 m reed width is running at 180 rpm. The shuttle enters and leaves the shed at 120° and 240° angular positions of crankshaft, respectively. If length of the shuttle is 0.25 m, then the mean velocity (in m/s) of the shuttle within the shed is ___________

Answer: (18.0 to 18.2)

49. The diameter and length of torsion rod used in a projectile loom are increased by 5% and 20%, respectively. If the torque required to twist the rod increases by X%, then the value of X, accurate to two decimal places, is _____________

Answer: (1.247 to 1.31)

50. Cloth cover factor of a square plain jammed cotton fabric, accurate to one decimal place, is _____________

Answer: (22.8 to 23.1)

51. In a vibroscope, a cotton fibre of 25 mm length is clamped at one end, led over a knifeedge support, tensioned by a weight of 350 mg, and is inclined to vibrate at a fundamental resonant frequency of 2.6 kHz. The linear density of the fibre (in tex), accurate to two decimal places, is ____________

Answer: (0.19 to 0.21)

52. The theoretical limit coefficient of variation (V_r in %) of the weight per unit length of cotton sliver is where N is the average number of fibres present in the crosssection of the sliver. To derive this expression, the coefficient of variation (in %) of the fibre weight per unit length, accurate to two decimal places, is considered as ______________

Answer: (35.00 to 36.00)

53. The bending length of a nonwoven fabric in machine direction is two times the bending length in cross-machine direction. The ratio of flexural rigidities of this fabric in machine direction to cross-machine direction is ______________

Answer: (8 to 8)

54. The standard deviation of population P is two times the standard deviation of population Q. The size of a random sample from population P is four times the size of a random sample from population Q. If 𝑒_P and 𝑒_Q denote the standard error of means of the samples from P and Q, respectively, then the ratio of 𝑒_P to 𝑒_Q is _____________

Answer: (1 to 1)

55. A crease resist (CR) agent is applied by padding on a fabric of 1 m width and 200 g/m²areal density. The concentration of CR agent in the pad bath is 100 gpl and the fabric speed is 50 m/min. The expression is 110% and the specific gravity of the pad liquor is 1.1. In order to maintain the bath concentration, the rate (in kg/min) at which the CR agent needs to be added to the bath, accurate to one decimal place, is_______________

Answer: (0.9 to 1.1)

GATE Exam 2018 Production and Industrial Engineering (PI) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _________.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

6. Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

(A) 0

(B) 2

(D) 8

Answer: (C)

7. A wire would enclose an area of 1936 m², if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

8. A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

10. An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Production and Industrial Engineering

Q. 1 – Q. 25 carry one mark each.

1. Vector triple product a × (b × c) of three vectors a, b and c is given by

(A) (a • c)b – (a • b)c

(B) (b • c)a – (a • c)b

(D) (b • c)a – (a • b)c

Answer: (A)

2. A real-valued function y of real variable x is such that y = 5|x|. At x = 0 the function is

(A) discontinuous but differentiable

(B) both continuous and differentiable

(D) continuous but not differentiable

Answer: (D)

3. Considering the coordinate system shown in the figure, a force of magnitude 10 kN has x-component of –6 kN. Possible y-component (s) of the force is/are

(A) +8 kN only

(B) +5 kN only

(D) +5 kN and –5 kN

Answer: (C)

4. When austenite decomposes upon cooling into two phases— ferrite and cementite, the reaction is called

(A) Eutectic

(B) Eutectoid

(D) Peritectoid

Answer: (B)

5. Match the geometric tolerances with their correct symbols:

(A) P – 1, Q – 3, R – 4, S – 2

(B) P – 3, Q – 1, R – 4, S – 2

(D) P – 3, Q – 2, R – 1, S – 4

Answer: (B)

6. Which one of the following instruments makes use of the principle of interference of light?

(A) Optical flat

(B) Auto-collimator

(D) Coordinate measuring machine

Answer: (A)

7. In ASME process chart, the symbol represents

(A) operation

(B) inspection

(D) transport

Answer: (B)

8. Which one of the following is the most appropriate control chart for measuring the variability of individual readings within a sample?

(A)

(B) R-chart

(D) c-chart

Answer: (B)

9. The machines and auxiliary facilities are located according to processing sequence of the product (produced in very large quantities) in

(A) Process Layout

(B) Fixed Position Layout

(D) Cellular Layout

Answer: (C)

10. Which one of the following defects is NOT associated with the casting process?

(A) Hot tear

(B) Porosity

(D) Central burst

Answer: (D)

11. In an oxy-acetylene gas welding process, oxygen and acetylene are mixed in a ratio of 1.5:1 (by volume). The flame is

(A) neutral

(B) carburizing

(D) oxidizing

Answer: (D)

12. Each of three firms P, Q and R manufactures 100 lakhs components. The number of defective components produced by P, Q and R are 30, 42 and 47, respectively. The firm(s) in conformance with Six Sigma standard is/are

(A) only P

(B) P and Q

(D) Q and R

Answer: (A)

13.To make holes of 0.5 mm diameter and 30 mm depth in a mild steel component, the most
suitable process is

(A) chemical machining

(B) electrochemical machining

(D) plasma arc machining

Answer: (B)

14. Which one of the following processes is NOT used for producing powders?

(A) Atomization

(B) Ball milling

(D) Electrolysis

Answer: (C)

15. The process in which molten thermoplastic is forced between rolls to produce thin sheets is called

(A) blow moulding

(B) compression moulding

(D) extrusion

Answer: (C)

16. The diagonal elements of a 3-by-3 matrix are –10, 5 and 0, respectively. If two of its eigenvalues are –15 each, the third eigenvalue is _______

Answer: (24.5 to 25.5)

17. Weights (in kg) of six products are 3, 7, 6, 2, 3 and 4. The median weight (in kg, up to one decimal place) is _______

Answer: (3.19 to 3.51)

18. The probabilities of occurrence of events F and G are P(F) = 0.3 and P(G) = 0.4, respectively. The probability that both events occur simultaneously is P(F∩G) = 0.2. The probability of occurrence of at least one event P(F∪G) is _______

Answer: (0.49 to 0.51)

19. A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______

Answer: (9.9 to 10.1)

20. A cylindrical wooden block of length 50 cm is floating in water in such a way that its axis is vertical. The densities of wood and water are 800 kg/m³ and 1000 kg/m³, respectively. The submerged depth, i.e., depth of immersion (in cm) of the cylinder is _______

Answer: (39 to 41)

21. A machine consists of three components P, Q and R connected serially. The reliabilities of P, Q and R are 0.97, 0.86 and 0.93, respectively. To increase the reliability of the machine, two additional stand-by units of Q are attached. The overall reliability (up to two decimal places) of the machine is _______

Answer: (0.88 to 0.91)

22. The mean time between failures of a machine is 400 hour. If the availability of the machine is 80%, the mean time to repair (in hour) is _______

Answer: (79 to 81)

23. Processing times on a single machine for 3 jobs are given below. All the jobs are available at time t = 0.

The mean flow time (in minute) as per the shortest processing time (SPT) sequence is _______

Answer: (11.8 to 12.2)

24. In a two-pass wire drawing process, there is a 40% reduction in wire cross-sectional area in 1st pass and further 30% reduction in 2nd pass. The overall reduction (in percentage) is ______

Answer: (57 to 59)

25. A double-start thread with a pitch of 2 mm is to be cut using a lathe machine. The pitch of the leadscrew of the lathe is 6 mm. The job rotates at 60 revolution per minute (RPM). The RPM of the leadscrew is ______

Answer: (39 to 41)

Q. 26 – Q. 55 carry two marks each.

26. Consider the analytic function f(z) = x2 – y2 + i2xy of the complex variable z = x + iy where The derivative f′(z) is

(A) 2x + i2y

(B) x² + iy²

(D) 2x – i2y

Answer: (A)

27. In order to evaluate the integral with Simpson’s 1/3rd rule, values of the function e^x are used at x = 0.0, 0.5 and 1.0. The absolute value of the error of numerical integration is

(A) 0.000171

(B) 0.000440

(D) 0.002718

Answer: (C)

28. A rigid link PQ of length 1.0 m is pinned at P. It rotates about P in a vertical plane with a uniform angular acceleration of 1.0 rad/s². At an instant when the angular velocity of the link is 1.0 rad/s, the magnitude of total acceleration (in m/s²) of point Q relative to point P is

(A) 1.41

(B) 1.73

(D) 2.83

Answer: (A)

29. In a shaft-hole system, the dimensions with tolerances (in mm) are as follows:

where both x and y are positive real numbers. Which one of the following will provide an interference fit?

(A) x = 0.05, y = 0.040

(B) x = 0.04, y = 0.035

(D) x = 0.02, y = 0.035

Answer: (D)

30. A machine is procured at a price of Rs. 47000 with a 2-year warranty. After two years, the annual maintenance cost (AMC) in Rs. is given by the following formula:

AMC = (i – 2) × 2000, for i > 2,

where i is the number of years elapsed since the machine was purchased. Neglect the scrap value of the machine, inflation, interest, etc. For minimizing the average cost, the machine should be replaced at the end of the year

(A) 2

(B) 4

(D) 10

Answer: (C)

31. In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per hour. The time for servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is

(A) 10

(B) 15

(D) 30

Answer: (B)

32. Actual and forecasted demands of a product are as follows:

The forecast error measured in terms of mean absolute deviation (MAD) and mean absolute percentage error (MAPE), respectively, are

(A) 13 and 7.84%

(B) 13 and 9.85%

(D) 17 and 9.85%

Answer: (D)

33. In a mass production firm, measurements are carried out on 10000 pairs of shaft and hole. The mean diameters of the shaft and the hole are 37.53 mm and 37.59 mm, respectively. The corresponding standard deviations are 0.03 mm and 0.04 mm. The mean clearance and its standard deviation (both in mm), respectively, are

(A) 0.06 and 0.07

(B) 0.06 and 0.06

(D) 0.07 and 0.01

Answer: (C)

34. A pressure die casting set-up was tested by injecting water (density 1000 kg/m³) at a pressure of 200 bar. Mould-filling time was found to be 0.05 s. Afterwards, the actual casting is made by injecting the liquid metal (density 2000 kg/m³) at an injection pressure of 400 bar. Neglect all losses (friction, viscous-effect, etc.). The approximate mould-filling time (in s) is

(A) 0.05

(B) 0.075

(D) 0.2

Answer: (A)

35. The value of the surface integral over the surface S of the sphere x² + y² +z² = 9, where n is the unit outward normal to the surface element d,S is ______

Answer: (675 to 681)

36. Consider the differential equation

The value of y (up to two decimal places) at t =1 is ______

Answer: (4.52 to 4.56)

37. One kg of air (that can be considered a calorically perfect gas with characteristic gas constant R = 287 J/kg-K and specific heat ratioΥ = 1.4 ) undergoes a constant-volume process from an initial static pressure of 1 bar to a final static pressure of 4 bar. The increase in entropy (in J/kg-K) of air is ______

Answer: (990 to 1000)

38. If u = 2(x² – y²) and v = –axy represent the x- and y-components of the two-dimensional velocity field of an incompressible flow, the value of the constant a is ______

Answer: (3.9 to 4.1)

39. A spherical pressure vessel (made of mild steel) of internal diameter 500 mm and thickness 10 mm is subjected to an internal gauge pressure of 4000 kPa. If the yield stress of mild steel is 200 MPa, the factor of safety (up to one decimal place) is ______

Answer: (3.6 to 4.4)

40. A square cross-section wooden column of length 3140 mm is pinned at both ends. For the wood, Young’s modulus of elasticity is 12 GPa and allowable compressive stress is 12 MPa. The column needs to support an axial compressive load of 200 kN. Using a factor of safety of 2.0 in the computation of Euler’s buckling load, the minimum cross-sectional area (in mm²) of the column is ______

Answer: (1575 to 1650)

41. Length, width and thickness of a plate are 400 mm, 400 mm and 30 mm, respectively. For the material of the plate, Young’s modulus of elasticity is 70 GPa, yield stress is 80 MPa and Poisson’s ratio is 0.33. When the plate is subjected to a longitudinal tensile stress of 70 MPa, the increase in the volume (in mm³) of the plate is ______

Answer: (1575 to 1650)

42. In a V-thread, a wire is fitted such that it makes contact with the flank of the thread on the pitch line as shown in the figure. If the pitch p of the thread is 3 mm and the included angle is 60°, the diameter (in mm, up to one decimal place) of the wire is ______

Answer: (1.6 to 1.8)

43. A project consists of three activities P, Q and R. The durations of activities follow Beta distribution. The predecessors and durations of activities are as per the following table:

The expected project completion time (in month) is ______

Answer: (13.9 to 14.1)

44. A company has two manufacturing plants (C₁ and C₂) and two distribution centres (D₁ and D₂). The capacities of C₁ and C₂ are 100 and 200 units, respectively. The demand for D₁ and D₂ are 190 and 110 units, respectively. The costs per unit (in Rs.) of transportation at different routes are as per the following matrix:

Answer: (6165 to 6175)

45. The annual demand of an item is 19845 units and the production rate is 100 units per day. The per-unit production cost (excluding setup cost) is Rs. 50, the per-unit holding cost is Rs. 10 per year and setup cost is Rs. 520 per setup. To minimize the total annual cost, the optimum quantity to be produced per setup is ______

Answer: (2100 to 2155)

46. A production line operates 7 hours a day in a 5-day week. The processing times for various job elements are as follows

If the line is designed for an output of 8400 units per week, the theoretical minimum number of work stations required is ______

Answer: (2.8 to 3.2)

47. In a work sampling study of a worker, the information available are as follows: total time of study: 30 hour, number of items produced: 320, total number of observations: 1000, number of observations when worker is found working: 850 and average performance rating: 105%. Company policy is to give allowance of 10% of total time on the job. The standard time (in minute per item, up to one decimal place) for manufacturing the item is ______

Answer: (5.2 to 5.8)

48. The breakeven point of a manufacturing company is 50000 units. The fixed cost is Rs. 200000 and the variable cost per unit is Rs. 20. The selling price per unit (in Rs.) of the product at this breakeven point is ______

Answer: (23.8 to 24.2)

49. A 10 mm thick plate is rolled to 7 mm thickness in a rolling mill using 1000 mm diameter rigid rolls. The neutral point is located at an angle of 0.3 times the bite angle from the exit. The thickness (in mm, up to two decimal places) of the plate at the neutral point is ______

Answer: (7.1 to 7.4)

50. A cylindrical workpiece is turned at a feed of 0.1 mm/rev with a perfectly sharp tool. In ASA system, the side and end cutting edge angles are 15° and 5°, respectively, as shown in the figure. The peak-to-valley roughness (in μm, up to one decimal place) of the machined surface is ______

Answer: (8.4 to 8.7)

51. The worktable in a CNC machine is driven by a leadscrew with a pitch of 2 mm. The leadscrew is directly coupled to a stepper motor of step angle 1.8°. The number of pulses required to move the worktable by 50 mm is ______

Answer: (4999 to 5001)

52. During orthogonal machining of a job at a cutting speed of 90 m/min with a tool of 10° rake angle, the cutting force and thrust force are 750 N and 390 N, respectively. Assume a shear angle of 35°. The power (in W) expended for shearing along the shear plane is ______

Answer: (630 to 641)

53. I n an electrochemical machining of aluminium with plane parallel electrodes, the current density is 70 A/cm². Cross-sectional area of each electrode is 3 cm². The current efficiency (i.e., the fraction of current used for dissolution of metal) is 80%. Gram atomic weight, valency and density of aluminium are 27 gram, 3 and 2700 kg/m³, respectively. Take Faraday’s constant as 96500 Coulomb. The volumetric material removal rate (in mm³/min) is ______

Answer: (345 to 351)

54. Two metallic sheets are spot welded by passing a current of 8000 A for 0.2 s. Assume that a cylindrical nugget of 8 mm diameter and 3 mm depth is formed. The density of the nugget is 7500 kg/m³, effective resistance of the total system is 222 micro-Ohm and heat required to produce 1.0 gram of nugget is 1400 J. The percentage of heat actually utilized in producing the nugget is ______

Answer: (53 to 58)

55. In a planar 2-degree-of-freedom robot, Link 1 of 30 cm length is connected to base by a revolute joint and Link 2 of length 20 cm is connected to Link 1 with a revolute joint as shown in the figure. The work-envelope area (in cm²), covered by point P, is ______

Answer: (3760 to 7600)

GATE Exam 2018 Physics (PH) Question Paper With Answer Key

June 7, 2023November 24, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Physics

Q. 1 – Q. 25 carry one mark each.

1. The eigenvalues of a Hermitian matrix are all

(A) real

(B) imaginary

(D) real and positive

Answer: (A)

2. Which one of the following represents the 3p radial wave function of hydrogen atom? (a₀ is the Bohr radius)

Answer: (B)

3. Given the following table,

which one of the following correctly matches the experiments from Group I to their inferences in Group II?

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

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

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

Answer: (C)

4. In spherical polar coordinates (𝑟,𝜃,𝜙), the unit vector at (10,𝜋/4,𝜋/2) is

Answer: (D)

5. The scale factors corresponding to the covariant metric tensor 𝑔_𝑖𝑗 in spherical polar coordinates are

(A) 1,𝑟²,𝑟²sin²𝜃

(B) 1,𝑟²,sin²𝜃

(D) 1,𝑟,𝑟sin𝜃

Answer: (D)

6. In the context of small oscillations, which one of the following does NOT apply to the normal coordinates?

(A) Each normal coordinate has an eigen-frequency associated with it

(B) The normal coordinates are orthogonal to one another

(D) The potential energy of the system is a sum of squares of the normal coordinates with constant coefficients

Answer: (B)

7. For the given unit cells of a two dimensional square lattice, which option lists all the primitive cells?

Answer: (C)

8. Among electric field and vector potential which is/are odd under parity (space inversion) operation?

Answer: (B)

9. The expression for the second overtone frequency in the vibrational absorption spectra of a diatomic molecule in terms of the harmonic frequency 𝜔_𝑒 and anharmonicity constant 𝑥_𝑒 is

(A) 2𝜔_𝑒(1−𝑥_𝑒)

(B) 2𝜔_𝑒(1−3𝑥_𝑒)

(D) 3𝜔_𝑒(1−4𝑥_𝑒)

Answer: (D)

10. Match the physical effects and order of magnitude of their energy scales given below, where is fine structure constant; 𝑚_𝑒 and 𝑚_𝑝 are electron and proton mass, respectively.

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

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

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

Answer: (C)

11. The logic expression can be simplified to

(A) 𝐴 XOR 𝐶

(D) 1

Answer: (A)

12. A t low temperatures (𝑇), the specific heat of common metals is described by (with 𝛼 and 𝛽 as constants)

(A) 𝛼 𝑇 + 𝛽 𝑇³

(B) 𝛽 𝑇³

(D) 𝛼 𝑇 + 𝛽 𝑇⁵

Answer: (A)

13. In a 2-to-1 multiplexer as shown below, the output X = A₀ if C = 0, and X = A₁ if C = 1.

Which one of the following is the correct implementation of this multiplexer?

Answer: (A)

14. T he elementary particle is placed in the baryon decuplet, shown below, at

(A) P

(B) Q

(D) S

Answer: (C)

15. The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (𝑎0 is the Bohr radius)

(A) −3𝑒𝑎₀

(B) zero

(D) 3𝑒𝑎₀

Answer: (B)

16. The high temperature magnetic susceptibility of solids having ions with magnetic moments can be described by with 𝑇 as absolute temperature and 𝜃 as constant. The three behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described, respectively, by

(A) 𝜃<0,𝜃>0,𝜃=0

(B) 𝜃>0,𝜃<0,𝜃=0

(D) 𝜃=0,𝜃>0,𝜃<0

Answer: (C)

17. Which one of the following is an allowed electric dipole transition?

(A) ¹ S₀ → ³ S₁

(B) ² P_3/2 → ² D_5/2

(C)² D_5/2 → ² P_1/2

(D) ³ P₀ → ⁵ D₀

Answer: (B)

18. In the decay, 𝜇⁺→𝑒⁺⁺𝜈_𝑒+𝑋, what is 𝑋?

(A) 𝛾

Answer: (D)

19. A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).

Answer: (0.185 to 0.189)

20. For an operational amplifier (ideal) circuit shown below,

if V₁ = 1 V and V₂ = 2 V, the value of V₀ is ________V (up to one decimal place).

Answer: (-3.7 to -3.5)

21. An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance 𝑟₁ to that at 𝑟₂(=2 𝑟₁) from the wire is ________.

Answer: (4 to 4)

22. A light beam of intensity 𝐼0 is falling normally on a surface. The surface absorbs 20% of the intensity and the rest is reflected. The radiation pressure on the surface is given by 𝑋_𝐼0/c, where X is ________ (up to one decimal place). Here 𝑐 is the speed of light.

Answer: (1.8 to 1.8)

23. The number of independent components of a general electromagnetic field tensor is ________.

Answer: (6.6)

24. If 𝑋 is the dimensionality of a free electron gas, the energy (𝐸) dependence of density of states is given by where 𝑌 is ________.

Answer: (1 to 1)

25. For nucleus ¹⁶⁴Er, a 𝐽^𝜋=2⁺ state is at 90 keV. Assuming ¹⁶⁴Er to be a rigid rotor, the energy of its 4⁺ state is ________ keV (up to one decimal place).

Answer: (297.0 to 300.1)

Q. 26 – Q. 55 carry two marks each.

26. Given which one of the following makes a complete set for a three dimensional real linear vector space ?

Answer: (D)

27. An interstellar object has speed 𝑣 at the point of its shortest distance 𝑅 from a star of much larger mass 𝑀. Given 𝑣2=2 𝐺𝑀/𝑅, the trajectory of the object is

(A) circle

(B) ellipse

(D) hyperbola

Answer: (C)

28. A particle moves in one dimension under a potential 𝑉(𝑥)=𝛼|𝑥| with some non-zero total energy. Which one of the following best describes the particle trajectory in the phase space?

Answer: (A)

29. Consider an infinitely long solenoid with 𝑁 turns per unit length, radius 𝑅 and carrying a current 𝐼(𝑡)=𝛼cos𝜔𝑡, where 𝛼 is a constant and 𝜔 is the angular frequency. The magnitude of electric field at the surface of the solenoid is

(D) 𝜇₀𝜔𝑁𝑅cos𝜔𝑡

Answer: (A)

30. A constant and uniform magnetic field pervades all space. Which one of the following is the correct choice for the vector potential in Coulomb gauge?

Answer: (C)

31. If 𝐻 is the Hamiltonian for a free particle with mass 𝑚, the commutator [𝑥,[𝑥,𝐻]] is

(A) ℏ²/𝑚

(B) −ℏ²/𝑚

(D) ℏ²/(2𝑚)

Answer: (B)

32. A long straight wire, having radius 𝑎 and resistance per unit length 𝑟, carries a current 𝐼. The magnitude and direction of the Poynting vector on the surface of the wire is

(A) 𝐼²𝑟2𝜋𝑎⁄ , perpendicular to axis of the wire and pointing inwards

(B) 𝐼²𝑟2𝜋𝑎⁄ , perpendicular to axis of the wire and pointing outwards

(D) 𝐼²𝑟𝜋𝑎⁄ , perpendicular to axis of the wire and pointing outwards

Answer: (A)

33. Three particles are to be distributed in four non-degenerate energy levels. The possible number of ways of distribution: (i) for distinguishable particles, and (ii) for identical Bosons, respectively, is

(A) (i) 24, (ii) 4

(B) (i) 24, (ii) 20

(D) (i) 64, (ii) 16

Answer: (C)

34. The term symbol for the electronic ground state of oxygen atom is

(A) ^1𝑆0

(B) ¹𝐷₂

(D) ³𝑃₂

Answer: (D)

35. The energy dispersion for electrons in one dimensional lattice with lattice parameter 𝑎 is given by where 𝑊 and 𝐸₀ are constants. The effective mass of the electron near the bottom of the band is

Answer: (A)

36. Amongst electrical resistivity (𝜌), thermal conductivity (𝜅), specific heat (𝐶), Young’s modulus (Y), and magnetic susceptibility (𝜒), which quantities show a sharp change at the superconducting transition temperature?

(A) 𝜌,𝜅,𝐶, Y

(B) 𝜌,𝐶, 𝜒

(D) 𝜅, Y, 𝜒

Answer: (B)

37. A quarter wave plate introduces a path difference of 𝜆/4 between the two components of polarization parallel and perpendicular to the optic axis. An electromagnetic wave with is incident normally on a quarter wave plate which has its optic axis making an angle 135° with the 𝑥-axis as shown.

The emergent electromagnetic wave would be

(A) elliptically polarized

(B) circularly polarized

(D) linearly polarized but with polarization at 90° to that of the incident wave

Answer: (C)

38. A p-doped semiconductor slab carries a current 𝐼=100 mA in a magnetic field 𝐵=0.2 T as shown. One measures 𝑉_𝑦=0.25 mV and 𝑉_𝑥=2 mV. The mobility of holes in the semiconductor is ________ m²V^–1s^–1 (up to two decimal places).

Answer: (1.55 to 1.58)

39. An n-channel FET having Gate-Source switch-off voltage V_GS(OFF) = – 2 V is used to invert a 0 – 5 V square-wave signal as shown. The maximum allowed value of R would be ________ k (up to two decimal places).

Answer: (0.70 to 0.73)

40. Inside a large nucleus, a nucleon with mass 939 MeVc^–2 has Fermi momentum 1.40 fm^–1 at absolute zero temperature. Its velocity is Xc, where the value of X is ________ (up to two decimal places).

(ℏ𝑐=197 MeV-fm)

Answer: (0.28 to 0.31)

41. 4 MeV 𝛾-rays emitted by the de-excitation of ¹⁹F are attributed, assuming spherical symmetry, to the transition of protons from 1d_3/2 state to 1d5/2 state. If the contribution of spin-orbit term to the total energy is written as the magnitude of 𝐶 is ________ MeV (up to one decimal place).

Answer: (1.6 to 1.6)

42. An 𝛼 particle is emitted by a nucleus. Assuming the potential to be purely Coulombic beyond the point of separation, the height of the Coulomb barrier is ________ MeV (up to two decimal places).

Answer: (24.4 to 27.6)

43. For the transformation

(where 𝛼 is a constant) to be canonical, the value of 𝛼 is________.

Answer: (2 to 2)

44. Given

and boundary conditions 𝑓(0)=1 and 𝑓(1)=0, the value of 𝑓(0.5) is ________ (up to two decimal places).

Answer: (0.81 to 0.84)

45. The absolute value of the integral

over the circle |𝑧−1.5|=1 in complex plane, is ________ (up to two decimal places).

Answer: (81.60 to 81.80)

46. A uniform circular disc of mass 𝑚 and radius 𝑅 is rotating with angular speed 𝜔 about an axis passing through its center and making an angle 𝜃=30∘ with the axis of the disc. If the kinetic energy of the disc is 𝛼𝑚𝜔²𝑅², the value of 𝛼 is ________ (up to 2 decimal places).

Answer: (0.21 to 0.23)

47. The ground state energy of a particle of mass 𝑚 in an infinite potential well is 𝐸0. It changes to 𝐸₀(1+𝛼×10⁻³), when there is a small potential bump of height and width 𝑎=𝐿/100, as shown in the figure. The value of 𝛼 is ________ (up to two decimal places).

Answer: (0.78 to 0.82)

48. An electromagnetic plane wave is propagating with an intensity 𝐼=1.0×10⁵ Wm–2 in a medium with 𝜖=3𝜖₀ and 𝜇=𝜇₀. The amplitude of the electric field inside the medium is ________ ×10³ Vm^–1 (up to one decimal place).

(𝜖₀= 8.85×10⁻¹² C₂ N^–1 m^–2, 𝜇₀=4𝜋×10⁻⁷NA^–2, 𝑐 = 3×10⁸ ms^–1)

Answer: (6.5 to 6.7)

49. A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy 𝜖 state. Both states are non-degenerate. If the total energy of this ensemble is 4𝜖, its entropy will be ________ 𝑘_𝐵 (up to one decimal place), where 𝑘_𝐵 is the Boltzmann constant.

Answer: (6.1 to 6.3)

50. A two-state quantum system has energy eigenvalues ±𝜖 corresponding to the normalized states At time 𝑡=0, the system is in quantum state The probability that the system will be in the same state at 𝑡=ℎ/(6𝜖) is ________ (up to two decimal places).

Answer: (0.25 to 0.25)

51. An air-conditioner maintains the room temperature at 27°C while the outside temperature is 47°C. The heat conducted through the walls of the room from outside to inside due to temperature difference is 7000 W. The minimum work done by the compressor of the air-conditioner per unit time is ________ W.

Answer: (466 to 4.67)

52. Two solid spheres A and B have same emissivity. The radius of A is four times the radius of B, and temperature of A is twice the temperature of B. The ratio of the rate of heat radiated from A to that from B is ________.

Answer: (256 to 256)

53. The partition function of an ensemble at a temperature 𝑇 is

where 𝑘_𝐵 is the Boltzmann constant. The heat capacity of this ensemble at is 𝑋 𝑁𝑘_𝐵, where the value of 𝑋 is ________ (up to two decimal places).

Answer: (0.41 to 0.43)

54. An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its 650 nm spectral line is 0.03 nm. The magnitude of the field is ________ Tesla (up to two decimal places).

( 𝑒=1.60×10⁻¹⁹ C, 𝑚𝑒=9.11×10⁻³¹ kg, 𝑐=3.0×108 ms^–1)

Answer: (1.51 to 1.53)

55. The quantum effects in an ideal gas become important below a certain temperature 𝑇_𝑄 when de Broglie wavelength corresponding to the root mean square thermal speed becomes equal to the inter-atomic separation. For such a gas of atoms of mass 2×10⁻²⁶ kg and number density 6.4×10²⁵ m^–3, 𝑇𝑄= __________ ×10⁻³ K (up to one decimal place).
(𝑘𝐵=1.38×10⁻²³ J/K, ℎ=6.6×10⁻³⁴ J-s)

Answer: (78 to 90)

GATE Exam 2018 Petroleum Engineering (PE) Question Paper With Answer Key

June 7, 2023November 24, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

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

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Petroleum Engineering

Q. 1 – Q. 25 carry one mark each.

1. The Taylor series expansion of the function,

around 𝑥 = 0 (up to 4th order term) is:

Answer: (B)

2. The inverse of the matrix is

Answer: (C)

3. The line integral of a vector function over a curve C in a simply connected domain D in space, is defined by:

The line integral is independent of path in D. 𝐹₁, 𝐹₂, and 𝐹₃ are continuous, and have continuous first partial derivatives in D. 𝐶′ is a closed curve in D.
Which one of the following is NOT ALWAYS true in domain D?

Answer: (B)

4. Which one of the following is the integrating factor (IF) for the differential equation, ?

(A) 𝑒^{tan 𝑥}

(B) 𝑒^{cos 𝑥}

(D) 𝑒^{sin 𝑥}

Answer: (A)

5. A phase diagram of a black oil is shown in the figure (Y is the critical point).

Match the following:

(P) Curve XY (I) Dew point curve

(Q) Curve YZ (II) Single phase liquid

(R) Phase I (III) Bubble point curve

(S) Phase II (IV) Single phase gas

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

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

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

Answer: (B)

6. Match the following chemicals to their respective oilfield applications:

(P) Hydrate inhibitor

(I) Formaldehyde

(Q) Well stimulation

(II) Xanthan gum

(R) Drilling fluid biocide

(III) Methanol

(S) Viscosifier

(IV) Hydrochloric acid

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

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

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

Answer: (D)

7. The CH₄-hydrate equilibrium curve (dashed) and CO₂-hydrate equilibrium curve (solid) on a pressure-temperature plane above 0°C are shown in the figure. The two curves divide the plane in four non-overlapping regions. In which region are CO₂-hydrates stable and CH₄– hydrates unstable?

(A) I

(B) II

(D) IV

Answer: (B)

8. Plot of ratio of pressure to gas compressibility factor (P/Z) vs. cumulative gas production (G_p) for a gas reservoir (represented by solid curve in the figure) was shown to a reservoir engineering student.

The student made the following statements:

(I) A water aquifer is attached to this gas reservoir.

(II) P/Z vs. Gp curve must always be a straight line for water encroachment in a gas reservoir.

(III) The ultimate gas recovery is diminished due to water encroachment.

Which of the above statements are TRUE?

(A) Only I and II

(B) Only II and III

(D) I, II, and III

Answer: (C)

9. Waste water from oil industry consists of oil in free and emulsified forms. The oil in the free form can be recovered by:

(A) Aerated lagoons

(B) Trickling filters

(D) Biological oxygen pond

Answer: (C)

10. A reservoir model consisting of two porous matrices M and N, separated by a fracture, is shown in the figure. The matrices are strongly water-wet and are saturated with oil of specific gravity 0.8. Water is injected only in the fracture at injection well A. If the Reynolds number for the flow in the fracture conduit is assumed to be less than unity, which one of the following force will dominate oil recovery from the porous matrix M during the water-flood operation?

(A) Capillary force

(B) Gravity force

(D) Inertial force

Answer: (A)

11. A fractional flow curve is given for a core for which the irreducible water saturation is 0.2 and the residual oil saturation is 0.3. The initial water saturation in the core is 0.3. If Welge’s method is applied to find the breakthrough saturation and fraction flow of water at breakthrough, which point should be used in the figure to draw a tangent line to the fractional flow curve.

(A) I

(B) II

(D) IV

Answer: (D)

12. Which one of the following curves represents behavior of oil phase viscosity as a function of pressure in the reservoir (where, P_b is the bubble point pressure of oil)?

(A) Curve I

(B) Curve II

(D) Curve IV

Answer: (D)

13. Pick out the INCORRECT statement.

(A) Flash point is always lower than fire point.

(B) Pour point of lube oil can be reduced by removing the wax from it.

(D) Coal bed methane typically contains more than 60% CO₂.

Answer: (D)

14. Which one of the following phenomena encountered during flooding is desirable for increasing oil recovery from a reservoir?

(A) Viscous fingering

(B) Formation damage

(D) Decrease in capillary pressure

Answer: (D)

15. CO₂ foams are used for enhanced oil recovery due to which of the following reasons?

(I) It can be used for CO₂ sequestration

(II) CO₂ can exist in the form of a dense fluid at reservoir conditions

(III) CO₂ can convert to hydrocarbon at the reservoir temperature and pressure

(IV) Solubility of CO₂ in oil is higher compared to gases like N₂

(A) Only I, II, and III

(B) Only I, II, and IV

(D) Only I, III, and IV

Answer: (B)

16. Which one of the following is FALSE about a typical offshore deepwater oil spill?

(A) Using boom boats to prevent spilled oil from spreading

(B) Allowing the spill to reach the shore before clearing

(D) Using a skimmer to collect the oil

Answer: (B)

17. Which one of these methods is NOT commonly used to deal with the problem of soil contamination by oil spillage?

(A) Biodegradation

(B) Leaching out the oil

(D) Using rain water to wash the contaminants

Answer: (D)

18. The factor on which the selection of an offshore platform for the reservoir does NOT depend:

(A) Water depth

(B) Reservoir fluid properties

(D) Best case weather forecast

Answer: (D)

19. Which one of the following options is correct about the effects of steam stimulation in increasing the oil production rate?

(I) Reduces the oil viscosity

(II) Increases the formation damage

(III) Reduces the interfacial tension

(IV) Increases the oil viscosity

(A) Only I and II

(B) Only II and III

(D) Only I and III

Answer: (D)

20. Which one of the following is INCORRECT about oil based drilling muds?

(A) Good rheological properties at higher temperatures (as high as 250oC)

(B) Effective against corrosion

(D) Less inhibitive than water based muds

Answer: (D)

21. Assume that viscous, gravity, and capillary are the only dominant forces for fluid flow in a given reservoir, a cone formed around the perforation zone will break into the well, when

(A) capillary forces are more than viscous and gravity forces.

(B) viscous forces are more than gravity forces.

(D) viscous and gravity forces are equal.

Answer: (B)

22. Two complex numbers, are related as follows:

where, is a scalar. Given principal argument of the principal argument of ______________. (rounded-off to two decimal places. (Use 𝜋 = 3.14)

Answer: (2.50 to 2.70)

23. A cylindrical sandstone core, 7.5 cm long and 3.5 cm diameter has grain density of 3 g/cm³. If the mass of the dry core is 200 g, the porosity of the core is __________%. (rounded-off to two decimal places)

Answer: (7.25 to 7.75)

24. In an oil reservoir the current average pressure is below bubble point pressure of the oil. The current oil production rate is 103 m³/day and total gas production rate is 105 m³/day at STP conditions (25°C and 1 atm). The formation volume factor of the oil is 1.2 and that of gas is 0.01 The dissolved gas oil ratio is 10 of soil

The gas flow rate at bottom-hole conditions is ______× 10² m³ per day. (rounded-off to two decimal places)

Answer: (8.90 to 9.10)

25. Exponential decline curve is to be used to estimate the oil reserves of a well. The current oil production rate is 1000 m³ per day and yearly decline rate is 6% per year. If the minimum oil flow rate economically sustainable for the well is 1 m³ per day, the reserves (economically producible) associated with the well are _____ × 10⁶ m³. (rounded-off to two decimal places. Use 1 year = 365 days)

Answer: (5.80 to 6.20)

Q. 26 – Q. 55 carry two marks each.

26. The probability density for three binomial distributions (D1, D2, and D3) is plotted against number of successful trials in the given figure.

Each of the plotted distributions corresponds to a unique pair of (n, p) values, where, n is the number of trials and p is the probability of success in a trial. Three sets of (n, p) values are provided in the table.

Pick the correct match between the (n, p) set and the plotted distribution.

(A) Set I – D1, Set II – D2, Set III – D3

(B) Set I – D3, Set II – D1, Set III – D2

(D) Set I – D2, Set II – D1, Set III – D3

Answer: (B)

27. Which of the following statements are true about Natural Gas Hydrates?

Natural gas hydrates:

(I) are formed under low temperature and high pressure.

(II) can store approximately 160 m3 of gas per m3 of hydrate at 25 oC and 1 atm.

(III) formation is an endothermic process.

(IV) are potential sources of methane.

(A) Only II, III & IV

(B) Only I, II & III

(D) Only I, III & IV

Answer: (C)

28. P_wf (bottom-hole well flowing pressure) vs. Q (flow rate) plots show the inflow performance relation (IPR) and vertical lift performance (VLP) curves. Figure I shows VLP curves for two well head pressures P_hw1 and P_hw2. Figure II shows VLP curves for two well diameters D₁ and D₂. Which one of the following statements is true?

(A) P_hw1 > P_hw2 and D₁ < D₂

(B) P_hw1 > P_hw2 and D₁ > D₂

(D) P_hw1 < P_hw2 and D₁ > D₂

Answer: (A)

29. Match the following:

(P) Weber Number (I) Ratio of inertial force to viscous force

(Q) Froude Number (II) Ratio of convective heat transfer to conductive heat transfer

(R) Reynolds number (III) Ratio of inertial force to interfacial force

(S) Nusselt number (IV) Ratio of inertial force to gravitational force

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

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

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

Answer: (A)

30. A dilute mixture of coal and sand particles, both of diameter 100 μm and densities 1800 kg/m³ and 2600 kg/m³, respectively, is to be classified by elutriation technique using water (density 1000 kg/m³, viscosity 10^-3 Pa.s). Assuming Stokes law is applicable, the minimum settling velocity of the particles in the mixture is (g = 9.81 m/s²):

(A) 4.36 × 10^-3 m/s

(B) 8.72 × 10^-3 m/s

(D) 1.29 × 10^-3 m/s

Answer: (A)

31. Oil flow rate and flowing bottom-hole pressure (FBHP) recorded with time during a multirate well test are shown.

Let k is the reservoir permeability, h is the formation thickness and μ is the viscosity of the oil. Δ𝑃_𝐷(𝑡) is constant-rate dimensionless pressure drop as a function of time. The total pressure drop till time, t, where t > t₁, will be:

Answer: (A)

32. Which one of the following options presents the correct combination?

(P) Reservoir limit test (I) Communication between wells

(Q) Modified isochronal test (II) Ideally zero flowing bottom hole pressure

(R) Interference test (III) Extended drawdown test

(S) Absolute open flow potential (IV) Drawdown and build-up test of equal duration

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

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

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

Answer: (C)

33. Which one of the following options presents the correct combination?

(P) Roller Cone bits (I) Long and widely spaced teeth

(Q) PDC bits (II) Journal (Pin) angle

(R) Soft formation (III) Short and wider teeth

(S) Hard formation (IV) Size of the cutting

(T) Back rake angle (V) 1400oC and 6×105 psi

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

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

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

Answer: (A)

34. Primary and secondary indicators of kick in a well where the indicators are:

1) flow rate increase,

2) gas, oil or water-cut muds,

3) pit volume increase,

4) flowing well with mud pump shut-off,

5) reduction in drill-pipe weight,

6) drilling break.

Which one of the following presents the correct combination?

(A) Primary (1, 3, 5) and Secondary (2, 4, 6)

(B) Primary (1, 2, 3) and Secondary (4, 5, 6)

(D) Primary (1, 3, 4) and Secondary (2, 5, 6)

Answer: (D)

35. Relative permeability curve for the two rock types (X: solid line and Y: dashed line) are shown in the diagram, where Sw is the fractional water saturation. Which one of the following statements is correct about wettability and consolidated nature of the two rock types?

(A) X is more consolidated and mixed wet, Y is less consolidated and water wet

(B) X is more consolidated and water wet, Y is less consolidated and mixed wet

(D) X is less consolidated and water wet, Y is more consolidated and mixed wet

Answer: (C)

36. Which one of the following options presents correct combinations of exploration methods with their respective frequency of operation?

(P) Seismic (I) ~106 Hz

(Q) Sonic (II) ~102 Hz

(R) Controlled Source EM (III) ~104 Hz

(S) Ultrasonic (IV) ~1 Hz

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

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

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

Answer: (B)

37. Which one of the following options presents the correct combinations?

(P) Borisov’s (I) Critical rate correlation in vertical wells with coning

(Q) Schols’ ( I I ) H o r i zontal well performance relation

(R) Efros’ (III) Vertical well performance relation

(S) Wiggins’ (IV) Critical rate correlation in horizontal wells with coning

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

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

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

Answer: (D)

38. Which one of the following options represents the typical sequence of applying cut-offs for pay zone identification in a conventional reservoir?

(A) porosity, saturation, shale

(B) porosity, permeability, saturation

(D) shale, porosity, permeability

Answer: (C)

39. Which one of the following options represents the correct sequence of arrival of acoustic wave energy recorded in a sonic log?

(A) shear, surface, compressional

(B) compressional, shear, surface

(D) compressional, surface, shear

Answer: (B)

40. The variation of the amount of salt in a tank with time is given by,

where, 𝑥 is the amount of salt in kg and 𝑡 is the time in minutes. Given that there is no salt in the tank initially, the time at which the amount of salt increases to 200 kg is __________ minutes. (rounded-off to two decimal places)

Answer: (10.50 to 12.50)

41. Solve the given differential equation using the 2nd order Runge-Kutta (RK2) method:

Use the following form of RK2 method with an integration step-size, ℎ = 0.5:

The value of 𝑦(𝑡 = 0.5) =__________________. (rounded-off to two decimal places)

Answer: (3.12 to 3.26)

42. A box contains 100 balls of same size, of which, 25 are black and 75 are white. Out of 25 black balls, 5 have a red dot. A trial consists of randomly picking a ball and putting it back in the same box, i.e., sampling is done with replacement. Two such trials are done. The conditional probability that no black ball with a red dot is picked given that at least one black ball is picked, is __________. (in fraction rounded-off to two decimal places)

Answer: (0.76 to 0.80)

43. A cylindrical pipeline of length 30 km is transporting naphtha. Pressure sensors are attached along pipe length to detect leaks. Under steady-state, leak-free operation, there is a linear pressure drop along the length (z) of the pipeline. If a leak occurs, the pressure profile develops a kink at the leak point 𝑧_leak.

Assume that there is only one leak-point (4 km < 𝑧_leak < 27 km) and a new steady-state is reached. The steady-state pressure measurements at four locations along the pipe-length are provided in the table. The location of the leak-point using the gradient intersection method is _______________km. (rounded-off to two decimal places)

Answer: (7.20 to 7.80)

44. A dry core was subjected to the mercury injection test in the laboratory. Following are the related details:

Average formation porosity = 0.2

Formation volume factor, BO = 1.2 reservoir-bbl/STB

Oil API° = 32, Specific gravity of water = 1.1

Hydrostatic gradient = 0.433 psi/ft

(𝜎_𝑂𝑊 cos 𝜃)res = 26 dyne/cm, where 𝜎_𝑂𝑊 is the oil-water interfacial tension and 𝜃 is the contact angle

(𝜎_𝐴𝑀 cos 𝜃)lab = 367 dyne/cm, where 𝜎_𝐴𝑀 is air- mercury interfacial tension and 𝜃 is the contact angle

Average drainage area = 80 acres

(1 acre-ft = 7758 bbl)

The Table shows the laboratory data for capillary pressure at different mercury saturations.

and the average water saturation (𝑆_𝑊) for the productive column is 0.25. The Original Oil in Place (OOIP) in the productive column where 𝑆_𝑊 ≤ 0.5 is ___________ MMSTB. (rounded-off to one decimal place)

Answer: (105.00 to 109.00)

45. A well is drilled with water based mud. The water saturation in the completely flushed zone (no formation fluid residual) is given by,

where, R_mf and R_xo are the mud filtrate resistivity and flushed zone resistivity, respectively.

Use, a = 1.0 and R_xo = 25 R_mf.

The calculated porosity (ϕ) of the formation is ______. (in fraction rounded-off to two decimal places)

Answer: (0.19 to 0.21)

46. An oil well is tested at a flow rate (Q) of 50 BOPD. The bottom hole flowing pressure (P_wf) is 500 psia. The shut-in pressure is 1000 psia. If P_wf is lowered to 300 psia and assuming the Vogel’s correlation holds, the estimated flow rate in the oil well is ______BOPD (rounded-off to two decimal places). The Vogel’s correlation is:

Answer: (61.00 to 63.00)

47. Using Miller, Dyes and Hutchinson (MDH) method, the skin factor of an oil well is found to be 𝑠 = – 3.5.

The reservoir and fluid properties are:

Formation porosity is 0.20

Total compressibility is 2.5 × 10-5 psia-1

Oil viscosity is 1.5 cP

Wellbore radius is 0.5 ft

Flowing bottom hole pressure at Δt = 0 is 2830 psia

Shut in pressure at Δt = 1 hr (PΔt=1hr) is 3000 psia

Slope of middle time region (MTR) line in MDH plot is 190 psia/cycle.

The permeability of the reservoir is __________mD. (rounded-off to two decimal places)

Answer: (25.00 to 29.00)

48. An oil well (producing under expansion drive only) in a reservoir is subjected to two pressure build-up tests. The average formation thickness of the reservoir is 13 ft, the total compressibility is 1×10^-5 psia^-1, and porosity is 0.2. The average formation volume factor of oil is 1.3 reservoir-bbl/STB. Average reservoir pressure during the first test and the second test was found to be 3500 psia and 3200 psia, respectively. If the oil produced between the two pressure build-up tests in 180 days is 250 STB/day, the area of the reservoir is __________acres. (rounded-off to two decimal places) (Use: 1 acre = 43560 ft², 1 bbl = 5.615 ft³)

Answer: (960.00 to 970.00)

49. A well in a very large reservoir has a wellbore radius of 10 cm. The sandstone, with a porosity of 0.25 and 12% (by grain volume) calcite (CaCO₃), is to be acidized with a preflush (HCl solution) so as to dissolve all the calcite upto a distance of 1 m from the wellbore. 1 m³ of preflush is able to dissolve 0.082 m³ CaCO₃. Assume that the reaction between HCl and CaCO₃ is instantaneous. The minimum preflush volume required per meter of the formation thickness is ______________m³. (rounded-off to two decimal places)

Answer: (4.40 to 5.50)

50. At a particular temperature, the vapour pressure of benzene and toluene are 4 atm and 1.2 atm, respectively. The composition of the liquid at equilibrium is 0.5 moles of benzene and 0.5 moles of toluene. Assuming ideal gas and ideal solution, the equilibrium vapour phase mole fraction of benzene is ________ . (rounded-off to two decimal places)

Answer: (0.72 to 0.80)

51. Saturated steam at 0.7 atm and 90°C condenses on a vertical pipe of 2 cm outside diameter and 40 cm length. The average condensation heat transfer coefficient on the tube is 12000 W/m²K. The outside surface temperature of the pipe is maintained constant at 85°C. The enthalpy values for saturated steam and condensate are 2660 kJ/kg and 375 kJ/kg, respectively. The rate of steam condensation is ____ kg/h. (rounded-off to two decimal places)

Answer: (2.10 to 2.60)

52. Oil is being transported between two reservoirs with the help of three parallel pipes at steady state. The diameters of these pipes are 2 cm, 3 cm and 4 cm, respectively. The pipes are equal in length and the flow is laminar. The discharge through the 4 cm diameter pipe is 50 liters/s. The discharge through the 2 cm diameter pipe is _____ liters/s. (rounded-off to two decimal places)

Answer: (3.00 to 3.20)

53. A driller finds an oil reservoir with a gas cap starting at a depth of 1000 m from the surface. The gas-oil contact was found at 1100 m depth and water-oil contact was found at 1300 m depth. The water pressure in the aquifer below the oil zone varies with depth from the surface (h, in meters) as, P = h × 10⁴ Pa. The density of the oil is 900 kg/m³ and that of the gas is 5 kg/m³ at the reservoir condition. The minimum density of the mud needed to stop the gas kick when the driller reaches at the top of the gas cap is _____kg/m³. (rounded-off to two decimal places. Use g = 9.81 m/s²)

Answer: (1115.00 to 1160.00)

54. The viscosity, μ (in Pa.s) of a power law fluid as a function of shear rate, 𝛾̇ (in s^-1) is given by the following relation:

This power law fluid lies between two infinitely large horizontal parallel plates separated by a distance (h) of 10^-3 m. The top plate is moving horizontally at a velocity (v) of 10^-3 m/s and the bottom plate is held stationary. Assuming laminar flow and neglecting gravity, the absolute value of steady-state shear stress acting on the bottom plate is ______ Pa. (rounded-off to two decimal places)

Answer: (0.49 to 0.51)

55. A heterogeneous rectangular rock of cross-sectional area 1 m² perpendicular to the flow is being flooded by water to measure the effective permeability from cross-section AA’ to cross-section CC’.

The pressure at the cross-sections AA’, BB’, and CC’ is 2 bar, 1.5 bar, and 1 bar, respectively. The permeability in mili-Darcy and lengths AB and BC in meters are given in the figure. The effective permeability of the rock from AA’ to CC’ is ______mD.
(rounded-off to two decimal places)

Answer: (2.00 to 2.50)

GATE Exam 2018 Metallurgical Engineering (MT) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Metallurgical Engineering

Q. 1 – Q. 25 carry one mark each.

1. For a laminar flow of a liquid metal over a flat plate, the thicknesses of the velocity and thermal boundary layers are δv and δt respectively. Kinematic viscosity (viscosity/density) of liquid metal is significantly lower than its thermal diffusivity
[thermal conductivity / (density × specific heat)]. Based on this information, pick the correct option.

(Note: The temperature of the liquid metal is different from that of the plate).

(A) δ_v < δ_t

(B) δ_v > δ_t

(D) Information insufficient

Answer: (A)

2. What is the most-abundant anion in a 2CaO.SiO₂ melt?

(A) (SiO₄)^4–

(B) (Si₂O₇)^6–

(D) (Si₄O₁₄)^10–

Answer: (A)

3. Analysis of a flow phenomenon in a system requires the following variables:

i. Pressure [M L^–1 T^–2]

ii. Velocity of the fluid [L T ^–1]

iii. Size of the system [L]

iv. Density of the fluid [M L^–3]

v. Viscosity of the fluid [M L^–1 T ^–1]

According to Buckingham Pi theorem (dimensional analysis) what is the number of independent DIMENSIONLESS variables needed to describe this system?

(A) 2

(B) 3

(D) 5

Answer: (A)

4. In froth flotation, the primary purpose of adding collectors is to:

(A) make the surface of the mineral hydrophobic.

(B) make the surface of the mineral hydrophilic.

(D) adjust the pH.

Answer: (A)

5. A rrange the following in the correct sequence of operations in an integrated steel plant:

i. Basic Oxygen Furnace (BOF)

ii. Blast Furnace (BF)

iii. Ruhrstahl Heraeus Degassing Process (RH)

iv. Ladle Furnace Process (LF)

(A) BOF→BF→LF→RH

(B) BF→LF→BOF→RH

(D) BF→BOF→LF→RH

Answer: (D)

6. During decarburization in a steel bath at 1550°C, the compositions of dissolved C (wt.%C) and dissolved O (wt.%O) follow the relation:

(wt.%C)(wt.%O) = K

When the partial pressure of CO (𝑝_𝐶𝑂) is 1 atm, K = 0.002. If 𝑝_𝐶𝑂 = 0.1 atm, what is the value of K, at the same temperature?
Note: Assume Henry’s law is applicable.

(A) 0.06

(B) 0.002

(D) 0.0002

Answer: (D)

7. During upset forging, and considering friction, which of the following profiles represents the axial compressive stress?

Note: In these profiles, the absolute value of the axial compressive stress is plotted on the y-axis.

(A) P

(B) Q

(D) S

Answer: (A)

8. Consider the following engineering components:

P. Gas turbine blades

Q. Tungsten-based heavy alloy penetrators

R. Self-lubricating bearings

S. Engine block of an automobile

Which of the following two components are produced by powder metallurgy?

(A) P & Q

(B) Q & R

(D) P & S

Answer: (B)

9. Which of the following materials are protected by passivation (i.e., formation of a thin adherent film on the surface) from corrosion?

P. Aluminium alloys

Q. Mild steel

R. Stainless steel

S. Silver

(A) P & Q

(B) Q & R

(D) P & R

Answer: (D)

10. The c/a ratio of Zn (hcp) is 1.856. Slip at room temperature occurs most easily on which of the following slip systems in Zn:

Note: In hcp metals, the ideal c/a ratio is 1.633.

Answer: (C)

11. At equilibrium, the maximum number of phases in a three-component system at CONSTANT PRESSURE is:

(A) 1

(B) 2

(D) 4

Answer: (D)

12. For a single phase system with K components, the exact differential of Gibbs free energy is given as :

Which one of the following can be derived from the above expression as a Maxwell’s relation?

Answer: (A)

13. For intrinsic Si at room temperature, the electron concentration = the hole concentration = 1 × 10¹⁶ m^–3, and the electron and hole mobilities are 0.1 and 0.2 m². V^–1. s^–1 respectively. What is the room temperature electrical conductivity?

The charge of an electron is 1.6 × 10⁻¹⁹C.

(A) 0 (Ω.m)^–1

(B) 1.6 × 10^–4 (Ω.m)^–1

(D) 4.8 × 10^–4 (Ω.m)^–1

Answer: (D)

14. To minimize refractory loss during BOF steel-making, slag is supersaturated with which of the following:

(A) Al₂O₃

(B) Fe₂O₃

(D) MgO

Answer: (D)

15. Which of the following welding processes is NOT suitable for joining thin metal sheets?

(A) Gas Metal Arc Welding

(B) Electro Slag Welding

(D) Laser Beam Welding

Answer: (B)

16. Which of the following categories of materials is suitable as a filler for brazing of steel sheets?

(A) Epoxy resins

(B) Near-eutectic alloys

(D) Large freezing range alloys

Answer: (B)

17. Arrange the following processes in INCREASING magnitude of surface roughness of the casting.

P. Investment casting

Q. Permanent mould casting

R. Pressure die casting

S. Sand casting

(A) R < S < Q < P

(B) P < S < Q < R

(D) Q < P < R < S

Answer: (B)

18. In a Jominy end-quench test of the eutectoid plain-carbon steel, which of the following represents the sequence of microstructures observed from the quenched end of the specimen?

(A) Fine Pearlite, Coarse Pearlite, Martensite and Pearlite, Martensite

(B) Martensite, Martensite and Pearlite, Fine Pearlite, Coarse Pearlite

(D) Martensite, Martensite and Pearlite, Coarse Pearlite, Fine Pearlite

Answer: (B)

19. A long oil pipeline made of steel is suspected to have developed a scale on the inner surface due to corrosion. Which of the following non-destructive techniques is the most suitable for detecting and quantifying such a defect?

(A) Dye penetrant test

(B) Magnetic particle inspection

(D) Acoustic emission

Answer: (C)

20. A steel is plastically worked in the temperature range below the nose of the TTT curve and above M_s, followed by quenching to produce fine martensite. What is this process called?

(A) Martempering

(B) Ausforming

(D) Normalizing

Answer: (B)

21. What is the requirement for equilibrium at a triple junction as shown in the schematic, with γ₁₂, γ₂₃ and γ₁₃ as grain boundary tensions and θ₁, θ₂ and θ₃ as dihedral angles?

Answer: (B)

22. In the A-rich end of the A-B binary eutectic phase diagram (shown below), the solidus and liquidus are straight lines.

The freezing range of the alloy with 16% B is _________ (in °C to one decimal place)

Answer: (95 to 105)

23. A vector field is given as follows:

The divergence of this field evaluated at (𝑥, 𝑦) = (2, 2) is _______________ .

Answer: (-0.1 to 0.1)

24. A plate of thickness h = 120 mm is cold rolled in a mill with a roll diameter of 200 mm. If the coefficient of friction μ is 0.1, the maximum possible reduction Δh in a single pass is ________ (in mm to one decimal place)

Answer: (0.9 to 1.1)

25. A copper-aluminium diffusion couple develops a certain concentration profile after an isothermal treatment at 600°C for 10 hours. The time required to achieve the same concentration profile at 500°C is _________ (in hours to 1 decimal place)

Given: The interdiffusion coefficient for copper in aluminium at 500°C and 600°C are 4 × 10^–14 ms^–1 and 8 × 10^–13 m² s^–1.

Answer: (180 to 220)

Q. 26 – Q. 55 carry two marks each.

26. T he molar free energy (J mol^–1) of a liquid solution of a binary A-B alloy as a function of temperature ( T ) and composition (x, the mole fraction of B) is given by:

where are the molar free energies of pure liquid A and pure liquid B. What is the excess molar free energy, G^{XS, L} , for an alloy with 𝑥 = 0.5 at 𝑇 = 1000 K?

Given: Gas constant R = 8.314 J K^–1 mol^–1

(A) 1000 J mol^–1

(B) –2000 J mol^–1

(D) –5763 J mol^–1

Answer: (A)

27. Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Assertion [A]: For a material exhibiting Coble creep, a reduction in grain size results in a significant increase in creep rate

Reason [R]: Grain boundaries act as a barrier to motion of dislocations

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

(B) Both [A] and [R] are true, but [R] is not the correct reason for [A]

(D) [A] is true but [R] is false

Answer: (B)

28. Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Assertion [A]: Refractory BCC metals like W and Mo are less ductile than FCC metals like Ni and Pt at room temperature

Reason [R]: BCC metals have fewer independent slip systems than FCC metals

(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)

29. A glass fibre of 5 micron diameter is subjected to a tensile stress of 20 MPa. The surface energy and elastic modulus of this material are 0.3 Jm^–2 and 70 GPa, respectively. Pick the correct answer based on the information provided above:

Note: The glass fibre contains a population of flaws of different lengths.

(A) The fibre will undergo brittle fracture

(B) The fibre will undergo plastic deformation, but not fracture

(D) The fibre will undergo buckling

Answer: (C)

30.

Two equal and opposite point charges + Q and –Q are located as shown in the figure above. A surface integral, 𝐹_𝑖 is defined on surface 𝑆_𝑖 of a sphere of radius 𝑟_𝑖 as follows:

where is the electric field, and is the unit normal to the surface of integration.

If 𝑟₁: 𝑟₂: 𝑟₃ are in the ratio 1: 2: 5, use the Gauss divergence theorem to determine the ratio 𝐹₁: 𝐹₂: 𝐹₃ .

(A) 1 : 2 : 5

(B) 5 : 2 : 1

(D) 1 : 1 : 0

Answer: (C)

31. Match the four tensile stress-strain curves (P,Q, R, S) with the materials listed in the box:

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

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

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

Answer: (C)

32. Match the metal in Group 1 with the appropriate extractive process in Group 2

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

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

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

Answer: (C)

33. Fe is produced in a reactor using pure Fe₂O₃, C and O₂. For every mole of Fe produced, 2.38 moles of C is used. The exit gas from the reactor contains CO and CO₂ in the molar ratio of 1:1. How many moles of O₂ is consumed for every mole of Fe produced?

(A) 1.035

(B) 2.072

(D) 4.147

Answer: (A)

34. What is the voltage required to electrolytically refine impure copper of activity 𝑎_𝐶𝑢 = 0.9

(Raoultian standard state) to pure copper at 300 K

Given: Gas constant R = 8.314 J mol^–1 K^–1, and Faraday’s constant F = 96500 C mol^–1.

(A) 1.36 mV

(B) 2.72 mV

(D) 5.44 mV

Answer: (A)

35. Consider the following Ordinary Differential Equation:

In a domain 0 ≤ 𝑥 ≤ 𝑡, with boundary conditions 𝑐(0) = 0.5 and 𝑐(𝑡) = 1.0, pick the appropriate choice for 𝑐(𝑥) from the following options:

(A) P

(B) Q

(D) S

Answer: (B)

36. Match the manufacturing processes in Group 1, with the types of cracks in Group 2:

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

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

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

Answer: (C or D)

37. Consider a dilute substitutional solid solution of X in a metal A. The powder diffraction pattern of this alloy reveals that all the peaks have shifted to the left when compared to those for pure A (with no splitting of peaks). If such a solute interacts and segregates to an edge dislocation, which of the following positions around the dislocation will it preferentially occupy?

(A) P

(B) Q

(D) S

Answer: (D)

38. A classroom of 20 students can be categorized on the basis of blood-types: 5 students each with “A”, “B”, “AB”, and “O” blood-types. If four students are selected at random from this class, what is the probability that each student has a different blood-type?

(A) 0.2500

(B) 0.1289

(D) 0.0156

Answer: (B)

39. If the solid-liquid interfacial energy increases by 10%, the energy barrier for homogeneous nucleation of a spherical solid from the liquid, will change by:

(A) 21%

(B) 33%

(D) 46%

Answer: (B)

40. Consider the following stress state imposed on a material:

If the material responds elastically with a volumetric strain Δ = 3.5 × 10^–4, what is its bulk modulus?

(A) 150 GPa

(B) 350 GPa

(D) 400 GPa

Answer: (C)

41. A continuous and aligned carbon-fiber composite consists of 25 vol. % of fibers in an epoxy matrix. The Young’s modulus of fiber and matrix, respectively are E_f = 250 GPa and E_m = 2.5 GPa.

If the composite is subjected to longitudinal loading (iso-strain condition and assuming elastic response), the fraction of load borne by the reinforcement is ________ (to two decimal places)

Answer: (0.96 to 0.98)

42. Pure iron transforms from body centered cubic (BCC) to face centered cubic (FCC) crystal structure at 912 °C. If the lattice parameter of the BCC phase is 0.293 nm and that of the FCC phase is 0.363 nm, the associated volume change is _______ (in % to one decimal place)

Answer: (-5.5 to -4.5)

43. A s shown in schematic below, an alloy is cast as a rectangular slab between two thick mould walls that differ in their thermal conductivities. Shrinkage defects are found at a distance L₁ from Mould-1 with thermal conductivity 𝑘₁ and distance L₂ from Mould-2 with thermal conductivity 𝑘₂. If the ratio L₁:L₂ = 3:2, and assuming 1-D heat transfer, the ratio (k₁/k₂) is _______ (to two decimal places)

Answer: (2.2 to 2.3)

44. The temperature profile (T in Kelvin) of an arc weld across its width is given as 𝑇 = 2000 exp(−0.3𝑥²) where 𝑥 (in mm) is the distance from the weld centre. The melting point of the base material is 1500 K. The width of the fusion zone is _______ (in mm to two decimal places).

Answer: (1.9 to 2.0)

45. The terminal velocity (𝑣) of a spherical inclusion of diameter D = 50 micrometers rising in liquid steel is __________ (in mm s^–1 to two decimal places)

Assume Stokes law; i.e., drag force 𝐹𝑑 = 3𝜋𝜇𝐷𝑣, where 𝜇 is the viscosity of steel.

Given: Density of liquid steel = 7900 kg m^–3; Viscosity of liquid steel = 0.0079 Pa s;

Density of the inclusion = 2500 kg m^–3; Acceleration due to gravity = 9.8 m s^–2

Answer: (0.9 to 1.0)

46. A single crystal of aluminium is subjected to 10 MPa tensile stress along the [321] crystallographic direction. The resolved shear stress on the slip system is ______ (in MPa to two decimal places)

47. If the net magnetic moment of an Fe atom in BCC structure is 2 𝜇_𝐵, then the saturation magnetization of Fe is ___________ (kA m^–1 to one decimal place)

Given: 𝜇_𝐵 = 9.273 × 10^–24 A m²; Lattice parameter of BCC iron is 0.287 nm

Note: kA is kiloAmperes

Answer: (1500 to 1600)

48. If 2 moles of Au and 3 moles of Ag are mixed to form a single-phase ideal solid solution, the total entropy of mixing is __________ (on J K^–1 to one decimal place )

Given: Gas constant R = 8.314 J K^–1 mol^–1

Answer: (24.9 to 29.0)

49. A spherical liquid metal droplet of diameter 1 mm is solidified in a stream of gas at 300 K. Assuming that the metal droplet remains at its melting point of 900 K and neglecting radiative losses, the time to complete the solidification is __________ (in seconds to one decimal place).

Given: The enthalpy of fusion for the metal is 4000 kJ kg^–1; The gas-droplet convective heat transfer coefficient is 200 W m^–2 K^–1; Density of liquid metal is 2700 kg m^–3.

Answer: (14.9 to 15.1)

50. At a temperature of 710 K, the vapour pressure of pure liquid Zn is given by:

pzn (Xzn = 1.0) = 3.6 × 10^–4 atm.

The Raoultian activity coefficient (𝛾_𝑍𝑛 ) of Zn in Zn-Cd alloy liquid at 710 K is approximated by:

ln(𝛾_𝑍𝑛 ) = 0.875 (1 – X_zn)²

The ratio for a liquid alloy with 𝑋_𝑧𝑛 = 0.7 is __________ (to two decimal places).

Answer: (0.74 to 0.78)

51. For the reaction: 4Ag(s, pure) + O₂(g) ⟶ 2Ag₂O(s, pure), the standard enthalpy change, Δ𝐻⁰ = − 61080 J, and the standard entropy change, Δ𝑆⁰ = − 132.22 J K⁻¹, in the temperature range from 298 K to 500 K. The temperature above which Ag2O decomposes in an atmosphere containing oxygen at a partial pressure 𝑝_𝑂2 = 0.3 atm is __________ (in K to one decimal place).

Given: Gas constant R = 8.314 J K⁻¹ mol⁻¹

Answer: (427 to 432)

52. In a powder diffraction experiment on BCC iron, the first peak occurs at 2𝜃 = 68.7°. The wavelength of X-rays is _________ (in nm to three decimal places).

Given: The lattice parameter of iron = 0.287 nm

Answer: (0.225 to 0.235)

53. A 1 mol piece of copper at 400 K is brought in contact with another 1 mol piece of copper at 300 K, and allowed to reach thermal equilibrium. The entropy change for this process is __________ (in J K⁻¹ to three decimal places)

Given: Specific heat capacity of copper (between 250 K and 500 K) is 22.6 J K⁻¹mol⁻¹.

Assume that the system containing the two pieces of copper remains isolated during this process.

Answer: (0.450 to 0.480)

54. Using the trapezoidal rule with two equal intervals (n = 2, Δ𝑥 = 1), the definite integral ______________ (to two decimal places).

Answer: (1.95 to 2.05)

55. The ideal plastic work involved in extruding a cylindrical billet of length 100 mm, from an initial diameter of 20 mm to a final diameter of 16 mm is __________ (in J to one decimal place).

The flow stress in compression is 40 MPa, and remains constant throughout the process.

Answer: (555.5 to 565.5)

GATE Exam 2018 Mining Engineering (MN) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-3

1. “ From where are they bringing their books? ________ bringing _______ books from _____.”

The words that best fill the blanks in the above sentence are

(A) Their, they’re, there

(B) They’re, their, there

(D) They’re, there, there

Answer: (B)

2. A _________ investigation can sometimes yield new facts, but typically organized ones are more successful.”

The word that best fills the blank in the above sentence is

(A) meandering

(B) timely

(D) systematic

Answer: (A)

3. The area of a square is 𝑑. What is the area of the circle which has the diagonal of the square as its diameter?

(A) πd

(B) πd²

Answer: (D)

4. What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of 7 in ach case?

(A) 3047

(B) 6047

(D) 63847

Answer: (C)

5. What is the missing number in the following sequence?

2, 12, 60, 240, 720, 1440, _____, 0

(A) 2880

(B) 1440

(D) 0

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen in the town and Rs 1000 to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only 8/9th of the eligible men and 2/3rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

(A) 1,50,000

(B) 2,00,000

(D) 1,51,000

Answer: (B)

7. If pqr ≠ 0 and what is the value of the product 𝑥𝑦𝑧?

(A) –1

(B) 1/pqr

(D) pqr

Answer: (C)

8. In a party, 60% of the invited guests are male and 40% are female. If 80% of the invited guests attended the party and if all the invited female guests attended, what would be the ratio of males to females among the attendees in the party?

(A) 2:3

(B) 1:1

(D) 2:1

Answer: (B)

9. In the figure below, ∠DEC + ∠BFC is equal to ____________.

(A) ∠𝐵𝐶𝐷 − ∠𝐵𝐴𝐷

(B) ∠𝐵𝐴𝐷 + ∠𝐵𝐶𝐹

(D) ∠𝐶𝐵𝐴 + ∠𝐴𝐷𝐶

Answer: (A)

10. A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

(A) Three green faces and four red faces.

(B) Four green faces and three red faces.

(D) Six green faces and one red face.

Answer: (C)

Mining Engineering

Q. 1 – Q. 25 carry one mark each.

Answer: (C)

2. The values of x satisfying the following condition are

(A) 6, 4

(B) 4, 9

(D) 3,7

Answer: (D)

3. An azimuth of 330° corresponds to a quadrant bearing of

(A) W60°N

(B) N30°W

(D) S30°E

Answer: (B)

4. Tri-cone drill bit is a type of

(A) cross bit

(B) button bit

(D) button drag bit

Answer: (C)

5. Exposure of weak roof in junctions of a development district in a coal mine can be decreased by

(A) increasing dimension of panel barrier

(B) stitching side walls

(D) staggering the junctions

Answer: (D)

6. The property that CANNOT be determined from uniaxial compressive strength test of a rock sample fitted with strain gauges is

(A) cohesion

(B) Poisson’s ratio

(D) dilation

Answer: (A)

7. The radial stress concentration around a long circular tunnel excavated in rock is given by the curve

(A) m

(B) n

(D) p

Answer: (D)

8. Ward-Leonard system is provided in the winding system in order to restrict

(A) over-winding of the cage

(B) deceleration of the cage

(D) over-speeding of the cage

Answer: (D)

9. The equipment NOT related to extraction of coal from longwall face operation is

(A) AFC

(B) road header

(D) DERD shearer

Answer: (B)

10. The correct figure depicting the extraction of contiguous seams in bord and pillar working is indicated by

Answer: (C)

11. The significance of ‘potentially explosive mixture’ in Coward flammability diagram is –

(A) leakage of fresh air may lead to explosive condition for the mixture

(B) leakage of firedamp may lead to explosive condition for the mixture

(D) introduction of a source of ignition may result in explosion of the mixture

Answer: (A)

12. Considering ‘I’ as ‘intake’ and ‘R’ as ‘return’, the ventilation symbol for the shaft-bottom air-lock in a coal mine is

Answer: (A)

13. From a coal seam of a mine 1000 tonnes of coal is produced per day. The seam has inflammable gas emission rate of 14000 m³ per day. Percentage of inflammable gas in general body of air is 0.14. The gassiness of the seam is

(A) Degree IV

(B) Degree III

(D) Degree I

Answer: (B)

14. The temperature profiles and the plume patterns that are most likely to result are given in the figures. The dotted line represents ‘adiabatic lapse rate’ and the bold line represents ‘environmental lapse rate’. The WRONG combination is

Answer: (C)

15. The inventory pattern shown does NOT represent the following.

(A) Inventory is replenished instantaneously

(B) Demand decreases with time

(D) Demand is uniform

Answer: (B)

16. The figure depicts a transportation problem along with the solution. The correct statement is

(A) unbalanced problem, optimal solution

(B) unbalanced problem, sub-optimal solution

(D) balanced problem, sub-optimal solution

Answer: (C)

17. The degree of the differential equation is ______________.

Answer: (1.0 to 1.0)

18. The slope of the line connecting the points (20, 6) and (40, 8) is ______________.

Answer: (0.1 to 0.1)

19. Two contours of RL 60 m and 70 m are separated by 34 m measured along dip of the seam. The dip of the seam in degree is ________________.

Answer: (16.5 to 17.5)

20. The RL of the initial station is 200 m. If ΣBS = 1.54m and ΣFS = 0.45 m, then the RL of the last station in m is ________________.

Answer: (201.09 to 201.09)

21. For the conveyor belt drive shown, the tension on the tight side (T1) is double that of the slack side. The coefficient of friction between belt and drum is 0.21. The minimum angle of lap (in degree) to avoid slippage of the belt is ________________.

Answer: (185.0 to 195.0)

22. In a bord and pillar development district, 6 headings driven along the strike direction are surrounded by panel barriers on the dip and rise sides. The maximum possible number of faces for the panel is ___________________.

Answer: (16.0 to 16.0)

23. A roadway in a mine, a single light source as shown, emits light uniformly in all directions. The floor level illumination at station A is 20 lux. The floor level illumination at a point B in lux is ______________.

Answer: (8.5 to 9.5)

24. A system of two identical components connected in series has reliability of 0.25. The reliability of each component is _______________.

Answer: (0.5 to0.5)

25. The operational status of an HEMM in a shift is shown in the diagram. The availability of the machine in % is _____________________.

Answer: (56.0 to 56.5)

Q. 26 – Q. 55 carry two marks each.

26. If c is a constant, the solution of the differential equation is

Answer: (D)

27. Match the following blasting elements with the corresponding initiators.

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

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

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

Answer: (B)

28. The following plot is developed for a rock type after a series of triaxial tests. The uniaxial compressive strength and tensile strength of the rock type, respectively, in MPa, are

(A) 30, 5

(B) 30, 6

(D) 24, 5

Answer: (A)

29. Match the following in the context of environmental management.

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

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

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

Answer: (D)

30. A panel in coal mine produces 400 tonne per day. The number of persons employed in each of the three shifts is 110, 130 and 120. As per CMR, the minimum quantity of air that needs to be circulated at the last ventilation connection of the panel in m³/min is

(A) 780

(B) 900

(D) 2400

Answer: (C)

31. A right conical iron ore stack on level ground of height 10 m has 60% Fe. The height of the conical stack is extended up to 20 m using iron ore of 50% Fe. The angle of repose of iron ore is 38°. The mean grade of the final stack in % Fe is ___________________.

Answer: (51.0 to 52.0)

32. The feasible region of a linear programming problem is shown in the figure. The maximum value of the objective function Z = 4X + 3Y is ____________________.

Answer: (74.0 to 74.0)

33. Cash flow of a project of duration 4 years is shown. The uniform income ‘R’, in Rs. crores, at the end of 2nd, 3rd and 4th years for an internal rate of return of 10% is ______________.

Answer: (4.4 to 4.5)

34. The grade values of alumina at three sample locations (A, B and C) in a bauxite deposit are as shown. Using the ‘inverse distance’ method, the computed grade in % alumina at location ‘Z’ is ___________________.

Answer: (36.0 to 37.5)

35. Economic feasibility of two methods is examined for meeting a targeted mine production. On a yearly basis, the following cost parameters (Rs in crores) are applicable for these methods.

The annual rate of production, ‘X’ in million tonnes for which both the methods will yield the same operating cost is ___________________.

Answer: (5.0 to 5.0)

36. A person standing 50 m away from an HEMM experiences 90 dB sound pressure level. If the person moves to a new location that is 70 m away from the HEMM, the sound pressure level experienced by the person, in dB, becomes _________________.

Answer: (86.75 to 87.25)

37. A portion of a ventilation system has two splits as shown. Split ‘A’ has a resistance of 0.2 Ns²/m⁸ and a regulator of size 2.0 m². The resistance of split ‘B’ in Ns²/m⁸ is ________

Answer: (0.24 to 0.28)

38. Air enters a bord and pillar panel at 10 ppm CO and 20.78% O₂. The air at the panel return has 80 ppm CO and 20.52% O₂. The ‘Graham’s ratio’ for the status of fire in the panel in % is __________________.

Answer: (2.65 to 2.75)

39. In a sublevel stope, 20 m high excavation is made with ring drilling in a 6 m wide orebody. In an effective shift time of 6 hrs, three rings are blasted resulting in 9 m extraction length. LHDs of 5.0 m³ bucket capacity and cycle time of 5 minutes are used for ore transportation. The number of LHDs required for this operation is _________________.

Answer: (3.0 to 3.0)

40. A coal seam lying at a depth of 200 m is developed by bord and pillar method. Pillars are 30 m centre to centre with a gallery width of 4 m. Unit weight of the overlying strata is 28 kN/m³. If the pillar strength is 9.32 MPa, the factor of safety of pillar is ____________.

Answer: (1.2 to 1.3)

41. Following information about a longwall retreating panel is given.

Panel length = 1800 m

Face length = 150 m

Depth of web = 0.6 m

Shearer travels at a speed of 1.5 m/min along the face.

Each cutting cycle requires a non-operational time of 2 h 20 min. The panel is fully extractable. The number of working days required to extract the panel is ______________.

Answer: (500.0 to 500.0)

42. In a direct rope haulage operating along a 1500 m long incline, 180 tonne of coal is hauled in 7 hours. The average rope speed is 7.5 km/h. The set changing time for the tubs is 2 minutes each at the top and bottom of the incline. If the tub capacity is 1.0 tonne, the number of tubs in the set is __________________.

Answer: (12.0 to 12.0)

43. An SDL of 1.0 tonne capacity operates with a cycle time of 6 minutes. The dimension of the face is 4 m x 3 m. Five blasts are conducted per shift with an average pull of 1.2 m. If the density of blasted coal is 0.8 tonne/m³, the time required by the SDL in the shift to lift all the prepared coal in hours is _________________.

Answer: (5.6 to 5.8)

44. A force diagram is shown below. Considering clockwise moments to be positive, the resultant moment about A in Nm is _________________.

Answer: (-400.0 to -400.0)

45. The experiment to determine permeability of a soil sample is illustrated below. The crosssectional area of the sample is 20.0 cm². The permeability of the soil sample in cm/s is ______________.

Answer: (0.02 to 0.02)

46. In underground face blasting, the pull is found to be 10% less than the drillhole length. The headings of 3.6 m width are supported by prop density of 1.44/m². The hole length is 1.5 m, and 6 rounds of blasting are done in the panel per shift. The number of props to be erected in a shift is ____________________.

Answer: (41.0 to 43.0)

47. T he immediate roof of a mine is supported by bolts of length 1.5 m, arranged in 1.2 m x 1.2 m grid pattern. If the unit weight of roof rock is 2.25 tonne/m³ and load carrying capacity of each bolt is 7.5 tonne, the factor of safety of the support system is _______________.

Answer: (1.4 to 1.6)

48. In a level terrain, a vertical orebody of 20 m uniform width is worked by surface mining method. The density of the ore is 2.5 tonne/m³. The ultimate pit has a depth of 60 m, width of 20 m at pit bottom, and a pit slope of 45°. The overall stripping ratio for this condition in m³/tonne is ____________________.

Answer: (1.2 to 1.2)

49. A 20 m long steel tape used for survey is found to be short by 10 cm. If the area measured with the steel tape is 5000 m², the actual area in m² is __________________.

Answer: (4945.0 to 4955.0)

50. The following figure shows the designed blast pattern of a bench. The explosive column is charged at 18 kg/m. If the unit weight of the blasted material is 2.5 tonne/m³, the powder factor for the blast in tonne/kg is _______________.

Answer: (2.00 to 2.15)

51. Two points on the equator have longitudes 55°E and 25°W. Considering radius of earth as 6400 km, the distance between the two points in km is ________________.

Answer: (8930.0 to 8940.0)

52. Sum of the series 5, 10, 15, ……….., 500 is __________________.

Answer: (25250.0 to 25250.0)

53. The sample standard deviation for the following set of observations is _______________. 40, 45, 50 and 55

Answer: (6.4 to 6.5)

54. For the given function f (x, y) = (3 + x) (4 + y), the value of and y = 1 is _________.

Answer: (10.0 to 10.0)

55. Given y = x² + x + 6, the value of is ________________.

Answer: (0.40 to 0.45)

GATE Exam 2018 Mechanical Engineering (ME-2) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _________.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

(A) 0

(B) 2

(D) 8

Answer: (C)

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Mechanical Engineering (Set 2)

Q. 1 – Q. 25 carry one mark each.

1. The Fourier cosine series for an even function f(x) is given by

The value of the coefficient a² for the function f(x) = cos²(x) in [0, π] is

(A) –0.5

(B) 0.0

(D) 1.0

Answer: (C)

2. The divergence of the vector field

(A) 0

(B) e^x cosy + e^x sin y

(D) 2e^x sin y

Answer: (C)

3. Consider a function u which depends on position x and time t. The partial differential equation

is known as the

(A) Wave equation

(B) Heat equation

(D) Elasticity equation

Answer: (B)

4. If y is the solution of the differential equation the value of y(–1) is

(A) −2

(B) −1

(D) 1

Answer: (C)

5. The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is

Answer: (B)

6. A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is

(A) 5

(B) 20

(D) 2000

Answer: (D)

7. In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?

(A) Transmissibility will increase.

(B) Transmissibility will decrease.

(D) Time period of free oscillations will decrease.

Answer: (C)

8. Pre-tensioning of a bolted joint is used to

(A) strain harden the bolt head

(B) decrease stiffness of the bolted joint

(D) prevent yielding of the thread root

Answer: (C)

9. The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 μm. If the peak wavelength of emitted radiation changes to 2.90 μm, then the temperature (in K) of the black body is

(A) 500

(B) 1000

(D) 8000

Answer: (B)

10. For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (Δs) from state 1 to 2?

Answer: (A)

11. Select the correct statement for 50% reaction stage in a steam turbine.

(A) The rotor blade is symmetric.

(B) The stator blade is symmetric.

(D) The absolute exit flow angle is equal to inlet angle of rotor blade.

Answer: (D)

12. Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by

Answer: (A or D)

13. During solidification of a pure molten metal, the grains in the casting near the mould wall are

(A) coarse and randomly oriented

(B) fine and randomly oriented

(D) coarse and ordered

Answer: (B)

14. Match the following products with the suitable manufacturing process

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

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

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

Answer: (C)

15. Feed rate in slab milling operation is equal to

(A) rotation per minute (rpm)

(B) product of rpm and number of teeth in the cutter

(D) product of rpm, feed per tooth and number of teeth in contact

Answer: (C)

16. Metal removal in electric discharge machining takes place through

(A) ion displacement

(B) melting and vaporization

(D) plastic shear

Answer: (B)

17. The preferred option for holding an odd-shaped workpiece in a centre lathe is

(A) live and dead centres

(B) three jaw chuck

(D) four jaw chuck

Answer: (D)

18. A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is

(A) 64

(B) 212

(D) 1200

Answer: (C)

19. If then det(A^–1) is ________(correct to two decimal places).

Answer: (0.25 to 0.25)

20. A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ________ (correct to two decimal places).

Answer: (35.24 to 35.44)

21. Fatigue life of a material for a fully reversed loading condition is estimated from

σ_a = 1100 N^–0.15

where σ_a is the stress amplitude in MPa and N is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of 1 × 10⁵ cycles under the same loading condition is ________ (correct to two decimal places).

Answer: (190.00 to 200.00)

22. The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is δ_L. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to δ_L)is ________ (correct to two decimal places).

Answer: (41.30 to 41.50)

23. An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in kJ/cycle) is ______ (correct to two decimal places).

Answer: (62.00 to 63.00)

24. The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).

Answer: (0.36 to 0.40)

25. A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in m) by the ball is __________ (correct to two decimal places).

Answer: (Marks to All)

Q. 26 – Q. 55 carry two marks each.

26. Let z be a complex variable. For a counter-clockwise integration around a unit circle C , centred at origin,

the value of A is

(A) 2/5

(B) 1/2

(D) 4/5

Answer: (A)

27. L et X₁ and X₂ be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X₁, X₂) is

(A) exponentially distributed with mean 1/6

(B) exponentially distributed with mean 2

(D) normally distributed with mean 1/6

Answer: (A)

28. For a position vector the norm of the vector can be defined as Given a function

Answer: (C)

29. In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180° m/s². If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2) of point R is

(A) 8∠233°

(B) 10∠225°

(D) 8∠217°

Answer: (D)

30. A rigid rod of length 1 m is resting at an angle θ = 45° as shown in the figure. The end P is dragged with a velocity of 5 U  m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is

(A) 5

(B) 6

(D) 10

Answer: (A)

31. A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment 𝑇 = 150 Nm is applied at a distance of 100 mm from end P. The torsional reactions (𝑇_𝑃, 𝑇_𝑄 ) in Nm at the ends P and Q respectively are

(A) (50, 100)

(B) (75, 75)

(D) (120, 30)

Answer: (C)

32. In a cam-follower, the follower rises by h as the cam rotates by δ (radians) at constant angular velocity ω (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period. Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is

(A) 4hω/δ

(B) hω

(D) 2hω

Answer: (C)

33. A bimetallic cylindrical bar of cross sectional area 1 m² is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10^–6 in Steel bar and compressive axial strain of magnitude 10^–6 in Aluminum bar, the magnitude of the required force P (in kN) along the indicated direction is

(A) 70

(B) 140

(D) 280

Answer: (D)

34. Air flows at the rate of 1.5 m³/s through a horizontal pipe with a gradually reducing crosssection as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2 kg/m³ and assume inviscid
incompressible flow. The change in pressure (p₁ – p₂) (in kPa) between sections 1 and 2 is

(A) –1.28

(B) 2.56

(D) 1.28

Answer: (A)

35. The problem of maximizing z = x₁ – x₂ subject to constraints x₁ + x₂ ≤ 10, x₁ ≥ 0, x₂ ≥ 0 and x₂ ≤ 5 has

(A) no solution

(B) one solution

(D) more than two solutions

Answer: (B)

36. Given the ordinary differential equation

with the value of y(1) is _________ (correct to two decimal places).

Answer: (1.45 to 1.48)

37. A thin-walled cylindrical can with rigid end caps has a mean radius R= 100 mm and a wall thickness of t = 5. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ___________ (correct to two decimal places).

Answer: (4.80 to 5.20)

38. A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between –10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the
material is 600 MPa. The bar cross-section is square with side a. If the factor of safety is 2, the value of a (in mm), according to the modified Goodman’s criterion, is ________ (correct to two decimal places).

Answer: (31.60 to 31.65)

39. A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s²) of the centre of the disc is ________ (correct to two decimal places).

Answer: (6.60 to 6.70)

40. A frictionless circular piston of area 10^–2 m² and mass 100 kg sinks into a cylindrical container of the same area filled with water of density 1000 kg/m³ as shown in the figure. The container has a hole of area 10^–3 m² at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is _____ (correct to three decimal places).

Answer: (1.400 to 1.500)

41. A 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is 350 K. The value of Stefan- Boltzmann constant, σ is 5.67 × 10^–8 W/m² K⁴. Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in W/m²) is ________ (correct to two decimalplaces).

Answer: (385.00 to 395.00)

42. Air is held inside a non-insulated cylinder using a piston (mass M=25 kg and area A=100 cm²) and stoppers (of negligible area), as shown in the figure. The initial pressure P_i and temperature T_i of air inside the cylinder are 200 kPa and 400°C, respectively. The ambient pressure P_∞ and temperature T_∞ are 100 kPa and 27°C, respectively. The temperature of the air inside the cylinder (°C) at which the piston will begin to move is _________ (correct to two decimal places).

Answer: (145.00 to 150.00)

43. A standard vapor compression refrigeration cycle operating with a condensing temperature of 35°C and an evaporating temperature of –10°C develops 15 kW of cooling. The p-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is 0.75, the magnitude of compressor power (in kW) is _________ (correct to two decimal places).

Answer: (9.50 to 10.50)

44. A mbient air is at a pressure of 100 kPa, dry bulb temperature of 30°C and 60% relative humidity. The saturation pressure of water at 30°C is 4.24 kPa. The specific humidity of air (in g/kg of dry air) is ________ (correct to two decimal places).

Answer: (16.00 to 16.50)

45. A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m³/s at 450 rpm. Take the water density and the acceleration due to gravity as 10³ kg/m³ and 10 m/s², respectively. Assume no losses both in model and prototype turbines. The power (in MW) of a full sized turbine while working under a head of 30 m is _______ (correct to two decimal places).

Answer: (28.85 to 29.25)

46. The true stress (in MPa) versus true strain relationship for a metal is given by

σ = 1020ε^0.4

The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is 100 mm². The cross-sectional area at the time of necking (in mm²) is ________ (correct to two decimal places)

Answer: (65.00 to 70.00)

47. A steel wire is drawn from an initial diameter (d_i) of 10 mm to a final diameter (d_f) of 7.5 mm. The half cone angle (α) of the die is 5° and the coefficient of friction (μ) between the die and the wire is 0.1. The average of the initial and final yield stress [σ_Y)avg] is 350 MPa. The equation for drawing stress σ_f, (in MPa) is given as:

The drawing stress (in MPa) required to carry out this operation is _________ (correct to two decimal places).

Answer: (315.00 to 317.00)

48. Following data correspond to an orthogonal turning of a 100 mm diameter rod on a lathe. Rake angle: +15° ; Uncut chip thickness: 0.5 mm; nominal chip thickness after the cut: 1.25 mm. The shear angle (in degrees) for this process is _______ (correct to two decimal places).

Answer: (22.00 to 24.00)

49. T aylor’s tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in 20 mm thick mild steel plates. In test 1, a drill lasted 300 holes at 150 rpm while in test 2, another drill lasted 200 holes at 300 rpm. The maximum number of holes that can be made by another drill from the above batch at 200 rpm is ______ (correct to two decimal places).

Answer: (252.00 to 254.00)

50. F or sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov’s law for the estimation of the total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal places)

Answer: (42.00 to 52.00)

51. The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is _______.

Answer: (7 to 7 or 11 to 11)

52. A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The material removal rate (in mm³/min) is expressed as

4 × 10⁴ IT^–1.23

where I = 300 A and the melting point of the material, T = 1600°C . The time (in minutes) for machining this hole is ________ (correct to two decimal places)

Answer: (7.00 to 7.30)

53. A welding operation is being performed with voltage = 30 V and current = 100 A. The cross-sectional area of the weld bead is 20 mm². The work-piece and filler are of titanium for which the specific energy of melting is 14 J/mm³. Assuming a thermal efficiency of the welding process 70%, the welding speed (in mm/s) is __________ (correct to two decimal places).

Answer: (7.49 to 7.51)

54. S team in the condenser of a thermal power plant is to be condensed at a temperature of 30°C with cooling water which enters the tubes of the condenser at 14°C and exits at 22°C. The total surface area of the tubes is 50 m², and the overall heat transfer coefficient is 2000 W/m² K. The heat transfer (in MW) to the condenser is ______ (correct to two decimal places).

Answer: (1.14 to 1.16)

55. A vehicle powered by a spark ignition engine follows air standard Otto cycle (γ=1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is _______ (correct to two decimal places).

Answer: (7.40 to 7.80)

GATE Exam 2018 Mechanical Engineering (ME-1) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

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

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Mechanical Engineering (Set 1)

Q. 1 – Q. 25 carry one mark each.

1. Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is

(A) 1/72

(B) 1/55

(D) 1/27

Answer: (B)

2. The rank of the matrix is

(A) 1

(B) 2

(D) 4

Answer: (B)

3. According to the Mean Value Theorem, for a continuous function f(x) in the interval [a, b], there exists a value ξ in this interval such that

(A) f(ξ) (b – a)

(B) f(b)(ξ – a)

(D) 0

Answer: (A)

4. F(z) is a function of the complex variable z = x + iy given by

F(z) = iz + k Re(z) + i Im(z)

For what value of k will F(z) satisfy the Cauchy-Riemann equations?

(A) 0

(B) 1

(D) y

Answer: (B)

5. A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

The tensions in the strings are

(A) T₁ = 100 N and T₂ = 0 N

(B) T₁ = 0 N and T₂ = 100 N

(D) T₁ = 25 N and T₂ = 75 N

Answer: (B)

6. If σ₁ and σ₃ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

Answer: (B)

7. The equation of motion for a spring-mass system excited by a harmonic force is

where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to

Answer: (D)

8. For an Oldham coupling used between two shafts, which among the following statements are correct?

I. Torsional load is transferred along shaft axis.

II. A velocity ratio of 1:2 between shafts is obtained without using gears.

III. Bending load is transferred transverse to shaft axis.

IV. Rotation is transferred along shaft axis.

(A) I and III

(B) I and IV

(D) II and IV

Answer: (B)

9. For a two-dimensional incompressible flow field given by where A > 0, which one of the following statements is FALSE?

(A) It satisfies continuity equation.

(B) It is unidirectional when x → 0 and y → ∞

(D) It is irrotational.

Answer: (C)

10. Which one of the following statements is correct for a superheated vapour?

(A) Its pressure is less than the saturation pressure at a given temperature.

(B) Its temperature is less than the saturation temperature at a given pressure.

(D) Its enthalpy is less than the enthalpy of the saturated vapour at a given pressure.

Answer: (A)

11. In a linearly hardening plastic material, the true stress beyond initial yielding

(A) increases linearly with the true strain

(B) decreases linearly with the true strain

(D) remains constant

Answer: (A)

12. The type of weld represented by the shaded region in the figure is

(A) groove

(B) spot

(D) plug

Answer: (C)

13. Using the Taylor’s tool life equation with exponent n = 0.5 if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

(A) 4

(B) 2

(D) 0.5

Answer: (A)

14. A grinding ratio of 200 implies that the

(A) grinding wheel wears 200 times the volume of the material removed

(B) grinding wheel wears 0.005 times the volume of the material removed

(D) ratio of volume of abrasive particle to that of grinding wheel is 200

Answer: (B)

15. Interpolator in a CNC machine

(A) controls spindle speed

(B) coordinates axes movements

(D) commands canned cycle

Answer: (B)

16. The time series forecasting method that gives equal weightage to each of the m most recent observations is

(A) Moving average method

(B) Exponential smoothing with linear trend

(D) Kalman Filter

Answer: (A)

17. The number of atoms per unit cell and the number of slip systems, respectively, for a facecentered cubic (FCC) crystal are

(A) 3, 3

(B) 3, 12

(D) 4, 48

Answer: (C)

18. A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is

(A) 33.3

(B) 3.33

(D) 0.0033

Answer: (C)

19. A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is ____ (correct to two decimal places).

Answer: (1.00 to 1.20)

20. A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is __________.

Answer: (1 to 1)

21. If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).

Answer: (8.00 to 8.50)

22. A flat plate of width L = 1 m is pushed down with a velocity U = 0.01 m/s towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, u_avg of the fluid (in m/s) draining out at the instant shown in the figure is _____________(correct to three decimal places).

Answer: (0.045 to 0.055)

23. An ideal gas undergoes a process from state 1 (T₁ = 300 K p₁ = 100 kPa) to state 2 (T2 = 600 K, p₂ = 500 kPa). The specific heats of the ideal gas are : C_p = 1 kJ/kg-K and C_v = 0.7 kJ/kg-K. The change in specific entropy of the ideal gas from state 1 to state 2 (in kJ/kg-K) is ___________(correct to two decimal places).

Answer: (0.20 to 0.22)

24. For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is _______ (correct to two decimal places).

Answer: (0.45 to 0.52)

25. T he height (in mm) for a 125 mm sine bar to measure a taper of 27 ̊ 32′ on a flat work piece is _______ (correct to three decimal places).

Answer: (57.000 to 58.000)

Q. 26 – Q. 55 carry two marks each.

26. Let X₁, X₂ be two independent normal random variables with means μ1, μ2 and standard deviations μ₁, μ₂, respectively. Consider Y = X₁ – X₂; μ1 = μ2 =1, σ₁ = 1, σ₂ = 2. Then,

(A) Y is normally distributed with mean 0 and variance 1

(B) Y is normally distributed with mean 0 and variance 5

(D) Y has mean 0 and variance 1, but is NOT normally distributed

Answer: (B)

27. The value of the integral

over the closed surface S bounding a volume V, where is the position vector and is the normal to the surface S, is

(A) V

(B) 2V

(D) 4V

Answer: (C)

28. A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s² and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

(A) 1

(B) 2

(D) ∞

Answer: (C)

29. The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress σ_y (in kPa) is

(A) 9.45

(B) 18.88

(D) 75.50

Answer: (C)

30. An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is

(A) 240

(B) –240

(D) –375

Answer: (C)

31. A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30° as shown in the figure.

The glue used at the interface fails if

Criterion 1: the maximum normal stress exceeds 2.5 MPa.

Criterion 2: the maximum shear stress exceeds 1.5 MPa.

Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface

(A) fails only because of criterion 1

(B) fails only because of criterion 2

(D) does not fail

Answer: (C)

32. A self-aligning ball bearing has a basic dynamic load rating (C₁₀, for 10⁶ revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in 10⁶ revolutions) is

(A) below 0.5

(B) 0.5 to 0.8

(D) above 1.0

Answer: (A)

33. A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m) where the jet strikes the floor is

(A) 0.5

(B) 1.0

(D) 4.0

Answer: (B)

34. In a Lagrangian system, the position of a fluid particle in a flow is described as x = x₀e^–kt and y = y₀e^kt where t is the time while 𝑥_𝑜, 𝑦_𝑜, and k are constants. The flow is

(A) unsteady and one-dimensional

(B) steady and two-dimensional

(D) unsteady and two-dimensional

Answer: (B)

35. The maximum reduction in cross-sectional area per pass ( R ) of a cold wire drawing process is

R = 1 – e^{–(n + 1)}

where n represents the strain hardening coefficient. For the case of a perfectly plastic material, R is

(A) 0.865

(B) 0.826

(D) 0.632

Answer: (D)

36. The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure is _______ (correct to two decimal places).

Answer: (52.00 to 54.00)

37. An explicit forward Euler method is used to numerically integrate the differential equation

using a time step of 0.1. With the initial condition y(0) = 1 , the value of (1) y computed by this method is ___________ (correct to two decimal places).

Answer: (2.55 to 2.65)

38. F(s) is the Laplace transform of the function

f(t) = 2t²e^–t

F(1) is ________ (correct to two decimal places).

Answer: (0.48 to 0.52)

39. A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).

Answer: (29.8 to 30.1)

40. A machine of mass 𝑚 = 200 kg is supported on two mounts, each of stiffness 𝑘 = 10 kN/m. The machine is subjected to an external force (in N) 𝐹(𝑡) = 50 cos 5𝑡. Assuming only vertical translatory motion, the magnitude of the dynamic force (in N)
transmitted from each mount to the ground is ______ (correct to two decimal places).

Answer: (33.00 to 33.50)

41. A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45° and a force of 40 N is acting towards the left on the slider. The length of the crank is 30 mm and the connecting rod is 70 mm. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is
_________ (correct to two decimal places).

Answer: (1.00 to 1.20)

42. A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles.

The total flow rate Q through the sprinkler is 1 litre/sec and the cross-sectional area of each exit nozzle is 1 cm². Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).

Answer: (9.50 to 10.50)

43. A solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall as shown in the figure below. A thin oil film of thickness h = 0.15 mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oil film is 0.04 m^2. The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7×10^-3 Pa-s and acceleration due to gravity as 10 m/s². Neglect weight of the oil. The terminal velocity V (in m/s) of the block is _________ (correct to one decimal place).

Answer: (10.6 to 10.8)

44. A tank of volume 0.05 m³ contains a mixture of saturated water and saturated steam at 200°C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg K) of the mixture is ___________ (correct to two decimal places).

Answer: (2.45 to 2.55)

45. Steam flows through a nozzle at a mass flow rate of with a heat loss of 5 kW. The enthalpies at inlet and exit are 2500kJ/kg and 2350 kJ/kg, respectively. Assuming negligible velocity at inlet (C₁ ≈ 0), the velocity (C₂ ) of steam (in m/s) at the nozzle exit is __________ (correct to two decimal places).

Answer: (445.00 to 450.00)

46. An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air: c_p = 1.005 kJ/kg K, c_v = 0.718 kJ/kg K, R = 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

Answer: (1402.0 to 1406.0)

47. A plane slab of thickness L and thermal conductivity k is heated with a fluid on one side (P), and the other side (Q) is maintained at a constant temperature, T_Q of 25°C, as shown in the figure. The fluid is at 45°C and the surface heat transfer coefficient, h, is 10 W/m²k . The steady state temperature, T_P, (in °C) of the side which is exposed to the fluid is _______
(correct to two decimal places).

Answer: (33.50 to 34.30)

48. The true stress (σ) – true strain (ε) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of 0.5. Then from point A, there is unloading up to point B, i.e., to stress of 100 MPa. Given that the Young’s modulus E = 200 GPa, the natural strain at point B (ε_B)is _________ (correct to three decimal places).

Answer: (0.498 to 0.498)

49. An orthogonal cutting operation is being carried out in which uncut thickness is 0.010 mm, cutting speed is 130 m/min, rake angle is 15° and width of cut is 6 mm. It is observed that the chip thickness is 0.015 mm, the cutting force is 60 N and the thrust force is 25 N. The ratio of friction energy to total energy is __________ (correct to two decimal places).

Answer: (0.39 to 0.49)

50. A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is _________________ (correct to two decimal places).

Answer: (0.69 to 0.70)

51. The minimum value of 3𝑥 + 5𝑦

such that:

is _______.

Answer: (0 to 0)

52. Pocessing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is ___________ (correct to two decimal places).

Answer: (6.31 to 6.35)

53. The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force 𝐹 = 100 𝑁 is applied at the free end of the lever as shown. Given that the coefficient of friction between the shoe and the drum is 0.3, the braking torque (in Nm ) applied on the
drum is _______ (correct to two decimal places).

Answer: (8.00 to 9.00)

54. Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. Assuming g = 10 m/s², the normal force (in N) at Q is _______ (correct to two decimal places).

Answer: (419.00 to 421.00)

55. An electrochemical machining (ECM) is to be used to cut a through hole into a 12 mm thick aluminum plate. The hole has a rectangular cross-section, 10 mm × 30 mm. The ECM operation will be accomplished in 2 minutes, with efficiency of 90%. Assuming specific removal rate for aluminum as 3.44 × 10^-2 mm³/(A s), the current (in A) required is __________ (correct to two decimal places).

Answer: (968.80 to 969.20)

GATE Exam 2018 Mathematics (MA) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _________.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

(A) 0

(B) 2

(D) 8

Answer: (C)

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Mathematics

Q.1–Q.25 carry one mark each

1. The principal value of (–1)^(–2i/π) is

(A) e²

(B) e²ⁱ

(D) e^–2

Answer: (A)

2. Let f : ℂ → ℂbe an entire function with f(0) = 1, f(1) = 2 and f′ (0) = 0. If there exists M > 0 such that |f″ (z)| ≤ M for all z ∈ ℂ, then f(2) =

(A) 2

(B) 5

(D) 5 + 2i

Answer: (B)

3. In the Laurent series expansion of valid for |z – 1| > 1, the coefficient of is

(A) –2

(B) –1

(D) 1

Answer: (C)

4. Let X and Y be metric spaces, and let f : X → Y be a continuous map. For any subset S of X, which one of the following statements is true?

(A) If S is open, then f(S) is open

(B) If S is connected, then f(S) is connected

(D) If S is bounded, then f(S) is bounded

Answer: (B)

5. The general solution of the differential equation is given by (with an arbitrary positive constant k)

Answer: (C)

6. Let p_n(x) be the polynomial solution of the differential equation

with p_n(1) = 1 for n = 1, 2, 3, …….. If

then α_n is

(A) 2n

(B) 2n + 1

(D) 2n + 3

Answer: (D)

7. In the permutation group S_6,the number of elements of order 8 is

(A) 0

(B) 1

(D) 4

Answer: (A)

8. Let R be a commutative ring with 1 (unity) which is not a field. Let I ⊂ R be a proper ideal such that every element of R not in I is invertible in R: Then the number of maximal deals of R is

(A) 1

(B) 2

(D) infinite

Answer: (A)

9. Let f : ℝ → ℝ be a twice continuously differentiable function. The order of convergence of the secant method for finding root of the equation f(x) = 0 is

Answer: (A)

10. The Cauchy problem uu_x + yu_y = x with u(x, 1) = 2x, when solved using its characteristic equations with an independent variable t, is found to admit of a solution in the form

Then f(s, t) =

Answer: (A)

11. An urn contains four balls, each ball having equal probability of being white or black. Three black balls are added to the urn. The probability that five balls in the urn are black is

(A) 2=7

(B) 3=8

(D) 5=7

Answer: (B)

12. For a linear programming problem, which one of the following statements is FALSE?

(A) If a constraint is an equality, then the corresponding dual variable is unrestricted in sign

(B) Both primal and its dual can be infeasible

(D) Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ

Answer: (D)

13. Let , where a, b, c, f are real numbers and f ≠ 0: The geometric multiplicity of the largest eigenvalue of A equals _______.

14. Consider the subspaces

of ℝ³ . Then the dimension of W₁ +W₂ equals ______.

Answer: (1 to 1)

15. Let V be the real vector space of all polynomials of degree less than or equal to 2 with real coefficients. Let T : V → V be the linear transformation given by

T(p) = 2p + p′

where p′ is the derivative of p. Then the number of nonzero entries in the Jordan canonical form of a matrix of T equals __________.

Answer: (5 to 5)

16. Let I = [2, 3), J be the set of all rational numbers in the interval [4, 6], K be the Cantor (ternary) set, and let L = {7 + x : x ∈ K}. Then the Lebesgue measure of the set I ∪ J ∪ L equals _____.

Answer: (1 to 1)

17. Let u(x, y, z) = x² – 2y + 4y² for (x, y, z) ∈ ℝ³. Then the directional derivative of u in the direction at the point (5, 1, 0) is _______.

Answer: (6 to 6)

18. If the Laplace transform of y(t) is given by then y(0) + y′(0) = ________.

Answer: (1 to 1)

19. The number of regular singular points of the differential equation

in the interval is equal to ________.

Answer: (2 to 2)

20. Let F be a field with 7⁶ elements and let K be a subfield of F with 49 elements. Then the dimension of F as a vector space over K is _________.

Answer: (3 to 3)

21. Let C([0, 1]) be the real vector space of all continuous real valued functions on [0, 1], and let T be the linear operator on C([0, 1]) given by

Then the dimension of the range space of T equals____________.

Answer: (2 to 2)

22. Let a ∈ (–1, 1) be such that the quadrature rule

is exact for all polynomials of degree less than or equal to 3: Then 3a² = ______.

Answer: (1 to 1)

23. Let X and Y have joint probability density function given by

If f_Y denotes the marginal probability density function of Y , then f_Y (1=2) =_______.

Answer: (1 to 1)

24. Let the cumulative distribution function of the random variable X be given by

Then ℙ (X = 1/2) = _______.

Answer: (0.25 to 0.25)

25. Let {X_j} be a sequence of independent Bernoulli random variables with ℙ (X_j = 1) = 1/4 and let Then Y_n converges, in probability to ________.

Answer: (0.25 to 0.25)

Q.26-Q.55 carry two marks each

26. Let Γ be the circle given by z = 4e^iθ, where θ varies from 0 to 2π Then

(A) 2πi(e² – 1)

(B) πi(1 – e²)

(D) 2πi(1 – e²)

Answer: (C)

27. The image of the half plane Re(z) + Im(z) > 0 under the map is given by

(A) Re(w) > 0

(B) Im (w) > 0

(D) |w| < 1

Answer: (D)

28. Let D ⊂ ℝ² denote the closed disc with center at the origin and radius 2. Then

(A) π(1 – e^–4)

(B)

(D)

Answer: (A)

29. Consider the polynomial p(X) = X⁴ + 4 in the ring ℚ[X} of polynomials in the variable X with coefficients in the field ℚ of rational numbers. Then

(A) the set of zeros of p(X) in C forms a group under multiplication

(B) p(X) is reducible in the ring ℚ[X]

(D) the splitting field of p(X) has degree 4 over ℚ

Answer: (B)

30. Which one of the following statements is true?

(A) Every group of order 12 has a non-trivial proper normal subgroup

(B) Some group of order 12 does not have a non-trivial proper normal subgroup

(D) Every group of order 12 has an element of order 12

Answer: (A)

31. For an odd prime p, consider the ring Then the element 2 in is

(A) a unit

(B) a square

(D) irreducible

Answer: (D)

32. Consider the following two statements:

P : The matrix has infinitely many LU factorizations, where L is lower triangular with each diagonal entry 1 and U is upper triangular

Q : The matrix has no LU factorization, where L is lower triangular with each diagonal entry 1 and U is upper triangular.

Then which one of the following options is correct?

(A) P is TRUE and Q is FALSE

(B) Both P and Q are TRUE

(D) Both P and Q are FALSE

Answer: (B)

33. If the characteristic curves of the partial differential equation μ(x, y) =c₁ and v(x, y) = c₂, where c₁ and c₂ are constants, then

Answer: (A)

34. Let f : X → Y be a continuous map from a Hausdorff topological space X to a metric space Y . Consider the following two statements:

P: f is a closed map and the inverse image f^–1 (y) = {x ∈ X : f(x) = y} is compact for each y ∈ Y.

Q: For every compact subset K ⊂ Y, the inverse image f^–1 (K) is a compact subset of X:

Which one of the following is true?

(A) Q implies P but P does NOT imply Q

(B) P implies Q but Q does NOT imply P

(D) neither P implies Q nor Q implies P

Answer: (C)

35. Let X denote ℝ² endowed with the usual topology. Let Y denote R endowed with the co-finite topology. If Z is the product topological space Y × Y, then

(A) the topology of X is the same as the topology of Z

(B) the topology of X is strictly coarser (weaker) than that of Z

(D) the topology of X cannot be compared with that of Z

Answer: (C)

36. Consider ℝⁿ with the usual topology for n = 1, 2, 3. Each of the following options gives topological spaces X and Y with respective induced topologies. In which option is X homeomorphic to Y ?

Answer: (A)

37. Let {X_i} be a sequence of independent Poisson() variables and let Then the limiting distribution of is the normal distribution with zero mean and variance given by

(A) 1

(B) √λ

(D) λ²

Answer: (C)

38. Let X₁, X₂, . . . , X_n be independent and identically distributed random variables with probability density function given by

Also let Then the maximum likelihood estimator of θ is

Answer: (C)

39. Consider the Linear Programming Problem (LPP):

where α is a constant. If (3, 0) is the only optimal solution, then

(A) α < –2

(B) –2 < α < 1

(D) α < 2

Answer: (D)

40. Let M₂(ℝ) be the vector space of all 2 ×2 real matrices over the field R: Define the linear transformation S : M₂(ℝ) → M₂(ℝ) by S(X) = 2X + X^T , where X^T denotes the transpose of the matrix X: Then the trace of S equals ____.

Answer: (10 to 10)

41. Consider ℝ³ with the usual inner product. If d is the distance from (1, 1, 1) to the subspace
span(1, 1, 0), (0, 1, 1)g of ℝ³then |3d² = _________.

Answer: (1 to 1)

42. Consider the matrix A = I₉ – 2u^Tu with where I9 is the 9 × 9 identity matrix and uT is the transpose of u. If λ and μ are two distinct eigenvalues of A, then |λ – μ| = _____.

Answer: (2 to 2)

43. Let f(z) = z³e^z2 for z ∈ ℂ and let Γ be the circle z = e^iθ, where θ varies from 0 to 4π. Then

Answer: (6 to 6)

44. Let S be the surface of the solid

V = {(x, y, z) : 0 ≤ x ≤ 1, 0 ≤ 2, 0 ≤ z ≤ 3}.

Let denote the unit outward normal to S and let

Then the surface integral equals ________.

Answer: (18 to 18)

45. Let A be a 3 × 3 matrix with real entries. If three solutions of the linear system of differential equations are given by

then the sum of the diagonal entries of A is equal to ______.

Answer: (2 to 2)

46. If is a solution of the differential equation xy″ + αy′ + βx³y = 0

For some real numbers α and β, then αβ = _______.

Answer: (4 to 4)

47. Let L²([0, 1]) be the Hilbert space of all real valued square integrable functions on [0, 1] with the usual inner product. Let Φ be the linear functional on L²([0, 1]) defined by

where μ denotes the Lebesgue measure on [0, 1] Then || Φ|| = ______.

Answer: (3 to 3)

48. Let U be an orthonormal set in a Hilbert space H and let x ∈ H be such that ||x|| = 2. Consider the set

Then the maximum possible number of elements in E is _______.

Answer: (64 to 64)

49. If p(x) = 2 –(x + 1) + x(x + 1) – βx(x + 1) (x – α) interpolates the points (x, y) in the table

then α + β = ______.

Answer: (3 to 3)

50. If then (a₀ + a₁)π = ______.

Answer: (2 to 2)

51. For n = 1, 2, . . ., let _____.

Answer: (1 to 1)

52. Let X₁, X2, X3, X4 be independent exponential random variables with mean 1, 1/2, 1/3, 1/4, respectively. Then Y = min(X1, X2, X3, X4) has exponential distribution with mean equal to _______.

Answer: (0.1 to 0.1)

53. Let X be the number of heads in 4 tosses of a fair coin by Person 1 and let Y be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of ℙ(X = Y ) correct up to three decimal places is

Answer: (0.272 to 0.274)

54. Let X₁ ad X₂ be independent geometric random variables with the same probability mas function given by ℙ(X = k) = p(1 – p)^k–1, k = 1, 2, …. . Then the value of ℙ(X₁ = 2|X₁ + X₂ = 4) correct up to three decimal places is_______.

Answer: (0.332 to 0.334)

55. A certain commodity is produced by the manufacturing plants P₁ and P₂ whose capacities are 6 and 5 units, respectively. The commodity is shipped to markets M₁, M₂, M₃ and M₄ whose requirements are 1, 2, 3 and 5 units, respectively. The transportation cost per unit from plant P_i to market M_j is as follows

Then the optimal cost of transportation is ________.

Answer: (57 to 57)

GATE Exam 2018 Instrumentation Engineering (IN) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Instrumentation Engineering

Q. 1 – Q. 25 carry one mark each.

1. Let 𝑁 be a 3 by 3 matrix with real number entries. The matrix 𝑁 is such that 𝑁² = 0. The eigen values of N are

(A) 0, 0, 0

(B) 0,0,1

(D) 1,1,1

Answer: (A)

2. Let be two complex variable functions. Here is the complex conjugate of z. Choose the correct answer.

(A) Both 𝑓₁(𝑧) and 𝑓₂(𝑧) are analytic

(B) Only 𝑓₁(𝑧) is analytic

(D) Both 𝑓₁(𝑧) and 𝑓₂(𝑧) are not analytic

Answer: (B)

3. 𝑋 and 𝑌 are two independent random variables with variances 1 and 2, respectively. Let 𝑍 = 𝑋 − 𝑌. The variance of 𝑍 is

(A) 0

(B) 1

(D) 3

Answer: (D)

4. Consider two functions 𝑓(𝑥) = (𝑥 − 2)² and 𝑔(𝑥) = 2𝑥 − 1, where 𝑥 is real. The smallest value of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥) 𝑖𝑠 _______.

Answer: (1 to 1)

5. Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is

(A) 5/16

(B) 3/16

(D) 9/16

Answer: (B)

6. A series R-C circuit is excited by a 1∠0 V sinusoidal ac voltage source. The locus diagram of the phasor current 𝐼= (x + jy) A, when C is varied, while keeping R fixed, is

Answer: (A)

7. The Thevenin equivalent circuit representation across terminals p-q of the circuit shown in the figure is a

(A) 1 V source in series with 150 kΩ

(B) 1 V source in parallel with 100 kΩ

(D) 2 V source in parallel with 200 kΩ

Answer: (C)

8. A coil having an impedance of (10 + j100) Ω is connected in parallel to a variable capacitor as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor is changed so that parallel resonance occurs. The impedance across terminals p-q at resonance (in Ω) is ______.

Answer: (1009 to 1011)

9. Two periodic signals 𝑥(𝑡) and 𝑦(𝑡) have the same fundamental period of 3 seconds. Consider the signal 𝑧(𝑡) = 𝑥(−𝑡) + 𝑦(2𝑡 + 1). The fundamental period of 𝑧(𝑡) in seconds is

(A) 1

(B) 1.5

(D) 3

Answer: (D)

10. Consider signal Let 𝛿(𝑡) denote the unit impulse (Dirac-delta) function. The value of the integral

(A) 2

(B) 1

(D) 3

Answer: (A)

11. An ideal square wave with period of 20 ms shown in the figure, is passed through an ideal low pass filter with cut-off frequency 120 Hz. Which of the following is an accurate description of the output?

(A) Output is zero.

(B) Output consists of both 50 Hz and 100 Hz frequency components.

(D) Output is a square wave of fundamental frequency 50 Hz.

Answer: (C)

12. An input 𝑝(𝑡) = sin(𝑡) is applied to the system The corresponding steady state output is 𝑦(𝑡) = sin(𝑡 + 𝜑), where the phase 𝜑 (in degrees), when restricted to 0° ≤ 𝜑 ≤ 360°, is ______ .

Answer: (90 to 90 or -270 to -270)

13. The approximate phase response of is

Answer: (A)

14. Consider the transfer function The phase margin of 𝐺(𝑠) in degrees is ____.

Answer: (180 to 180 or -180 to -180)

15. I n the given circuit, assume that the opamp is ideal and the transistor has a β of 20. The current Io (in μA) flowing through the load Z_L is ____.

Answer: (0 to 0)

16. The diodes given in the circuit are ideal. At t = 60 ms, V_pq (in Volts) is ____.

Answer: (10 to 10)

17. For the 3-bit binary counter shown in the figure, the output increments at every positive transition in the clock (CLK). Assume ideal diodes and the starting state of the counter as 000. If output high is 1 V and output low is 0 V, the current I (in mA) flowing through the 50 Ω resistor during the 5th clock cycle is (up to one decimal place) ______.

18. The representation of the decimal number (27.625)10 in base-2 number system is

(A) 11011.110

(B) 11101.101

(D) 10111.110

Answer: (C)

19. The number of comparators required for implementing an 8-bit flash analog-to-digital converter is

(A) 8

(B) 128

(D) 256

Answer: (C)

20. A voltage of 6 cos(100πt) V is fed as y-input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively

(A) 1 V/div and 1 ms/div

(B) 1 V/div and 2 ms/div

(D) 2 V/div and 2 ms/div

Answer: (D)

21. A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100th division. The power consumed by the load (in Watts) is _____ .

Answer: (200 to 200)

22. As shown in the figure, temperature θ is measured using a K type thermocouple. It has a sensitivity of 40 μV/°C. The gain (G) of the ideal instrumentation amplifier is 25. If the output V_o is 96 mV, then the value of θ (in °C) is ____.

Answer: (95 to 97)

23. A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of 0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a static constant pressure of 100 kPa. Its steady-state output will be

(A) 0 V

(B) 0.1 V

(D) 10 V

Answer: (A)

24. An amplitude modulated signal is shown in the figure. The modulation index is (up to one decimal place) ______.

Answer: (0.3 to 0.3)

25. An optical pulse containing 6 × 10⁶ photons is incident on a photodiode and 4.5 × 10⁶ electron-hole pairs are created. The maximum possible quantum efficiency (in %) of the photodiode is _______ .

Answer: (75 to 75)

Q. 26 – Q. 55 carry two marks each.

26. Given the value of the line integral along the straight line c from (0,0,0) to (1,1,1) is

(A) 3/16

(B) 0

(D) –1

Answer: (D)

27. Two bags 𝐴 and 𝐵 have equal number of balls. Bag 𝐴 has 20% red balls and 80% green balls. Bag 𝐵 has 30% red balls, 60% green balls and 10% yellow balls. Contents of Bags 𝐴 and 𝐵 are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

(A) 20%

(B) 25%

(D) 40%

Answer: (B)

28. Consider the following system of linear equations:

3𝑥 + 2𝑘𝑦 = −2
𝑘𝑥 + 6𝑦 = 2

Here 𝑥 and 𝑦 are the unknowns and 𝑘 is a real constant. The value of 𝑘 for which there are infinite number of solutions is

(A) 3

(B) 1

(D) −6

Answer: (C)

29. Consider the following equations

where p and q are constants. 𝑉(𝑥, 𝑦) that satisfies the above equations is

Answer: (D)

30. In the given circuit, superposition is applied. When V₂ is set to 0 V, the current I₂ is -6 A. When V₁ is set to 0 V, the current I₁ is +6 A. Current I₃ (in A) when both sources are applied will be (up to two decimal places) _____.

Answer: (0.95 to 1.05)

31. In the figure, an RLC load is supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is ________.

Answer: (66 to 68)

32. In the given circuit, the mesh currents I₁, I₂ and I₃ are

(A) I₁ = 1 A, I₂ = 2 A and I₃ = 3 A

(B) I₁ = 2 A, I₂ = 3 A and I₃ = 4 A

(D) I₁ = 4 A, I₂ = 5 A and I₃ = 6 A

Answer: (A)

33. The Fourier transform of a signal 𝑥(𝑡), denoted by x(𝑗ω), is shown in the figure.

Let 𝑦(𝑡) = 𝑥(𝑡) + 𝑒^𝑗𝑡 𝑥(𝑡). The value of Fourier transform of 𝑦(𝑡) evaluated at the angular frequency ω= 0.5 rad/s is

(A) 0.5

(B) 1

(D) 2.5

Answer: (C)

34. Let 𝑦[𝑛] = 𝑥[𝑛] ∗ ℎ[𝑛], where ∗ denotes convolution and 𝑥[𝑛] and ℎ[𝑛] are two discrete time sequences. Given that the 𝑧-transform of 𝑦[𝑛] is 𝑌(𝑧) = 2 + 3𝑧⁻¹ + 𝑧⁻², the 𝑧-transform of 𝑝[𝑛] = 𝑥[𝑛] ∗ ℎ[𝑛 − 2] is

(A) 2 + 3𝑧 + 𝑧⁻²

(B) 3𝑧 + 𝑧⁻²

(D) 2𝑧⁻²+ 3𝑧⁻³ + 𝑧⁻⁴

Answer: (D)

35. For the sequence 𝑥[𝑛] = {1,−1,1,−1}, with 𝑛 = 0,1,2,3, the DFT is computed as for 𝑘 = 0,1,2,3. The value of 𝑘 for which 𝑋(𝑘) is not zero is

(A) 0

(B) 1

(D) 3

Answer: (C)

36. Consider the standard negative feedback configuration with and H(S) = 1/2. The number of clockwise encirclements of (−1,0) in the Nyquist plot of the Loop transfer-function 𝐺(𝑠)𝐻(𝑠) is _____

Answer: (0 to 0)

37. Consider the linear system with initial condition The solution 𝑥(𝑡) for this system is

(B).

Answer: (D)

38. Consider a standard negative feedback configuration with and For the closed loop system to have poles on the imaginary axis, the value of 𝛼 should be equal to (up to one decimal place)_____.

Answer: (8.9 to 9.1)

39. Unit step response of a linear time invariant (LTI) system is given by 𝑦(𝑡) = (1 − 𝑒^−2𝑡)𝑢(𝑡). Assuming zero initial condition, the transfer function of the system is

Answer: (D)

40. In the given relaxation oscillator, the opamps and the zener diodes are ideal. The frequency (in kHz) of the square wave output v_o is _____.

Answer: (Marks to All)

41. An opamp that is powered from a ±5V supply is used to build a non-inverting amplifier having a gain of 15. The slew rate of the opamp is 0.5 × 10⁶ V/s. For a sinusoidal input with amplitude of 0.3 V, the maximum frequency (in kHz) up to which it can be operated without any distortion is (up to one decimal place) ___.

Answer: (17.5 to 17.9)

42. The circuit given uses ideal opamps. The current I (in μA) drawn from the source vs is (up to two decimal places) ____.

Answer: (0.98 to 1.00)

43. The product of sum expression of a Boolean function 𝐹(𝐴, 𝐵, 𝐶) of three variables is given by

The canonical sum of product expression of 𝐹(𝐴, 𝐵, 𝐶) is given by

Answer: (B)

44. A 2-bit synchronous counter using two J-K flip flops is shown. The expressions for the inputs to the J-K flip flops are also shown in the figure. The output sequence of the counter starting from Q₁Q₂ = 00 is

(A) 00 → 11 → 10 → 01 → 00 ⋅ ⋅ ⋅
(B) 00 → 01 → 10 → 11 → 00 ⋅ ⋅ ⋅
(C) 00 → 01 → 11 → 10 → 00 ⋅ ⋅ ⋅
(D) 00 → 10 → 11 → 01 → 00 ⋅ ⋅ ⋅

Answer: (C)

45. A portion of an assembly language program written for an 8-bit microprocessor is given below along with explanations. The code is intended to introduce a software time delay. The processor is driven by a 5 MHz clock. The time delay (in μs) introduced by the program is _______.

MVI B, 64H ; Move immediate the given byte into register B. Takes 7 clock periods.

LOOP : DCR B ; Decrement register B. Affects Flags. Takes 4 clock periods.

JNZ LOOP ; Jump to address with Label LOOP if zero flag is not set. Takes 10 clock periods when jump is performed and 7 clock periods when jump is not performed.

Answer: (279 to 282)

46. The Boolean function 𝐹( 𝑋, 𝑌) realized by the given circuit is

Answer: (A)

47. The voltage and current drawn by a resistive load are measured with a 300 V voltmeter of accuracy ±1% of full scale and a 5 A ammeter of accuracy ±0.5% of full scale. The readings obtained are 200 V and 2.5 A. The limiting error (in %) in computing the load resistance is (up to two decimal places) ____.

Answer: (2.49 to 2.53)

48. A high Q coil having distributed (self) capacitance is tested with a Q-meter. First resonance at ω₁ = 10⁶ rad/s is obtained with a capacitance of 990 pF. The second resonance at ω₂ = 2 × 10⁶ rad/s is obtained with a 240 pF capacitance. The value of the inductance (in mH) of the coil is (up to one decimal place) ______.

Answer: (0.9 to 1.1)

49. The inductance of a coil is measured using the bridge shown in the figure. Balance (D = 0) is obtained with C₁ = 1 nF, R₁ = 2.2 MΩ, R₂ = 22.2 kΩ, R₄ = 10 kΩ. The value of the inductance Lx (in mH) is ______.

Answer: (221 to 223)

50. The average velocity v of flow of clear water in a 100 cm (inner) diameter tube is measured using the ultrasonic flow meter as shown in the figure. The angle θ is 45°. The measured transit times are t₁ = 0.9950 ms and t₂ = 1.0000 ms. The velocity v (in m/s) in the pipe is (up to one decimal place) ___.

Answer: (3.5 to 5.7)

51. A 1000 Ω strain gage (R_g) has a gage factor of 2.5. It is connected in the bridge as shown in figure. The strain gage is subjected with a positive strain of 400 μm/m. The output V_o (in mV) of the bridge is (up to two decimal places) _____.

Answer: (0.48 to 0.51)

52. Assuming ideal opamp, the RMS voltage (in mV) in the output V_o only due to the 230 V, 50 Hz interference is (up to one decimal place) _____.

Answer: (10.6 to 11.0)

53. The sampling rate for Compact Discs (CDs) is 44,000 samples/s. If the samples are quantized to 256 levels and binary coded, the corresponding bit rate (in bits per second) is _____.

Answer: (35200 to 35200)

54. A Michelson Interferometer using a laser source of wavelength 𝜆₀ = 500 nm, with both the mirrors (𝑀₁& 𝑀₂) fixed and positioned equidistant from the splitter/combiner is shown in the figure. When a dielectric plate of refractive index 𝑛 = 1.5, of thickness 𝒕 , is placed in front of the mirror 𝑀₂, a dark fringe is observed on the detector. When the dielectric plate is removed without changing the position of the mirrors 𝑀₁& 𝑀₂, a bright fringe is observed on the detector. The minimum thickness 𝒕 (in nm) of the dielectric is ________.

Answer: (249 to 251)

55. A multi-mode optical fiber with a large core diameter has a core refractive index 𝑛₁ = 1.5 and cladding refractive index 𝑛₂ = 1.4142. The maximum value of 𝜃_𝐴 (in degrees) for which the incident light from air will be guided in the optical fiber is ±______.

Answer: (29 to 31)

GATE Exam 2018 Geology and Geophysics (GG) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

PART A: COMPULSORY SECTION FOR ALL CANDIDATES

Q. 1 – Q. 25 carry one mark each.

1. Which one of the following periods has the longest time duration?

(A) Ordovician

(B) Cretaceous

(D) Silurian

Answer: (B)

2. A siliciclastic sedimentary rock consisting predominantly of the same type of gravel-sized clasts is called

(A) Polymict conglomerate.

(B) Arkose.

(D) Petromict conglomerate.

Answer: (C)

3. Brown coal that has high moisture content and commonly retains many of the original wood fragments is called

(A) Anthracite.

(B) Bituminous coal.

(D) Peat.

Answer: (C)

4. The speed of revolution of the Earth around the Sun is

(A) maximum at Perihelion.

(B) minimum at Perihelion.

(D) equal at Aphelion and Perihelion.

Answer: (A)

5. The geometrical factor for the following electrode configuration is

(A) 𝜋𝑎

(B) 2𝜋𝑎

(D) 4𝜋𝑎

Answer: (D)

6. Which one of the following geophysical methods uses the physical property ‘Dielectric Constant’?

(A) Gravity

(B) Ground Penetrating Radar

(D) Self-Potential

Answer: (B)

7. Pascal second is a unit of

(A) seepage force.

(B) dynamic viscosity.

(D) permeability.

Answer: (B)

8. Which one of the following statements is CORRECT?

(A) Strength of a rock decreases with increase in confining pressure.

(B) Strength of a rock increases with increase in temperature.

(D) Strength of a rock increases with increase in pore water pressure.

Answer: (C)

9. The geomorphic feature ‘horns’ are formed by

(A) wind erosion.

(B) river erosion.

(D) glacial erosion.

Answer: (D)

10. A melanocratic porphyritic rock containing phenocrysts of biotite, with feldspar restricted to the groundmass, is called

(A) trachyte.

(B) dacite.

(D) lamprophyre.

Answer: (D)

11. The supercontinent that existed in the late Mesoproterozoic to early Neoproterozoic time was

(A) Kenorland.

(B) Columbia.

(D) Pangaea.

Answer: (C)

12. The figure below shows the triple junction between three plates A, B and C. The boundary between the plates A and B is a ridge with a half-spreading rate of 4 cm/year. The A-C and B-C boundaries are collinear and orthogonal to the A-B ridge. The A-C boundary is a dextral transform fault with a relative velocity of 6 cm/year. The boundary between plates B and C is a

(A) dextral transform fault with a relative velocity of 10 cm/year.

(B) dextral transform fault with a relative velocity of 2 cm/year.

(D) sinistral transform fault with a relative velocity of 6 cm/year.

Answer: (C)

13. A rock follows Mohr-Coulomb failure criterion. Which one of the Mohr-Coulomb failure envelopes shown below allows failure of the rock under stress state Y, but not under stress state X?

(A) PP’

(B) QQ’

(D) SS’

Answer: (A)

14. The maximum and the minimum principal stresses are denoted by σ1 and σ3, respectively. The differential stress can have an absolute value greater than σ1 when

(A) σ₁ and σ₃ are both compressive.

(B) σ₁ is compressive and σ₃ is tensile.

(D) σ₁ and σ₃ are both tensile.

Answer: (B)

15. The geoid can be best defined as

(A) an oblate spheroid that best approximates the shape of the earth.

(B) a surface over which the value of gravity is constant.

(D) an equipotential surface of gravity of the earth.

Answer: (D)

16. For a layered isotropic medium with a flat horizontal free surface, match the wave types listed in Group-I with their corresponding polarizations listed in Group II.

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

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

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

Answer: (B)

17. A ‘gentle’ fold with an interlimb angle equal to 160° appears tight (apparent interlimb angle equal to 20) in horizontal section. According to the plunge of the fold axis, it can also be classified as

(A) horizontal fold.

(B) gently plunging fold.

(D) vertical fold.

Answer: (B)

18. The unit of shear modulus (rigidity modulus) is

(A) kg m^-1s^-2

(B) m² s^-2

(D) m^-1

Answer: (A)

19. With increasing activity of silica, the CORRECT order of appearance of minerals in a weathering environment with constant ratio of activities of K⁺ and H⁺ is

(A) gibbsite → kaolinite → pyrophyllite

(B) gibbsite → pyrophyllite → kaolinite

(D) pyrophyllite → gibbsite → kaolinite

Answer: (A)

20. Match the items listed in Group-I with those listed in Group-II.

Group-I Group-II
P. Mica 1. Beldih
Q. Uranium 2. Koderma
R. Phosphate 3. Agucha
S. Zinc 4. Gogi

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

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

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

Answer: (B)

21. Which one of the following corrections is always added during reduction of the observed gravity data?

(A) Latitude

(B) Free-air

(D) Terrain

Answer: (D)

22. The magnitudes of the total geomagnetic field at the equator and pole are denoted by B_E and B_P, respectively. Which one of the following is TRUE?

(A) B_P ≈ 4 B_E

(B) B_P ≈ 2 B_E

(D) B_P ≈ 1/2 B_E

Answer: (B)

23. Assume a flat earth with crustal thickness of 35 km and average crustal and upper mantle P-wave velocities of 6.4 km.s^–1 and 8.1 km.s^–1, respectively. The minimum distance from the epicenter of a near surface earthquake at which Pn-waves are observed is _______ km.

Answer: (85 to 95)

24. Given that the velocity of P-waves in a sandstone matrix is 5600 m/s and that in oil is 1200 m/s, the velocity of P-wave propagation in oil saturated sandstone with 30% porosity is ___________ m/s. (Use Wyllie time average equation.)

Answer: (2660 to 2670)

25. If the total porosity of a soil is 20%, its void ratio (%) is _________.

Answer: (25 to 25)

PART B (SECTION 1): FOR GEOLOGY CANDIDATES ONLY

Q. 26 – Q. 55 carry two marks each.

26. Which one of the following Himalayan lithounits predates India-Eurasia collision?

(A) Kasauli sandstone

(B) Rangit Pebble Slate

(D) Lower Karewa sandstone

Answer: (B)

27. Which one of the following ore minerals shows internal reflection?

(A) Orpiment

(B) Magnetite

(D) Molybdenite

Answer: (A)

28. Which one is CORRECT for the following equilibrium reaction between quartz and magnetite:

(A) 1000 ln α = Δ_qtz-mg where α = K^1/n (K is the equilibrium constant at the specified temperature and n is a constant quantity)

(B) 1000 ln α = Δ_qtz-mgwhere α = Kⁿ (K is the equilibrium constant at the specified temperature and n is the number of exchangeable atomic sites)

(C) (ln α/1000) = Δ_qtz-mgwhere α = K^1/n (K is the equilibrium constant at the specified temperature and n is a constant quantity)

(D) 1000 ln α = Δ_qtz-mg where α = K^1/n (K is the equilibrium constant at the specified temperature and n is the number of exchangeable atomic sites)

Answer: (D)

29. Match the modes of life (listed in Group I) with the corresponding bivalve genera (listed in Group II).

Group I Group II
P. Burrowing 1. Mytilus
Q. Recumbent unattached 2. Pecten
R. Byssally attached 3. Mya
S. Swimming 4. Gryphaea

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

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

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

Answer: (B)

30. Based on the hypothetical litholog given below that shows a continuous succession of sedimentary rocks, which one of the following statements is CORRECT?

(A) The rocks range from Cambrian to Cretaceous and show change in depositional environment from marine to continental.

(B) The rocks range from Cambrian to Triassic and show change in depositional environment from marine to continental.

(D) The rocks are Palaeozoic in age and show change in depositional environment from marine to continental.

Answer: (A)

31. Which one of the following cladograms shows the CORRECT interrelationships among the major groups of vertebrates?

(A) Cladogram I

(B) Cladogram II

(D) Cladogram IV

Answer: (A)

32. Which one of the following stratigraphic successions is in the CORRECT chronological order (from older to younger)?

(A) Rajmahal, Dubrajpur, Barakar

(B) Fenestella Shale, Muth Quartzite, Syringothyris Limestone

(D) Singhbhum Granite, Kolhan Group, Older Metamorphic Gneiss

Answer: (C)

33. Match the items listed in Group I with their appropriate description listed in Group II.

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

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

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

Answer: (B)

34. Which one of the following is an image rectification technique?

(A) Histogram equalization

(B) Density slicing

(D) Rubbersheeting

Answer: (D)

35. Match the items listed in Group I with those in Group II.

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

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

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

Answer: (D)

36. Match the items listed in Group I with those listed in Group II.

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

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

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

Answer: (A)

37. In the hypothetical isobaric ternary liquidus projection diagram given below, solid phases A, B, C, D and E exist in equilibrium with liquid. The reaction taking place at the isobaric invariant point W is

(A) Liquid (at W) = B + D + E

(B) Liquid (at W) = A + B + D

(D) Liquid (at W) + B + D = E

Answer: (D)

38. Match the optical properties listed in Group I with the corresponding mineral in Group II.

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

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

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

Answer: (A)

39. The reaction

muscovite + quartz = K-feldspar + sillimanite + water

(A) takes place within the greenschist facies.

(B) takes place within the amphibolite facies.

(D) takes place within the granulite facies.

Answer: (B)

40. Match the items listed in Group I with those in Group II.

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

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

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

Answer: (C)

41. The figure below is a schematic section showing the initial stages of development of a thrust fault (FF’) having a typical ramp and flat geometry, with the thrust sheet being transported from east to west. With respect to the synform and antiform created in Stage 2, which one of the options below is CORRECT for the next increment of movement on the fault plane?

(A) The synform and the antiform will both move westward.

(B) The synform will remain in position, while the antiform will grow in amplitude.

(D) The geometry will remain unchanged.

Answer: (B)

42. Which one of the following is the CORRECT chronological sequence for Iron formations?

(A) Algoma type > Superior type > Rapitan type > Minette type

(B) Superior type > Algoma type > Rapitan type > Minette type

(D) Algoma type > Minette type > Superior type > Rapitan type

Answer: (A)

43. Assertion (a): High-temperature, low-pressure metamorphism occurs on the over-riding plate near convergent plate margins.

Reason (r): Partial melting in the mantle wedge generates magmas that rise to form the arc.

(A) (a) is true but (r) is false.

(B) (a) is false but (r) is true.

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

Answer: (C)

44. Two coeval primary aqueous biphase fluid inclusions, X (liquid-rich) and Y (vapour-rich), occur in the same grain of the host mineral. Which one of the following situations most likely indicates boiling of the fluid?

(A) X homogenizes to liquid and Y homogenizes to vapour at different temperatures.

(B) Both homogenize to liquid at the same temperature.

(D) X homogenizes to liquid and Y homogenizes to vapour at the same temperature.

Answer: (D)

45. Du ring bench blasting in a quarry, 50 kg of an explosive with a yield of 5 MegaJoule/kg isrequired to break 100 m³ of marble. In this case, the energy expended in breaking a unit volume of marble in MegaNewton/m² would be _________________.

Answer: (2.5 to 2.5)

46. The stretching lineation on the axial plane (S₂) of a reclined fold on the S1 foliation makes an angle of 30° with the S₁/S₂ intersection lineation. The rake of the stretching lineation on the axial plane in degrees is ______________.

Answer: (60 to 60)

47. A basaltic magma has an initial nickel concentration of 300 ppm. Olivine crystallizes from this magma by equilibrium crystallization (Case I) or fractional crystallization (Case II). Then, the absolute value of the difference between the nickel concentrations of the liquids remaining after 25% crystallization in these two cases is _______________. (Use K_D,Ni olivine/melt = 10).

Answer: (69 to 71)

48. The difference in the number of faces in forms {hkl} and {111} in the holosymmetric class of the isometric system is _______________.

Answer: (40 to 40)

49. An inclined cylindrical confined aquifer has coefficient of permeability of 40 m/day. The horizontal distance between two vertical wells penetrating the aquifer is 800 m. The water surface elevations in the wells are 50 m and 45 m above a common horizontal datum. The absolute value of Darcy flux through the aquifer is ______________ m/day.

Answer: (0.25 to 0.25)

50. The mass and volume of a natural soil sample are 2.1 kg and 1×10^-3 m³, respectively. When fully dried, the mass of the soil sample becomes 2 kg without any change in volume. Assuming the specific gravity of soil particles to be 2.5, and water density of 1000 kg/m³, the degree of saturation of the natural soil sample is _______________%.

Answer: (50 to 50)

51. For a granitic rock mass, joint set number (Jn) = 9, joint water reduction factor (Jw) = 1, joint alteration number (Ja) = 1, stress reduction factor (SRF) = 1, rock quality designation (%) = 84 and joint roughness number (Jr) = 3. The Q-value as per Barton’s Q-system of rock mass classification (year 1974) is _______________.

Answer: (28 to 28)

52. A sun synchronous satellite is at an altitude of 300 km and the spectrometer makes an angular coverage angle of 12. The Swath (GFOV) of the satellite is ______________ km.

Answer: (62 to 64)

53. The stability field boundary between two minerals A and B is linear with a positive slope in P-T space. The molar entropy of A and B are 85.5 and 92.5 Joules K^-1, respectively and their respective molar volumes are 35.5 and 38.2 cc. The slope of the phase boundary in P-T space is _____________ bar K^-1.

Answer: (24 to 26)

54. Five moles of gas A (volume V₁) and 3 moles of gas B (volume V₂) were kept in separate containers. These two gases are completely transferred to a new container of volume V. Assuming isothermal condition, and that the work done is only mechanical, the entropy change of the system is ____________ Joules K^-1. (R = 8.3 J K^-1 mole^-1)

Answer: (42 to 45)

55. The value of Eh corresponding to the upper limit of natural surface aqueous environment at pH of 8.0 is _____________ V.

Answer: (0.7 to 0.8)

PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY

Q. 56 – Q. 85 carry two marks each.

56. The maximum number of linearly independent rows of an m × n matrix G where m > n is

(A) m.

(B) n.

(D) 0.

Answer: (B)

57. The impulse response of the Kirchhoff pre-stack time migration operator for non-zero offsets in a homogeneous and isotropic medium is _______.

(A) a circle.

(B) a parabola.

(D) an ellipse.

Answer: (D)

58. A solution to the eikonal equation |∇τ| = 1/υ₀ for a homogeneous and isotropic medium in cartesian coordinates is

Answer: (A)

59. The formula for the ‘forward’ Fourier transform is and that for the ‘inverse’ Fourier transform is Then, the forward Fourier transform of the function f(ω) = e^–2ω is

(A) 2𝛿(𝑡).

(B) 𝛿(2𝑡).

(D) 𝛿(𝑡 − 2).

Answer: (C or D)

60. Which one of the following rock types has the highest bulk magnetic susceptibility value?

(A) Gabbro

(B) Marble

(D) Limestone

Answer: (A)

61. Figure 1 is a schematic diagram of four seismic events in t-x (time-offset) domain and Figure 2 is the result of transformation from t-x domain to f-kx (frequency-horizontal wavenumber) domain. Match the events in t-x domain in Figure 1 with their counterparts in f-kx domain in Figure 2.

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

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

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

Answer: (C)

62. There is a change in the values of the bulk modulus and density across the Gutenberg discontinuity (from mantle to outer core). Which one of the following statements is CORRECT?

(A) Both bulk modulus and density increase.

(B) Both bulk modulus and density decrease.

(D) Bulk modulus increases and density decreases.

Answer: (A)

63. Multi-electrode resistivity survey is carried out by placing 10 equispaced electrodes (denoted by arrows in the figure below) on the surface of the earth. The points of observations in the distance-apparent depth plane are marked as solid dots in the figure shown below. Considering the mid-point of the 4-electrode array as the point of observation in the lateral direction, identify the CORRECT electrode configuration used for the survey.

(A) Multi-electrode Wenner array.

(B) Multi-electrode Axial Dipole-dipole array.

(D) Multi-electrode Axial Pole-dipole array.

Answer: (B)

64. Match the Electromagnetic methods in Group I with the corresponding quantity measured by them given in Group II.

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

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

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

Answer: (C)

65. Dip angle electromagnetic response measured along a profile over multiple conductors is shown in the figure below. Which of the crossover points P, Q and R represent the CORRECT locations of conductors beneath them?

(A) P, Q and R

(B) Q and R

(D) P and Q

Answer: (C)

66. The effect of small scale near surface inhomogeneities can be removed from magnetic data by

(A) upward continuation.

(B) downward continuation.

(D) reduction to pole.

Answer: (A)

67. The frequencies of the primary magnetic field generated by worldwide thunderstorm activity vary in the range

(A) 10^-6 Hz -10^-3 Hz

(B) 10^-3 Hz ^-1 Hz

(D) 10³ Hz -10⁶ Hz

Answer: (C)

68. Assertion (a): The Static Self-Potential for a thick, clean freshwater bearing sandstone formation is positive.

Reason(r): Resistivity of the formation water is less than the resistivity of salt water mudfiltrate.

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

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

(D) (a) is true but (r) is false.

Answer: (D)

69. Which one of the following well log responses characterizes an overpressured zone in the subsurface?

(A) High velocity and high resistivity.

(B) Low velocity and low density.

(D) Low velocity and high density.

Answer: (B)

70. The angle of inclination of the remanent magnetization measured on a basalt flow at a location P (28°N 85°E) is 40°. The palaeomagnetic latitude of the basalt flow is _______°N.

Answer: (22.5 to 23.0)

71. Using the Gutenberg-Richter recurrence relationship, the mean annual rate of exceedance of earthquake occurrence in a seismic belt is 0.3 per year for an earthquake of magnitude 6.0. The return period for an earthquake of magnitude 6.0 in this belt is ______ years.

Answer: (3.0 to 3.5)

72. In the figure below, Z denotes the depth to the center of a buried sphere from the surface and X_1/2 denotes the half-width of the profile at half the maximum value of gravity. Then, the ratio Z/X_1/2 is ________.

Answer: (1.2 to 1.4)

73. Two survey vessels with shipborne gravimeters are cruising towards each other at a speed of 6 knots each along an east-west course. The difference in gravity readings of the two gravimeters is 63.5 mGal at the point at which the survey vessels cross each other. The latitude along which the survey vessels are cruising is ______°N.

Answer: (44.5 to 46.0)

74. A gravity reading is taken in a stationary helicopter hovering 1 km above mean-sea level at a particular location. The difference in the value of g measured in the helicopter and at mean sea level vertically beneath the helicopter is ____________ mGals.

Answer: (300 to 320 or -320 to -300)

75. The P-wave velocity and the Poisson’s ratio for a homogeneous and isotropic sedimentary rock are 2500 m/s and 0.3, respectively. The S-wave velocity for the rock is ________m/s.

Answer: (1330 to 1340)

76. A plane electromagnetic (EM) wave travelling vertically downwards with a frequency of 1000 Hz in a homogeneous medium has a skin depth of 100 m. The ratio of the amplitude of the EM wave at a depth of 75 m with respect to the amplitude at the Earth’s surface is ___________.

Answer: (0.46 to 0.49)

77. A student interpreted a four layer Schlumberger resistivity sounding data and obtained the resistivities (ρ) and thicknesses (h) as follows: ρ₁=100 Ωm, ρ₂=20 Ωm, ρ₃=1500 Ωm and ρ₄=50 Ωm; h1=50 m, h₂=10 m and h₃=20 m. The same data is interpreted by another student who obtains ρ₃=2000 Ωm. Then, according to the principle of equivalence, the value of h₃ interpreted by the second student is ________m. (All other model parameters estimated by both the students are the same.)

Answer: (15 to 15)

78. The apparent resistivities obtained at 0.1 Hz and 10 Hz in the frequency domain I.P. measurement are 100 Ωm and 80 Ωm, respectively. The Percentage Frequency Effect is _________.

Answer: (25 to 25)

79. A 15 Volt power supply is applied across a cylindrical container (diameter = 0.20 m and length = 0.50 m). Currents of 750 mA and 500 mA are measured when the container is filled with (i) brine only, and (ii) rock sample fully saturated with brine, respectively. The formation factor of the rock sample is __________.

Answer: (1.50 to 1.50)

80. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is _______.

Answer: (6.9 to 7.1)

81. Consider a laterally homogeneous and isotropic earth model with a flat horizontal surface and three horizontal layers underlain by a half-space. A seismic reflection survey was simulated on this model with the sources and receivers placed on the surface. The table below lists the root mean square (rms) velocities, Vr_ms, and zero-offset two-way traveltimes t0 for the three reflection events from the bottom of each of the three layers observed in a pre-stack CDP (CMP) gather. The interval velocity of the second layer is _______ m/s.

Answer: (1770 to 1790)

82. A spherically symmetric vector field The flux of the vector field through a sphere of unit radius is _________.

(Use 𝜋 = 3.14)

Answer: (-3.142 to -3.140)

83. A horizontally travelling surface wave with a wavelength of 20 m is attenuated by a linear and uniform receiver array consisting of 4 receivers if the minimum receiver spacing is ________ m.

Answer: (5.0 to 5.0)

84. An end-on marine survey is carried out with equal and uniform shot and receiver spacing. If the total number of shots fired is 50 and a total of 10000 traces are recorded, the maximum fold for the survey is _______.

Answer: (50 to 50 or 100 to 100)

85. The highest singular value of the matrix

Answer: (2.8 to 3.0)

GATE Exam 2018 Ecology and Evolution (EY) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

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

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Ecology and Evolution

Q. 1 – Q. 25 carry one mark each.

1. During the Pleistocene, which of the following groups experienced the largest mass extinction?

(A) Large dinosaurs

(B) Large mammals

(D) Trilobites

Answer: (B)

2. In group living species, the term “dilution effect” refers to

(A) reduction in aggression among individuals with increasing group size

(B) reduction in the mobility of individuals with increasing group size

(D) reduction in the risk of predation of individuals with increasing group size

Answer: (D)

3. Which of the following diversity indices best captures species turnover across habitats?

(A) α

(B)β

(D) δ

Answer: (B)

4. A duck egg is removed from its mother’s nest and incubated by a barnyard hen. The duckling hatches out in the presence of the barnyard hen and stays in her nest. After a couple of days, the duckling is presented with a choice between its biological
mother and the hen that incubated it. The duckling approaches and follows the hen. This set of observations demonstrates the phenomenon of

(A) habituation

(B) imprinting

(D) sensitization

Answer: (B)

5. If both of your ears were located next to each other in the middle of your face, you would have difficulty in resolving the

(A) direction of a sound

(B) duration of a sound

(D) pitch of a sound

Answer: (A)

6. Forager bees communicate the distance of a food source using a waggle dance uponreturn to the hive. It is observed that the number of waggles of a dance increases linearly with the distance to the food source. This tells us that the

(A) number of waggles and distance to food source is negatively correlated

(B) number of waggles and distance to food source is positively correlated

(D) number of waggles and the distance to the food source are uncorrelated

Answer: (B)

7. Male frogs display to females by producing loud acoustic signals. The use of these signals by bats to locate frogs and prey upon them is an example of

(A) aposematism

(B) deception

(D) mimicry

Answer: (C)

8. A non-venomous, non-toxic species of snake is brightly coloured and closely resembles a venomous snake species in the same habitat. This is most likely a case of

(A) aggressive mimicry

(B) Batesian mimicry

(D) Müllerian mimicry

Answer: (B)

9. The value of the resting membrane potential of a typical neuron is closest to the equilibrium potential of which of the following ions?

(A) Ca⁺⁺

(B) K⁺

(D) Na⁺

Answer: (B)

10. A plant species found in India produces flowers that are white, fragrant, and tubular.

Which of the following is the most likely pollinating agent?

(A) Hummingbirds

(B) Lorises

(D) Wind

Answer: (C)

11. Which of the following can be used to test differences between mean tree heights in a tropical versus a temperate forest?

(A) Binomial test

(B) Linear regression

(D) Student’s t-test

Answer: (D)

12. For a species, assuming a relatively short time scale and no evolution, increased interspecific competition will result in a

(A) larger fundamental niche

(B) larger realized niche

(D) smaller realized niche

Answer: (D)

13. In which of the following mating systems is sperm competition likely to evolve?

(A) Monoandry

(B) Monogamy

(D) Polygyny

Answer: (C)

14. Copies of genes that arrive in a particular genome by horizontal gene transfer are known as

(A) analogs

(B) homologs

(D) xenologs

Answer: (D)

15. In which of the following plants is the dominant stage of the life cycle haploid?

(A) Cycads

(B) Ferns

(D) Mosses

Answer: (D)

16. Which of the following is NOT typically a characteristic of early successional pioneer plants relative to late successional plants in a tropical rain forest?

(A) Higher shade tolerance

(B) Smaller seed size

(D) Wind dispersed seeds

Answer: (A)

17. Natural populations often deviate from Hardy-Weinberg equilibrium. One possible reason for this is

(A) no migration

(B) no selection

(D) small population sizes

Answer: (D)

18. Which of the following is NOT an example of phenotypic plasticity?

(A) Density-dependent swarming behavior in locusts

(B) Increase in DDT resistance in mosquitos

(D) Temperature-dependent sex determination in turtles

Answer: (B)

19. Which of the following is NOT a characteristic of r-selected species?

(A) Early sexual maturity

(B) High juvenile mortality

(D) Large number of offspring

Answer: (C)

20. A scientist finds a new species of insect and sends a sample to a museum for confirmation. The curator of the museum designates it as a holotype for the newly identified species and asks the scientist to also provide samples of the opposite sex.

This sample of the opposite sex is called the

(A) allotype

(B) isotype

(D) neotype

Answer: (A)

21. Which of the following is NOT essential for a behavioural trait to evolve by natural selection?

(A) The behavioural trait differs among individuals

(B) The behavioural trait is determined at least in part by genes

(D) The behavioural trait is determined entirely by genes

Answer: (D)

22. El Niño Southern Oscillation (ENSO) events have occurred approximately every 3-7 years over the last century. The cause of these ENSO events is related to

(A) large-scale air-sea interactions in the Pacific Ocean

(B) strong monsoon winds in the Indian Ocean

(D) unsustainable overfishing in North Atlantic Ocean

Answer: (A)

23. If the mean of a sample is 5, and the variance is 25, the PERCENT coefficient of variation is ___.

Answer: (99 to 101)

24. Consider a diploid population at Hardy-Weinberg equilibrium. For a locus with two alleles, the frequency of the A1A1 genotype is 0.01. The frequency of heterozygotes A₁A₂ is ____ (answer up to 2 decimal places).

Answer: (0.179 to 0.181)

25. In a food chain, the efficiency of transfer of energy from one trophic level to the next is 10%. The PERCENTAGE of energy that is expected to transfer from the second to the fourth level is ____.

Answer: (0.99 to 1.01)

Q. 26 – Q. 55 carry two marks each.

26. Which of the following is an adaptation for osmoregulation in freshwater teleost fish?

(A) Excreting large quantities of dilute urine

(B) Excreting large quantities of uric acid

(D) Excreting large quantities of uracil

Answer: (A)

27. The latitudinal diversity gradient is defined as the decrease in the number of species from the equator to the poles. This can result from

(A) greater energy input at the poles

(B) greater land mass at the poles

(D) greater speciation rates at the poles

Answer: (C)

28. Identify the graph in which natural selection on beak size is LEAST likely to be occurring? For each of the graphs, the slope of the regression line and the associated p-value is given.

Answer: (C)

29. Some species of spiders add additional silk ‘decorations’ to their webs. It is hypothesized that these decorations serve either to lure flies (prey) or to decrease bird (predator) attacks on the spiders. The appropriate way to test these hypotheses would be to compare numbers of

(A) predators and prey approaching decorated webs

(B) predators and prey approaching undecorated webs

(D) predators and prey approaching both decorated and undecorated webs

Answer: (D)

30. The figure below shows mean annual temperatures (°C) and mean annual precipitation (cm per year) from multiple sites in four regions in India.

From this climatic information, we can infer that P, Q, R, and S are LIKELY to be located in:

(A) P: Andaman, Q: Meghalaya, R: Ladakh, S: Rajasthan

(B) P: Ladakh, Q: Rajasthan, R: Andaman, S: Meghalaya

(D) P: Rajasthan, Q: Andaman, R: Meghalaya, S: Ladakh

Answer: (B)

31. For a pair of interacting species, increased specialization and decreased niche breadth in both species would result in

(A) decreased intraspecific competition and increased interspecific competition

(B) decreased intraspecific competition and decreased interspecific competition

(D) increased intraspecific competition and decreased interspecific competition

Answer: (D)

32. Males of a bird species provide parental care by feeding nestlings before they fledge. Which of the following is a PROXIMATE explanation for this behaviour?

(A) Feeding nestlings increases their survivorship after fledging

(B) High prolactin levels cause males to feed their nestlings

(D) Males that provide parental care have higher fitness

Answer: (B)

33. The courtship display of a spider species consists of both visual and vibrational signals. Females respond to the display by approaching males. In an experiment, females were presented with 3 treatments: i) only videos of displaying males, ii) only vibrational signals of the display, and iii) both videos of displaying males and vibrational signals. The results are given below:

Results from this experiment show that

(A) vibrational signals are necessary to evoke a response

(B) vibrational signals are sufficient to evoke a response

(D) visual signals are necessary to evoke a response

Answer: (D)

34. Moth ears typically consist of a membranous eardrum backed by an air cavity. Ears in different phylogenetic groups of moths have evolved on different body parts. Moth ears are thus best described as

(A) convergent organs

(B) homologous organs

(D) vestigeal organs

Answer: (A)

35. Increased anthropogenic disturbance has resulted in an overall decrease in densities of trees and an increase in fragmentation of forests. Which of the following types of trees will have the greatest reduction in reproductive success?

(A) Dioecious species

(B) Monoecious species

(D) Self-incompatible hermaphrodites

Answer: (A)

36. A study examined the effect of neighbours on plants when grown at low or high altitudes. The researcher measured Relative Neighbour Effect (RNE), defined as: RNE = Biomass with neighbours – Biomass without neighbours.

The results shown above demonstrate

(A) competition at both altitudes

(B) competition at high altitudes, and facilitation at low altitudes

(D) facilitation at both altitudes

Answer: (C)

37. Match the combination of flora and fauna from the list, to the state where they are found.

(A) P: Assam; Q: Jammu & Kashmir; R: West Bengal; S: Sikkim

(B) P: Jammu & Kashmir; Q: Assam; R: West Bengal; S: Sikkim

(D) P: Sikkim; Q: West Bengal; R: Assam; S: Jammu & Kashmir

Answer: (C)

38. A parent population (P) is split into three daughter populations (Q, R, and S) which grow in three different habitats. After 1000 generations, the equilibrium frequency distribution of a trait in each of the daughter populations is shown in the figure below. For reference, the vertical line represents the mean of the parent population.

From this information, one can infer that the subpopulations experienced the following selection regimes

(A) Q: Directional; R: Stabilizing; S: No selection

(B) Q: Directional; R: Stabilizing; S: Stabilizing

(D) Q: Stabilizing; R: Directional; S: No selection

Answer: (A)

39. The character matrix below lists four taxa (P-S) and their nine characters (i-ix). A character state is designated as ‘0’ if it is ancestral and ‘1’ if it is derived. Which of the following phylogenetic trees is obtained by cladistic analysis of these data?

Answer: (A)

40. The reactions below (R1 and R2) represent different carbon fixation pathways in photosynthesis.

RuBP represents Ribulose bisphosphate.

Rubisco represents RuBP carboxylase-oxygenase.

PGA represents Phosphoglyceric acid.

PEP represents Phosphoenolpyruvate.

Which of the following is CORRECT?

(A) R1 and R2 both occur in C-3 and CAM photosynthesis

(B) R1 occurs in C-4 photosynthesis; R2 occurs in C-3 photosynthesis

(D) R1 occurs in C-4 and CAM photosynthesis; R2 occurs in C-3 photosynthesis

Answer: (C)

41. A fish species is sexually dimorphic: males possess ultraviolet (UV) spots on their bodies which are lacking in females. Females prefer males with larger and more intense UV spots as mates. Which of the following statements is a plausible reason
for the spots being coloured ultraviolet?

(A) Females assess males from long distances

(B) Females are not sensitive to UV light

(D) Ultraviolet spots are more conspicuous to predators

Answer: (A or D)

42. A climate scientist notices a trend in atmospheric CO₂ concentrations (in ppm) at a research station. Although overall CO₂ is rising over decades, there are intra-annual fluctuations, as shown in the figure below.

These fluctuations can be attributed to

(A) burning of fossil fuels by automobiles and industry

(B) oscillations due to El Niño and La Niña events

(D) seasonal trends in photosynthesis and respiration

Answer: (D)

43. Four islands differ in size (small = 10 km², large = 100 km²) and distance from the mainland (near = 50 km, far = 500 km).

Island P is small and near the mainland;

Island Q is small and far from the mainland;

Island R is large and near the mainland;

Island S is large and far from the mainland

Let NP, NQ, NR and NS denote the number of species on islands P, Q, R and S, respectively. Which of the following is consistent with the theory of island biogeography?

(A) N_Q > N_S > N_P > N_R

(B) N_R > N_Q > N_P > N_S

(D) N_R > N_P > N_S > N_Q

Answer: (D)

44. The rate of population growth (dN/dt) over time (t) is shown below.

For the above population, which of the following plots of population (Popn.) size (N) vs. time (t) is CORRECT?

(A)

(B)

(C)

(D)

Answer: (A)

45. The pedigree below details a late onset genetic disease among humans. Males are represented as squares and females as circles. Individuals with the disease are depicted as black, and those without it are depicted as white. Which of the following
best describes the pattern of inheritance of the disease-causing gene?

(A) Mitochondrial

(B) X-linked dominant

(D) Y-linked

Answer: (C)

46. Match the following scientists with the concepts or theories they are associated with.

(A) P-iii, Q-i, R-iv, S-ii

(B) P-ii, Q-iii, R-iv, S-i

(D) P-ii, Q-iii, R-i, S-iv

Answer: (C)

47. Which of the following is an example of complete intrinsic post-zygotic reproductive isolation between two species P and Q?

(A) P and Q can mate and have fertile offspring

(B) P and Q can mate but their offspring are inviable

(D) P and Q have different courtship behaviour

Answer: (B)

48. Match the animals to their locomotor adaptation.

(A) P-iv, Q-i, R-iii, S-ii

(B) P-iv, Q-iii, R-ii, S-i

(D) P-ii, Q-iii, R-i, S-ii

Answer: (B)

49. Paralogs are genes that are the products of gene duplication events within a species. Orthologs are genes in different species that share a common ancestral gene. The figure below describes the evolutionary history of a hypothetical gene X in organism Y. This gene undergoes a duplication event. Later, Y splits into two species Y₁ and Y₂, and this gives rise to four copies of the gene – P, Q, R and S. Which option best describes the relationships between the four copies of the gene X?

(A) P & Q are orthologs, Q & R are paralogs

(B) R & S are orthologs, S & Q are paralogs

(D) P & R are orthologs, R & S are paralogs

Answer: (D)

50. The frequency distribution of beak sizes of a bird species is symmetric but not normally distributed. If the mean value of beak size is 6 mm, standard deviation is 25 mm and kurtosis is 10, then the median is ____ mm.

Answer: (5.9 to 6.1)

51. An altruist provides help worth 10 units of fitness to a recipient, at a personal cost of 1 unit of fitness. As per kin-selection theory, the minimum value of genetic relatedness between the actors and the recipients that is necessary to maintain altruism in the population is _____ (answer up to 1 decimal place).

Answer: (0.09 to 0.11)

52. A population grows from a size of 100 individuals at t = 0, to 1000 individuals at t = 100, following density-independent growth. The ratio of per-capita growth rates at the initial (at t = 0) to the final (t = 100) time is ____.

Answer: (0.99 to 1.01)

53. The probability that a bush has a cricket is 0.1. The probability of a spider being present on a bush is 0.2. When both a spider and a cricket are present on a bush, the probability of encountering each other is 0.2. The probability of a spider consuming a cricket it encounters is 0.5. Assuming that predation only occurs on bushes, the probability that a cricket is preyed on by a spider is ____ (answer up to 3 decimal places).

Answer: (0.0019 to 0.0021)

54. A plant produces seeds that can be dispersed by birds or mammals. The probability that a seed is dispersed by a bird is 0.25, and by a mammal is 0.5. The bird can disperse a seed to three patches A, B, or C with a probability 0.5, 0.4 or 0.1, respectively. On the other hand, the mammal disperses a seed to the same patches A, B, or C, with a probability 0.15, 0.8 and 0.05, respectively. The probability that a given seed is dispersed to patch B is ___ (answer up to 1 decimal place).

Answer: (0.49 t 0.51)

55. The species area relationship of trees in Mudumalai Tiger Reserve is given by S = 0.1 × A^0.3, where S is the number of species in a given area A. When log S is plotted against log A, the slope of the resulting relationship is _____ (answer up to 1
decimal place).

Answer: (0.299 to 0.301)

GATE Exam 2018 Electrical Engineering (EE) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-6

Q. 1 – Q. 5 carry one mark each.

1. “ Since you have gone off the ________, the _________ sand is likely to damage the car.”

The words that best fill the blanks in the above sentence are

(A) course, coarse

(B) course, course

(D) coarse, coarse

Answer: (A)

2. “ A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas.”

The word that best fills the blank in the above sentence is

(A) detailed

(B) simple

(D) convoluted

Answer: (D)

3. The three roots of the equation 𝑓(𝑥) = 0 are 𝑥 = {−2, 0, 3}. What are the three values of 𝑥 for which 𝑓(𝑥 − 3) = 0?

(A) −5, −3, 0

(B) −2, 0, 3

(D) 1, 3, 6

Answer: (D)

4. For what values of 𝑘 given below is an integer?

(A) 4, 8, 18

(B) 4, 10, 16

(D) 8, 26, 28

Answer: (C)

5. Functions 𝐹(𝑎, 𝑏) and 𝐺(𝑎, 𝑏) are defined as follows:

𝐹(𝑎, 𝑏) = (𝑎 − 𝑏)2 and 𝐺(𝑎, 𝑏) = |𝑎 − 𝑏|, where |𝑥| represents the absolute value of 𝑥.

What would be the value of 𝐺(𝐹(1, 3), 𝐺(1, 3))?

(A) 2

(B) 4

(D) 36

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

6. An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

(A) 6,760

(B) 13,520

(D) 1,05,456

Answer: (C)

7. In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

(A) RSTN

(B) TLPH

(D) XSVR

Answer: (C)

8. A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

(A) 0

(D) 5/12

Answer: (Marks to All)

9. A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design?

(A) 35.75

(B) 40.25

(D) 46.25

Answer: (C)

10. P , Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.

(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.

(ii) P is unable to row when someone else is in the boat.

(iii) Q is unable to row with anyone else except R.

(iv) Each person rowed for at least one trip.

(v) Only one person can row during a trip.

Who rowed twice?

(A) P

(B) Q

(D) S

Answer: (C)

Electrical Engineering

Q. 1 – Q. 25 carry one mark each.

1. A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

(A) 4.8

(B) 6.8

(D) 10.8

Answer: (A)

2. I n a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

(A) 0

(B) 45

(D) 90

Answer: (B)

3. A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?

(A) v_o ≥ 0 & i_o < 0

(B) v_o < 0 & i_o <0

(D) v_o > 0 & i_o ≥ 0

Answer: (C)

4. Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are)

(A) Triac only

(B) Triac and MOSFET

(D) Thyristor and Triac

Answer: (B)

5. Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

(A) 0.532

(B) 0.632

(D) 0.866

Answer: (D)

6. Consider a lossy transmission line with V₁ and V₂ as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be

Answer: (B)

7. The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

(A) 11

(B) 12

(D) 14

Answer: (B)

8. In the figure, the voltages are 𝑣₁(𝑡) = 100cos⁡(𝜔𝑡), 𝑣₂(𝑡) = 100cos⁡(𝜔𝑡 + 𝜋/18) and 𝑣₃(𝑡) = 100cos⁡(𝜔𝑡 + 𝜋/36). The circuit is in sinusoidal steady state, and 𝑅 << 𝜔𝐿. 𝑃₁, 𝑃₂ and 𝑃₃ are the average power outputs. Which one of the following statements is true?

(A)⁡𝑃₁ = 𝑃₂ = 𝑃3 = 0

(B)⁡𝑃₁ < 0, 𝑃₂ > 0, 𝑃3 > 0

(C)⁡𝑃₁ < 0, 𝑃₂ > 0, 𝑃3 < 0

(D)⁡𝑃₁ > 0, 𝑃₂ < 0, 𝑃3 > 0

Answer: (C)

9. Match the transfer functions of the second-order systems with the nature of the systems given below.

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

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

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

Answer: (C)

10. A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x – y plane to be a conducting ground plane. Take ∈₀ = 8.85 × 10^–12 The z component of the E field at (0, 0, 0.1) is closest to

(A) 899.18 V/m

(B) –899.18 V/m

(D) –999.09 V/m

Answer: (D)

11. Let f be a real-valued function of a real variable defined as f(x) = x² for x ≥ 0 and f(x) = –x² for x < 0.Which one of the following statements is true?

(A) f(x) is discontinuous at x = 0.

(B) f(x)is continuous but not differentiable at x = 0.

(D) f(x) is differentiable but its first derivative is not differentiable at x = 0.

Answer: (D)

12. The value of the directional derivative of the function Φ(x, y, z) = xy² + yz² + zx² at the point (2, -1, 1) in the direction of the vector 𝐩 = 𝐢 + 2𝐣 + 2𝐤 is

(A) 1

(B) 0.95

(D) 0.9

Answer: (A)

13. The value of the integral in counter clockwise direction around a circle 𝐶 of radius 1 with center at the point 𝑧 = −2 is

(A) πi/2

(B) 2πi

(D) –2πi

Answer: (A)

14. In the logic circuit shown in the figure, Y is given by

(A) Y = ABCD

(B) Y = (A + B)(C + D)

(D) Y = AB + CD

Answer: (D)

15. The op-amp shown in the figure is ideal. The input impedance v_in/i_in is given by

Answer: (B)

16. A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

(A) k x(t) , where k is an eigenvalue

(B) k e^jωtx(t) , where k is an eigenvalue and e^jωt is a complex exponential signal

(D) k H(ω) , where k is an eigenvalue and H(ω) is a frequency response of the system

Answer: (A)

17. Consider a non-singular 2×2 square matrix A . If trace(A) = 4 and trace(A²) = 5, the determinant of the matrix A is _________(up to 1 decimal place).

Answer: (5.5 to 5.5)

18. Let f be a real-valued function of a real variable defined as f(x) = x – [x], where [x] denotes the largest integer less than or equal to x. The value of is _______ (up to 2 decimal places).

Answer: (0.49 to 0.51)

19. In the two-port network shown, the h₁₁ parameter in ohms is _____________ (up to 2 decimal places).

Answer: (0.45 to 0.55)

20. The series impedance matrix of a short three-phase transmission line in phase coordinates If the positive sequence impedance is (1 + 𝑗⁡10)⁡Ω, and the zero sequence is (4 + ⁡𝑗⁡31)⁡Ω, then the imaginary part of 𝑍𝑚 (in Ω) is ______(up to 2 decimal places).

Answer: (7.0 to 7.0)

21. The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are 𝑗0.1 pu,⁡ 𝑗0.05 pu and 𝑗0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is 𝑗0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

Answer: (73.0 to 74.0)

22. A 1000 × 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).

Answer: (3500.0 to 3500.0)

23. The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I0 = 20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).

Answer: (16.90 to 17.70)

24. A separately excited dc motor has an armature resistance 𝑅_𝑎 = 0.05⁡Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed of the motor (in radian/s) for an armature voltage of 150 V is _____ (up to 2 decimal places).

Answer: (600.0 to 600.0)

25. Consider a unity feedback system with forward transfer function given by

The steady-state error in the output of the system for a unit-step input is _________(up to 2 decimal places).

Answer: (0.65 to 0.69)

Q. 26 – Q. 55 carry two marks each.

26. A transformer with toroidal core of permeability μ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius r << R, and neglecting any leakage flux, the best estimate for the mean radius R is

Answer: (D)

27. A 0-1 Ampere moving iron ammeter has an internal resistance of 50 mΩ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in mΩ of the shunt coil respectively are

(A) 2, 5.55

(B) 2, 1

(D) 11.1, 2

Answer: (A)

28. The positive, negative and zero sequence impedances of a three phase generator are 𝑍₁, 𝑍₂ and 𝑍₀ respectively. For a line-to-line fault with fault impedance 𝑍_𝑓 ,⁡the fault current is ⁡𝐼_𝑓1 = 𝑘𝐼_𝑓 , where 𝐼_𝑓 is the fault current with zero fault impedance. The relation between 𝑍_𝑓 and 𝑘 is

Answer: (A)

29. Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G₁and G₂ are Q_G1 and Q_G2 respectively. The per unit values of Q_G1, Q_G2, and line reactive power loss (Q_loss) respectively are

(A) 5. 00, 12.68, 2.68

(B) 6.34, 10.00, 1.34

(D) 5.00, 11.34, 1.34

Answer: (C)

30. The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, 𝑃 = 1.4 sin 𝛿 + 0.15 sin 2𝛿, where 𝛿 is the load angle. Newton- Raphson method is used to calculate the value of 𝛿 for 𝑃 = ⁡0.8 pu. If the initial guess is 30°, then its value (in degree) at the end of the first iteration is

(A) 15°

(B) 28.48°

(D) 31.20°

Answer: (C)

31. A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the figure. Assume i(0) = 0, v(0) = 0. Which one of the following circular loci represents the plot of i(t) versus v(t) ?

(A)

(B)

(C)

(D)

Answer: (B)

32. The equivalent impedance Z_eq for the infinite ladder circuit shown in the figure is

(A) j12 Ω

(B) –j12 Ω

(D) 13 Ω

Answer: (A)

33. Consider a system governed by the following equations

The initial conditions are such that and Which one of the following is true?

(A) x_1f < x_2f < ∞

(B) x_2f < x_1f < ∞

(D) x_1f = x_2f = ∞

Answer: (C)

34. The number of roots of the polynomial, 𝑠⁷ +⁡𝑠⁶ + 7𝑠⁵ + 14𝑠⁴ + 31𝑠³ + 73𝑠² + 25𝑠 + 200,⁡in the open left half of the complex plane is

(A) 3

(B) 4

(D) 6

Answer: (A)

35. If 𝐶⁡is a circle |𝑧| = 4 and

(A) 1

(B) 0

(D) -2

Answer: (B)

36. Which one of the following statements is true about the digital circuit shown in the figure

(A) It can be used for dividing the input frequency by 3.

(B) It can be used for dividing the input frequency by 5.

(D) It cannot be reliably used as a frequency divider due to disjoint internal cycles.

Answer: (B)

37. Digital input signals 𝐴, 𝐵, 𝐶 with 𝐴 as the MSB and 𝐶 as the LSB are used to realize the Boolean function 𝐹 = 𝑚₀ + 𝑚₂ + 𝑚₃ + 𝑚₅ + 𝑚₇, where⁡𝑚𝑖 ⁡denotes⁡the⁡𝑖𝑡ℎ⁡minterm. In addition, 𝐹 has a don’t care for 𝑚1. The simplified expression for 𝐹 is given by

Answer: (B)

38. Consider the two continuous-time signals defined below:

These signals are sampled with a sampling period of T = 0.25 seconds to obtain discretetime signals x₁[n] and x₂[n], respectively. Which one of the following statements is true?

(A) The energy of x₁[n]is greater than the energy of x₂[n].

(B) The energy of x₂[n] is greater than the energy of x₁[n].

(D) Neither x₁[n] nor x₂[n] is a finite-energy signal.

Answer: (A)

39. The signal energy of the continuous-time signal x(t) =[(t -1) u(t -1)]-[(t -2)u(t -2)]-[(t -3)u(t -3)]+[(t -4)u(t -4)] is

(A) 11/3

(B) 7/3

(D) 5/3

Answer: (D)

40. The Fourier transform of a continuous-time signal x(t) is given by and ω denotes frequency. Then the value of |lnx(t)| at t = 1 is ___________ (up to 1 decimal place). ( ln denotes the logarithm to base e )

Answer: (9.5 to 10.5)

41. In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain 𝛽 = 100. The base-emitter voltage drop is a constant, 𝑉_𝐵𝐸 = 0.7⁡𝑉. The value of the Thevenin equivalent resistance 𝑅_𝑇ℎ (in Ω) as shown in the figure is ______ (up to 2 decimal places).

Answer: (89.0 to 91.5)

42. As shown in the figure, 𝐶 is the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of the integral ∫_C (y² + 2yx)dx + (2xy + x²)dy

Answer: (0.0 to 0.0)

43. Let f(x) = 3x³ – 7x² + 5x + 6. The maximum value of f (x) over the interval [0, 2] is _______ (up to 1 decimal place).

Answer: (11.5 to 12.5)

44. Let and B = A³ – A²– 4A + 5I, where I is the 3 × 3 identity matrix. The determinant of B is ________ (up to 1 decimal place).

Answer: (0.9 to 1.1)

45. The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).

Answer: (2.50 to 2.55)

46. The unit step response y(t) of a unity feedback system with open loop transfer function is shown in the figure. The value of K is _______ (up to 2 decimal places).

Answer: (8.0 to 8.0)

47. A three-phase load is connected to a three-phase balanced supply as shown in the figure. If V_an = 100∠0° V, V_bn = 100∠–120° V and V_cn = 100∠–240° V(angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________Ω (up to 2 decimal places).

Answer: (5.70 to 5.85)

48. The voltage across the circuit in the figure, and the current through it, are given by the following expressions:

𝑣(𝑡) = 5 − 10 cos(𝜔𝑡 + 60°)⁡V
𝑖(𝑡) = 5 + 𝑋 cos(𝜔𝑡) A

where 𝜔 = 100⁡𝜋⁡radian/s. If the average power delivered to the circuit is zero, then the value of 𝑋 (in Ampere) is _____ (up to 2 decimal places).

Answer: (10.0 to 10.0)

49. A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by where V_m = 80π volts and 𝛼 is the firing angle. If the power delivered to the lossless battery is 1600 W, 𝛼 in degree is________ (up to 2 decimal places).

Answer: (90.0 to 90.0)

50. T he figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value. The load resistance is 1Ω. The capacitor voltage has negligible ripple. Both converters operate in the continuous conduction mode. The switching frequency is 1 kHz, and the switch control signals are as shown. The circuit operates in the steady state. Assuming that the converters share the load equally, the average value of 𝑖_𝑆1, the current of switch S1 (in Ampere), is _____ (up to 2 decimal places).

Answer: (11.50 to 13.50)

51. A 3-phase 900 kVA, 3 kV/√3 kV (Δ/Y), 50 Hz transformer has primary (high voltage side) resistance per phase of 0.3 Ω and secondary (low voltage side) resistance per phase of 0.02 Ω. Iron loss of the transformer is 10 kW. The full load % efficiency of the transformer operated at unity power factor is _______ (up to 2 decimal places).

Answer: (97.20 to 97.55)

52. A 200 V DC series motor, when operating from rated voltage while driving a certain load, draws 10 A current and runs at 1000 r.p.m. The total series resistance is 1 Ω. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by 44%. The speed of the motor in r.p.m. (rounded to the nearest integer) is ________ .

Answer: (823 to 827)

53. A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value of the inductor, L is 5 mH and the ideal switch, S is operated with a switching frequency of 5 kHz with a duty ratio of 0.4. Once the circuit has attained steady state and assuming the diode D to be ideal, the power transferred from B1 to B2 (in Watt) is ___________ (up to 2 decimal places).

Answer: (12.0 to 12.0)

54. The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are R₁ = R₂= X₁₁ = X₁₂ = 12Ω, X_M = 240Ω and s is the slip. At no-load, the motor speed can be approximated to be the synchronous speed. The no-load lagging power factor of the motor is___________ (up to 3 decimal places).

Answer: (0.104 to .0112)

55. The voltage 𝑣(𝑡) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency 𝜔 = 100 radian/s. When the inductor current 𝑖(𝑡) is in phase with the voltage 𝑣(𝑡), the magnitude of the impedance Z (in Ω) seen between the terminals a and b is ________ (up to 2 decimal places).

Answer: (50.0 to 50.0)

GATE Exam 2018 Electronics and Communication Engineering (EC) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-5

Q. 1 – Q. 5 carry one mark each.

1. “ By giving him the last ______ of the cake, you will ensure lasting _____ in our house today.”

The words that best fill the blanks in the above sentence are

(A) peas, piece

(B) piece, peace

(D) peace, peas

Answer: (B)

2. “ Even though there is a vast scope for its ________, tourism has remained a/an _________ area.”

The words that best fill the blanks in the above sentence are

(A) improvement, neglected

(B) rejection, approved

(D) interest, disinterested

Answer: (A)

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

(A) 0

(B) 2

(D) 6

Answer: (B)

4. What is the value of

(A) 2

(B) 7/4

(D) 4/3

Answer: (D)

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

(A) 1.5

(B) 3

(D) 6

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

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

(A) 5,00,000

(B) 6,21,000

(D) 7,50,000

Answer: (B)

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

(A) 5:10

(B) 7:13

(D) 9:13

Answer: (B)

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

(i) Even as a junior cricketer, John was considered a good captain.

(ii) Finding a complete captain is a challenge.

(iii) Fans and the Cricket Board have differing views on what they want in a captain.

(iv) Over the past three seasons John has accumulated big scores.

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

(B) (iii) and (iv) only

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

Answer: (C)

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

(i) 85% of cabs in the city are green and the remaining cabs are blue.

(ii) A witness identified the cab involved in the accident as blue.

(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.

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

(A) 12%

(B) 15%

(D) 80%

Answer: (C)

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

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

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

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

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

Answer: (D)

Electronics and Communication Engineering

Q. 1 – Q. 25 carry one mark each.

1. Two identical nMOS transistors M₁ and M₂ are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. V_bias and V_D are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as while the output resistance is where 𝑖𝐷 is the current flowing into the drain of M₂ . Let 𝑔_𝑚1, 𝑔_𝑚2 be the transconductances and 𝑟_𝑜1, 𝑟_𝑜2 be the output resistances of transistors M₁ and M₂, respectively.

Which of the following statements about estimates for 𝑔_𝑚 and 𝑟_𝑜 is correct?

Answer: (C)

2. In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e. 𝑣𝐼𝑁 (𝑡) = 𝑢(𝑡) volts. Also, at 𝑡 = 0, the voltage across each of the capacitors is zero.

The time 𝑡, in milliseconds, at which the output voltage 𝑣_𝑂𝑈𝑇 crosses −10 V is

(A) 2.5

(B) 5

(D) 10

Answer: (C)

3. A good transimpedance amplifier has

(A) low input impedance and high output impedance.

(B) high input impedance and high output impedance.

(D) low input impedance and low output impedance.

Answer: (D)

4. Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

Answer: (C)

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

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

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

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

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

Answer: (D)

6. Consider 𝑝(𝑠) = 𝑠³ + 𝑎²𝑠² + 𝑎¹𝑠 + 𝑎0 with all real coefficients. It is known that its derivative 𝑝′(𝑠) has no real roots. The number of real roots of 𝑝(𝑠) is

(A) 0

(B) 1

(D) 3

Answer: (B)

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

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

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

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

Answer: (D)

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

(A) NOR

(B) AND

(D) XOR

Answer: (D)

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

where, are the complements of the respective variables. The product of sums (POS) form of the function F is

Answer: (C)

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

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

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

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

Answer: (C)

11. Let M be a real 44 matrix. Consider the following statements:

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?

(A) S1 implies S2

(B) S1 implies S3

(D) S3 implies S2

Answer: (C)

12. Let where a and b are constants. If at x = 1 and y = 2, then the relation between a and b is

(A) a = b/4

(B) a = b/2

(D) a = 4b

Answer: (D)

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

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

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

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

Answer: (B)

14. Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎_𝑘, that is

The same function 𝑥(𝑡) can also be considered as a periodic function with period 𝑇′ = 40. Let 𝑏_𝑘 be the Fourier series coefficients when period is taken as 𝑇′. If then is equal to

(A) 256

(B) 64

(D) 4

Answer: (C)

15. Consider the following amplitude modulated signal:

𝑠(𝑡) = cos(2000 𝜋𝑡) + 4 cos(2400 𝜋𝑡) + cos(2800 𝜋𝑡).

The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is __________.

Answer: (0.12 to 0.13)

16. Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in this code is at least 2. The maximum number of codewords such a code can contain is _________.

Answer: (16 to 16)

17. A binary source generates symbols 𝑋 ∈ {−1,1} which are transmitted over a noisy channel. The probability of transmitting 𝑋 = 1 is 0.5. Input to the threshold detector is 𝑅 = 𝑋 + 𝑁. The probability density function 𝑓𝑁(𝑛) of the noise 𝑁 is shown below.

If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.

Answer: (0.12 to 0.14)

18. A p-n step junction diode with a contact potential of 0.65V has a depletion width of 1μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is _______.

Answer: (0.40 to 0.43)

19. A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is _______.

Answer: (5 to 5)

20. There are two photolithography systems: one with light source of wavelength λ1 = 156 nm (System 1) and another with light source of wavelength λ₂ = 325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are Lmin1 and Lmin2 respectively, the ratio L_min1/L_min2 (correct to two decimal places) is__________.

Answer: (0.47 to 0.51)

21. A lossy transmission line has resistance per unit length R = 0.05 Ω . The line is distortionless and has characteristic impedance of 50Ω . The attenuation constant (in Np/m, correct to three decimal places) of the line is _______.

Answer: (0.001 to 0.001)

22. Consider matrix The number of distinct real values of k for which the equation Ax = 0 has infinitely many solutions is _______.

Answer: (2 to 2)

23. Let X₁ , X₂ , X₃ and X₄ be independent normal random variables with zero mean and unit variance. The probability that 4 X is the smallest among the four is _______.

Answer: (0.25 to 0.25)

24. Taylor series expansion of around 𝑥 = 0 has the form

𝑓(𝑥) = 𝑎₀ + 𝑎₁𝑥 + 𝑎²𝑥² + ⋯

The coefficient 𝑎₂ (correct to two decimal places) is equal to _______.

Answer: (-0.01 to 0.01)

25. The ABCD matrix for a two-port network is defined by:

The parameter B for the given two-port network (in ohms, correct to two decimal places) is _______.

Answer: (4.3 to 5.3)

Q. 26 – Q. 55 carry two marks each.

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

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

(A) 186 Ω and 10 mW

(B) 100 Ω and 40 mW

(D) 186 Ω and 40 mW

Answer: (B)

27. Let c(t) = A_c cos(2πf_ct) and m(t) = cos(2πf_mt). It is given that f_c >> 5f_m. The signal c(t) + m(t) is applied to the input of a non-linear device, whose output v₀(t) is related to the input vi(t) as v₀(t) = av_i(t) + bv_i²(t), where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f_c and bandwidth 3f_m , to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then a/b is

(A) 0.25

(B) 0.5

(D) 2

Answer: (D)

28. Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density S_N(f) = 0.5 W/Hz as input to a filter with impulse response 0.5e^–t2/2 (where 𝑡 is in seconds) resulting in output 𝑌(𝑡). The power in 𝑌(𝑡) in watts is

(A) 0.11

(B) 0.22

(D) 0.44

Answer: (B)

29. The state equation and the output equation of a control system are given below:

The transfer function representation of the system is

Answer: (A)

30 Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The builtin voltages of red, green and blue diodes are V_R, V_G and V_B, respectively. Assume donor and acceptor doping to be the same (NA and N_D, respectively) in the p and n sides of all the three diodes.
Which one of the following relationships about the built-in voltages is TRUE?

(A) V_R > V_G > V_B

(B) V_R < V_G < V_B

(D) V_R > V_G < V_B

Answer: (B)

31. A four-variable Boolean function is realized using 41 multiplexers as shown in the figure.

The minimized expression for F(U,V,W, X) is

Answer: (C)

32. A 2 × 2 ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals that select the word lines and B0 and B1 are signals that are output of the sense amps based on the stored data corresponding to the bit lines during the read operation.

During the read operation, the selected word line goes high and the other word line is in a high impedance state. As per the implementation shown in the circuit diagram above, what are the bits corresponding to D_ij (where i = 0 or 1 and j = 0 or 1) stored in the ROM?

(A)

(B)

(C)

(D)

Answer: (A)

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

(A) 0.12

(B) 0.23

(D) 2.3

Answer: (B)

34. A curve passes through the point (x = 1, y = 0) and satisfies the differential equation The equation that describes the curve is

Answer: (A)

35. For the circuit given in the figure, the voltage V_C (in volts) across the capacitor is

Answer: (C)

36. For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is _______.

Answer: (0.284 to 0.348)

37. A dc current of 26μA flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, the diode has a junction capacitance of 0.5 nF . Its neutral region resistances can be neglected. Assume that the room temperature thermal equivalent voltage is 26 mV.

For ω = 2 × 10⁶ rad/s , the amplitude of the small-signal component of diode current (in μA, correct to one decimal place) is _______.

Answer: (6.2 to 6.6)

38. An op-amp based circuit is implemented as shown below.

In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node A, connected to the negative input of the op-amp as indicated in the figure is _________.

Answer: (0.4 to 0.6)

39. T he input 4sinc(2𝑡) is fed to a Hilbert transformer to obtain 𝑦(𝑡), as shown in the figure below:

Here The value (accurate to two decimal places) of is _______.

Answer: (8 to 8)

40 A random variable 𝑋 takes values −0.5 and 0.5 with probabilities 1/4 and 3/4, respectively. The noisy observation of 𝑋 is 𝑌 = 𝑋 + 𝑍, where 𝑍 has uniform probability density over the interval (−1, 1). 𝑋 and 𝑍 are independent. If the MAP rule based detector outputs as

then the value of 𝛼 (accurate to two decimal places) is _______.

Answer: (-0.5 to -0.5)

41. For a unity feedback control system with the forward path transfer function

The peak resonant magnitude M_r of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.

Answer: (14 to 17)

42. The figure below shows the Bode magnitude and phase plots of a stable transfer function

Consider the negative unity feedback configuration with gain 𝑘 in the feedforward path. The closed loop is stable for 𝑘 < 𝑘₀ . The maximum value of 𝑘₀ is ______.

Answer: (0.1 to 0.1)

43. In the circuit shown below, the (𝑊/𝐿) value for M2 is twice that for M₁. The two nMOS transistors are otherwise identical. The threshold voltage 𝑉𝑇 for both transistors is 1.0V. Note that 𝑉_𝐺𝑆 for M₂ must be > 1.0 V.

Answer: (0.41 to 0.435)

44. A solar cell of area 1.0 cm² , operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open circuit voltage of 0.65 V. Assuming room temperature operation and thermal equivalent voltage of 26mV, the open circuit voltage (in volts, correct to two decimal places) at 0.2 sun intensity is _______.

Answer: (0.59 to 0.63)

45. A junction is made between p^– Si with doping density N_A1 = 10¹⁵ cm^–3 and p Si with doping density N_A2 = 10¹⁷ cm^–3.

Given: Boltzmann constant k = 1.38 x 10^–23 J.K^–1, electronic charge q = 1.6 x 10^–19 C. Assume 100% acceptor ionization.

At room temperature (T = 300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be _________________.

Answer: (0.11 to 0.13)

46. In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data 𝐷_𝑖𝑛 using clock 𝐶𝐾. The XOR gate outputs 3.3 volts for logic HIGH and 0 volts for logic LOW levels. The data bit and clock periods are equal and the value of Δ𝑇/𝑇_𝐶𝐾 = 0.15, where the parameters Δ𝑇 and 𝑇_𝐶𝐾 are shown in the figure. Assume that the Flip-Flop and the XOR gate are ideal.

If the probability of input data bit (𝐷_𝑖𝑛) transition in each clock period is 0.3, the average value (in volts, accurate to two decimal places) of the voltage at node 𝑋, is _______.

Answer: (0.82 to 0.86)

47. The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for
LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes are intentionally shorted to implement “wired logic”. Such shorted nodes will be HIGH only if the outputs of all the gates whose outputs are shorted are HIGH.

The number of distinct values of 𝑋₃𝑋₂𝑋₁𝑋₀ (out of the 16 possible values) that give 𝑌 = 1 is _______.

Answer: (8 to 8)

48. T he cutoff frequency of TE₀₁ mode of an air filled rectangular waveguide having inner dimensions a cm × b cm ( ab ) is twice that of the dominant TE₁₀ mode. When the waveguide is operated at a frequency which is 25% higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be 4 cm. The value of b (in cm, correct to two decimal places) is _______.

Answer: (0.7 to 0.8)

49. A uniform plane wave traveling in free space and having the electric field

is incident on a dielectric medium (relative permittivity > 1, relative permeability = 1) as shown in the figure and there is no reflected wave.

The relative permittivity (correct to two decimal places) of the dielectric medium is ___________.

Answer: (1.9 to 2.1)

50. The position of a particle 𝑦(𝑡) is described by the differential equation:

The initial conditions are The position (accurate to two decimal places) of the particle at 𝑡 = 𝜋 is _______.

Answer: (-0.23 to -0.19)

51. The contour C given below is on the complex plane z = x + iy , where

The value of the integral is _______.

Answer: (2 to 2)

52. Let r = x² + y – z and z³ – xy + yz + y³ = 1.Assume that 𝑥 and 𝑦 are independent variables. At (𝑥, 𝑦, 𝑧) = (2, −1,1), the value (correct to two decimal places) of is ________.

Answer: (4.4 to 4.6)

53. Consider the network shown below with 𝑅1 = 1Ω, 𝑅2 = 2Ω and 𝑅3 = 3Ω. The network is connected to a constant voltage source of 11V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is _______.

Answer: (7.9 to 8.1)

54. A band limited low-pass signal 𝑥(𝑡) of bandwidth 5 kHz is sampled at a sampling rate 𝑓𝑠. The signal 𝑥(𝑡) is reconstructed using the reconstruction filter 𝐻(𝑓) whose magnitude response is shown below:

The minimum sampling rate 𝑓_𝑠 (in kHz) for perfect reconstruction of 𝑥(𝑡) is _______.

Answer: (13 to 13)

55. Let 𝑋[𝑘] = 𝑘 + 1, 0 ≤ 𝑘 ≤ 7 be 8-point DFT of a sequence 𝑥[𝑛],

where

The value (correct to two decimal places) of

Answer: (2.90 to 3.10)

GATE Exam 2018 Chemistry (CY) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

CHEMISTRY

Q. 1 – Q. 25 carry one mark each.

1. The major product formed in the following reaction is

Answer: (C)

2. The major product formed in the following reaction is

Answer: (D)

3. The major product of the following intramolecular cycloaddition reaction is

Answer: (D)

4. The major product of the following reaction is

Answer: (B)

5. The major product formed in the following reaction sequence is

Answer: (B)

6. The major product formed in the following reaction sequence is

Answer: (A)

7. The spherical harmonic function, with appropriate values of l and m, is an eigenfunction of operator. The corresponding eigenvalue is

(A)

(B)

(C)

(D)

Answer: (A)

8. Consider the operators, are the
position and linear momentum operators, respectively. The commutator, is equal to

(A) ih

(B) –ih

(D) –h

Answer: (C)

9. The temperature derivative of electrochemical cell potential E at constant pressure, is given by

Answer: (B)

10. For an ionic micelle-forming surfactant near its critical micelle concentration (CMC), the dependence of molar conductivity and surface tension on surfactant concentration is best represented by

Answer: (B)

11. According to Eyring transition state theory for a bimolecular reaction, the activated complex has

(A) no vibrational degrees of freedom.

(B) vibrational degrees of freedom but they never participate in product formation.

(D) one low frequency vibration that leads to product formation.

Answer: (D)

12. Based on Wade’s rule, the structure-type of [B₅H₈]^– is

(A) closo

(B) nido

(D) hypho

Answer: (B)

13. The coordination geometries around the copper ion of plastocyanin (a blue-copper protein) in oxidized and reduced form, respectively, are

(A) tetrahedral and square-planar

(B) square-planar and tetrahedral

(D) ideal tetrahedral for both

Answer: (C)

14. The water exchange rates for the complex ions follow the order

Answer: (D)

15. The lowest energy d → d transition of the complexes follow the order

Answer: (A)

16. T he symmetry label of valence p orbitals of a metal ion in an octahedral ligand field is

(A) t1_g

(B) t1_u

(D) t2_g

Answer: (B)

17. The bond angle (Ti—C—C) in the crystal structure of

is severely distorted due to

(A) hydrogen-bonding interaction

(B) agostic interaction

(D) higher formal charge on metal

Answer: (B)

18. The molar heat capacity of a substance is represented in the temperature range 298 K to 400 K by the empirical relation C_{p, m} = 14 + bT J K^–1 mol^–1, where b is a constant. The molar enthalpy change when the substance is heated from 300 K to 350 K is 2 kJ mol^–1. The value of b is___________ J K^–2 mol^–1. (Up to two decimal places)

Answer: (0.07 to 0.09)

19. For low partial pressure of ozone (O₃), the adsorption of ozone on graphite surface is fully dissociative in nature, and follows Langmuir isotherm. Under these conditions, if the dependence of the surface coverage of graphite (θ) on partial pressure of ozone (P_O3) is given by the value of x is___________. (Up to two decimal places)

Answer: (0.32 to 0.34)

20. For the radioactive isotope ¹³¹I, the time required for 50% disintegration is 8 days. The time required for the 99.9% disintegration of 5.5 g of ¹³¹I is ________ days. (Up to one decimal place)

Answer: (79.1 to 80.6)

21. Two moles of an ideal gas X and two moles of an ideal gas Y, initially at the same temperature and pressure, are mixed under isothermal-isobaric condition. The entropy change on mixing is __________J K^–1. (Up to one decimal place. Use R = 8.31 J K^–1 mol^–1)

Answer: (22.0 to 24.0)

22. The energy of a hydrogen molecule in its ground state equilibrium configuration is –31.7 eV. Its dissociation energy is _________ eV. (Up to one decimal place)

Answer: (4.4 to 4.6)

23. The total number of valence electrons in W(η³-Cp)(η⁵-Cp)(CO)₂ is ______. (Atomic number of W = 74)

Answer: (18.0 to 18.0)

24. In the 1H NMR spectrum of an organic compound recorded on a 300 MHz instrument, a proton resonates as a quartet at δ4.20 ppm. The individual signals of the quartet appear at δ4.17, 4.19, 4.21 and 4.23 ppm. The coupling constant J in Hz is ______.

Answer: (6.0 to 6.0)

25. In the electron ionization (EI) mass spectra, methyl hexanoate, methyl heptanoate and methyl octanoate give the same base peak. The m/z value of the base peak is ______.

Answer: (73.8 to 74.2)

Q. 26 – Q. 55 carry two marks each.

26. In the following reaction,

(A) X is the major product and Y is the minor product

(B) X is the only product

(D) X is the minor product and Y is the major product

Answer: (A)

27. The enantiomeric pair, among the following, is

(A)

(B)

(C)

(D)

Answer: (D)

28. The major product formed in the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (A)

29. The major product in the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (A)

30. The major product formed in the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (D)

31. The major product of the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (D)

32. The major product formed in the following retro-aldol reaction is

(A)

(B)

(C)

(D)

Answer: (B)

33. The elimination product of the following reaction is

(A) I₂

(B) CH₃I

(D) I₃^–

Answer: (C)

34. A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is Using only the first order correction, the total ground state energy of the anharmonic oscillator is

(Note: For a one-dimensional harmonic oscillator

Answer: (A)

35. The O₂ coordinated to metal ion centres in oxy-myoglobin and oxy-hemocyanin exists, respectively, as

(A) superoxide and peroxide

(B) superoxide and superoxide

(D) superoxide and oxygen

Answer: (A)

36. Spectroscopic ground state term symbols of cobalt ions in [Co(H₂O)₆]²⁺ and [CoCl₄]^2–, respectively, are

(A) ²T_1g and ^4A2

(B) ⁴T1_g and ^4A2

(D) ²T₁ and ⁴A₁

Answer: (B)

37. Generally, the coordination number and the nature of the electronic absorption band (f → f transition) of lanthanide(III) ion in their complexes are, respectively,

(A) greater than 6 and sharp

(B) 6 and broad

(D) greater than 6 and broad

Answer: (A)

38. Second-order rate constant for the reaction between [Co(NH₃)₅X]ⁿ⁺ (n = 3 for X = NH₃ and H₂O; n = 2 for X = Cl^–) and [Cr(H₂O)₆]²⁺ at room temperature varies with the X as

(A) NH₃ > H₂O > Cl^–

(B) Cl^– > H₂O > NH₃

(D) H₂O > NH₃ > Cl^–

Answer: (B)

39. For the following reaction sequence,

X and Y, respectively, are

(A) {HB(NH)}₃ and {H(OH)B(NH₂)}₃

(B) {HB(NH)}₃ and {HB(NH₂OH)}₃

(D) (NH₄){(H)₂(BH₂)₃} and {HB(NH₂OH)}₃

Answer: (A)

40. For an inverse spinel, AB2O4, the A and B, respectively, can be

(A) Ni(II) and Ga(III)

(B) Zn(II) and Fe(III)

(D) Mn(II) and Mn(III)

Answer: (A)

41. The reaction of PCl₃ with PhLi in 1:3 molar ratio yields X as one of the products, which on further treatment with CH₃I gives Y. The reaction of Y with n-BuLi gives product Z. The products X, Y and Z, respectively, are

(A) [PPh₄]Cl, [Ph₂P=CH₂] and Ph₂P(n-Bu)

(B) PPh₃, [Ph₃PI](CH₃) and Ph₂P(n-Bu)₃

(D) [PPh₄]Cl, [Ph₃P=CH₂] and [Ph₃P(n-Bu)]Li

Answer: (C)

42. The reaction of equimolar quantities of Fe(CO)5 and OH– gives a complex species X which on further reaction with MnO2 gives species Y. X and Y, respectively, are

(A) [Fe(CO)₅(OH)]^– and Fe²(CO)⁹

(B) [Fe(CO)₄]^2– and Mn₂(CO)₁₀

(D) [HFe(CO)₄]– and Fe₃(CO)₁₂

Answer: (D)

43. The rate constant of a first order reaction, X → Y is 1.6 × 10^–3 s^–1 at 300 K. Given that the activation energy of the reaction is 28 kJ mol^–1 and assuming Arrhenius behavior for the temperature dependence, the total time required to obtain 90% of Y at 350 K is_____________ s. (Up to one decimal place. Use R = 8.31 J K^–1 mol^–1 )

Answer: (280 to 300)

44. The molar conductivity of a 0.01 M weak acid (HX) at 298 K, measured in a conductivity cell with cell constant of 0.4 cm^–1, is 64.4 S cm² mol^–1. The limiting molar conductivities at infinite dilution of H+ and X– at 298 K are 350 and 410 S cm² mol^–1, respectively. Ignoring activity coefficients, the pKa of HX at 298 K is___________. (Up to two decimal places)

Answer: (4.01 to 4.21)

45. The Latimer diagram of oxygen is given below. The value of x is ________ V. (Up to two decimal places)

Answer: (1.22 to 1.24)

46. At temperature T, the canonical partition function of a harmonic oscillator with fundamental frequency (ν) is given by

For , the probability of finding the harmonic oscillator in its ground vibrational state is ________. (Up to two decimal places)

Answer: (0.93 to 0.97)

47. The enthalpy of vaporization of a liquid at its boiling point (T_b = 200 K ) is 15.3 kJ mol^–1. If the molar volumes of the liquid and the vapour at 200 K are 110 and 12000 cm³ mol^–1respectively, then the slope of the liquid-vapour boundary is _________ kPa K^–1. (Up to two decimal places. Note: 1 Pa = 1 J m^–3)

Answer: (6.20 to 6.60)

48. In a molecule XY, let Ψ_X and Ψ_Y denote normalized atomic orbitals of atoms X and Y, respectively. A normalized molecular orbital of XY is given by Ψ₊= 0.56(Ψ_X + Ψ_Y ) . The value of the overlap integral of X and Y is _________________. (Up to two decimal places)

Answer: (0.55 to 0.65)

49. The absorption maxima of two dyes X and Y are 520 and 460 nm, respectively. The absorbance data of these dyes measured in a 1 cm path length cell are given in the table below.

The concentration of Y in the mixture is __________ mM. (Up to two decimal places)

Answer: (7.4 to 8.2)

50. The π electrons in benzene can be modelled as particles in a ring that follow Pauli’s exclusion principle. Given that the radius of benzene is 1.4 Å, the longest wavelength of light that is absorbed during an electronic transition in benzene is __________ nm. (Up to one decimal place. Use me = 9.1 × 10^–31 kg, h = 6.6 × 10^–34 J s, c = 3.0 × 10⁸ ms^–1)

Answer: (210.0 to 216.0)

51. The spacing between the two adjacent lines of the microwave spectrum of H³⁵Cl is 6.35 × 10¹¹ Hz . Given that the bond length of D³⁵Cl is 5% greater than that of H³⁵Cl, the corresponding spacing for D³⁵Cl is _______ × 10¹¹ Hz (Up to two decimal places)

Answer: (2.80 to 3.10)

52. For a diatomic vibrating rotor, in vibrational level υ = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm^–1. Its equilibrium oscillation frequency is 2998.3 cm^–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm^–1. The value of J is ___________. (Up to nearest integer)

Answer: (12 to 12)

53. Number of carbonyl groups present in the final product of the following reaction sequence is ___________.

Answer: (4.0 to 4.0)

54. A tetrapeptide, made up of natural amino acids, has alanine as the N-terminal residue which is coupled to a chiral amino acid. Upon complete hydrolysis, the tetrapeptide gives glycine, alanine, phenylalanine and leucine. The number of possible sequences of the tetrapeptide is ____.

Answer: (4.0 to 4.0)

55. The strongest band observed in the IR spectrum of the final product of the following reaction appears, approximately, at ______ × 100 cm^–1. (Up to one decimal place)

Answer: (16.99 to 17.31)