**GATE-2023**

**CH: Chemical Engineering**

**GA-General Aptitude**

**Q.1 – Q.5 Carry ONE mark each.**

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(C) you’re

(D) yore

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(C) Cite

(D) Plagiarise

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(C) 9/2

(D) 35/4

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(C) All Fields medalists are part-time poets.

(D) Some Fields medalists have dropped out of college.

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

(A) 3

(B) 4

(C) 5

(D) 6

**Q.6 – Q.10 Carry TWO marks Each**

6. Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(C) only (i) and (ii)

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

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(C) 800

(D) 200

8. The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sri Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households.

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(C) According to the World Bank, Sri Lanka does not yet have an adequate macroeconomic policy framework.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

9. The coefficient of x^{4} in the polynomial (x − 1)^{3 }(x − 2)^{3} is equal to _______.

(A) 33

(B) −3

(C) 30

(D) 21

10. Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

(A) circle

(B) regular octagon

(C) regular pentagon

(D) rhombus

**CH: Chemical Engineering**

**Q.11 – Q.35 Carry ONE mark Each**

11. Which one of the following is the CORRECT value of y, as defined by the expression given below?

(A) 1

(B) 2

(C) 0

(D) ∞

12. The vector is defined as

Which one of the following is the CORRECT value of divergence of evaluated at the point (x, y, z) = (3, 2, 1)?

(A) 0

(B) 3

(C) 14

(D) 13

13. Given that

where z_{1} = 2 + 3i and z_{2} = −2 + 3i with i = √−1, which one of the following options is CORRECT?

(A) F < 0

(B) F < 1

(C) F > 1

(D) F = 1

14. For a two-dimensional plane, the unit vectors, of the polar coordinate system and of the Cartesian coordinate system, are related by the following two equations.

Which one of the following is the CORRECT value of

(A) 1

(B)

(C)

(D)

15. Which one of the following statements related to octane number is NOT correct?

(A) Linear alkanes with higher carbon number have higher octane number.

(B) Branching in linear alkanes increases their octane number.

(C) Catalytic reforming of hydrocarbons increases their octane number.

(D) Gasoline quality is measured in terms of octane number.

16. Which one of the following options represents the major components of oleum?

(A) Sulfuric acid and nitric acid

(B) Concentrated sulfuric acid and petroleum jelly

(C) Sulfuric acid and hydrochloric acid

(D) Sulfuric acid and sulfur trioxide

17. For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, K is the thermodynamic equilibrium constant. Which one of the following figures shows the CORRECT dependence of K on temperature T?

18. Nitrile rubber is manufactured via polymerization process. Which one of the following options is the CORRECT pair of monomers used in this process?

(A) Acrylonitrile and styrene

(B) Acrylonitrile and butadiene

(C) Butadiene and styrene

(D) Butadiene and isoprene

19. John and Jane independently performed a thermodynamic experiment, in which X and Y represent the initial and final thermodynamic states of the system, respectively. John performed the experiment under reversible conditions, for which the change in entropy of the system was ∆S_{rev}. Jane performed the experiment under irreversible conditions, for which the change in entropy of the system was ∆S_{irr}. Which one of the following relationships is CORRECT?

(A) ∆S_{rev} = ∆S_{irr}

(B) ∆S_{rev} > ∆S_{irr}

(C) ∆S_{rev} < ∆S_{irr}

(D) ∆S_{rev} = 2∆S_{irr}

20. For a packed-bed comprising of uniform-sized spherical particles of diameter D_{p}, the pressure drop across the bed is given by the Kozeny-Carman equation when the particle Reynolds number (Rep) < 1. Under this condition, minimum fluidization velocity is proportional to D_{p}^{n}. Which one of the following is the CORRECT value of exponent n?

(A) 2

(B) −1

(C) −2

(D) 1

21. Match the quantities in Group 1 with their units in Group 2 listed in the table below.

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

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

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

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

22. A slab of thickness L, as shown in the figure below, has cross-sectional area A and constant thermal conductivity k. T_{1} and T_{2} are the temperatures at x = 0 and x = L, respectively. Which one of the following options is the CORRECT expression of the thermal resistance for steady-state one-dimensional heat conduction?

(A) L/kA

(B) k/LA

(C)

(D) A/Lk

23. Spray dryers have many advantages. Which one of the following is NOT an advantage of a typical spray dryer?

(A) Has short drying time

(B) Produces hollow spherical particles

(C) Has high heat efficiency

(D) Is suitable for heat sensitive materials

24. Which one of the following quantities of a flowing fluid is measured using a rotameter?

(A) Static pressure

(B) Dynamic pressure

(C) Volumetric flow rate

(D) Viscosity

25. A liquid surge tank has F_{in} and F_{out} as the inlet and outlet flow rates respectively, as shown in the figure below. F_{out} is proportional to the square root of the liquid level ℎ. The cross-sectional area of the tank is 20 cm^{2}. Density of the liquid is constant everywhere in the system. At steady state, F_{in }= F_{out} =10 cm^{3}s^{−1} and h = 16 cm. The variation of h with F_{in} is approximated as a first order transfer function. Which one of the following is the CORRECT value of the time constant (in seconds) of this system?

(A) 20

(B) 32

(C) 64

(D) 128

26. A packed distillation column, with vapor having an average molecular weight of 45 kg.kmol^{−1}, density of 2 kg.m^{−3} and a molar flow rate of 0.1 kmol.s^{−1}, has a flooding velocity of 0.15 m.s^{−1}. The column is designed to operate at 60 % of the flooding velocity. Which one of the following is the CORRECT value for the column diameter (in m)?

(A) 5/√π

(B) 5√π

(C) 4π

(D) 10/√π

27. An isothermal jacketed continous stirred tank reactor (CSTR) operating at 150°C is shown in the figure below. The cold feed entering the system at 30 oC is preheated to a temperature T (T < 150°C) using a heat exchanger HX_{1}. This preheated feed is further heated to 150°C using the utility heater HX_{2}. The mass flow rate and heat capacity are same for all the process streams, and the overall heat transfer coefficient is independent of temperature. Which one of the following statements is the CORRECT action to take if it is desired to increase the value of T?

(A) Increase both heat transfer area of HX_{1} and heat duty of HX_{2}.

(B) Decrease both heat transfer area of HX_{1} and heat duty of HX_{2}.

(C) Increase the heat transfer area of HX_{1} and decrease the heat duty of HX_{2}.

(D) Decrease the heat transfer area of HX_{1} and increase the heat duty of HX_{2}.

28. Consider a system where a Carnot engine is operating between a source and a sink. Which of the following statements about this system is/are NOT correct?

(A) This engine is reversible.

(B) The engine efficiency is independent of the source and sink temperatures.

(C) This engine has the highest efficiency among all engines that operate between the same source and sink.

(D) The total entropy of this system increases at the completion of each cycle of the engine.

29. For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, which of the following statements is/are CORRECT?

(A) Reynolds stress, averaged over a sufficiently long time, is zero everywhere inside the pipe.

(B) Reynolds stress at the pipe wall is zero.

(C) Average velocity of the fluid is half of its center-line velocity.

(D) Average pressure gradient in the flow direction is constant.

30. Given that E (in W.m^{−2}) is the total hemispherical emissive power of a surface maintained at a certain temperature, which of the following statements is/are CORRECT?

(A) E does not depend on the direction of the emission.

(B) E depends on the viewfactor.

(C) E depends on the wavelength of the emission.

(D) E does not depend on the frequency of the emission.

31. The position x(t) of a particle, at constant ω, is described by the equation

The initial conditions are x(t = 0) = 1 and The position of the particle at t = (3π/ω) is __________ (in integer).

32. Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and water vapor. Methane is fed to the combustor at 100 mol.hr^{−1}, of which 50 % reacts. The theoretical oxygen requirement (in mol.hr^{−1}) is ________ (rounded off to one decimal place).

33. The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter 0.5 mm and length 1.5 m. The fluid flow is laminar, steady and fully developed. For a flow rate of 1 cm^{3}s^{−1}, the pressure drop across the length of the tube is 1 MPa. If the viscosity of the fluid is k × 10^{−}^{3}s, the value of k is ___________ (rounded off to two decimal places).

34. A liquid L containing a dissolved gas S is stripped in a countercurrent operation using a pure carrier gas V. The liquid phase inlet and outlet mole fractions of S are 0.1 and 0.01, respectively. The equilibrium distribution of S between V and L is governed by ye = xe, where ye and xe are the mole fractions of S in V and L, respectively. The molar feed rate of the carrier gas stream is twice as that of the liquid stream. Under dilute solution conditions, the minimum number of ideal stages required is __________ (in integer).

35. In a binary gas-liquid system, N_{A,EMD} is the molar flux of a gas A for equimolar counter diffusion with a liquid B. N_{A,UMD} is the molar flux of A for steady one-component diffusion through stagnant B. Using the mole fraction of A in the bulk of the gas phase as 0.2 and that at the gas-liquid interface as 0.1 for both the modes of diffusion, the ratio of N_{A,UMD} to N_{A,EMD} is equal to ______ (rounded off to two decimal places).

**Q.36 – Q.65 Carry TWO marks Each**

36. An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons X and Y entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?

(A) 5/9

(B) 4/9

(C) 2/9

(D) 7/9

37. Simpson’s one-third rule is used to estimate the definite integral

with an interval length of 0.5. Which one of the following is the CORRECT estimate of I obtained using this rule?

38. Match the products in Group 1 with the manufacturing processes in Group 2 listed in the table below.

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

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

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

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

39. Match the reactions in Group 1 with the catalysts in Group 2 listed in the table below.

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

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

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

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

40. Water in a container at 290 K is exposed to air containing 3 % CO_{2} by volume. Air behaves like an ideal gas and is maintained at 100 kPa pressure. The liquid phase comprising of dissolved CO_{2} in water behaves like an ideal solution. Use Henry’s constant of CO_{2} dissolved in water at 290 K as 12 MPa. Under equilibrium conditions, which one of the following is the CORRECT value of the mole fraction of CO_{2} dissolved in water?

(A) 2.9 × 10^{−}^{4}

(B) 0.9 × 10^{−}^{4}

(C) 2.5 × 10^{−}^{4}

(D) 0.5 × 10^{−}^{4}

41. The enthalpy (H, in J.mol^{−1}) of a binary liquid system at constant temperature and pressure is given as

H = 40x_{1} + 60x_{2} + x_{1}x_{2}(4x_{1} + 2x_{2}),

where x_{1} and x_{2} represent the mole fractions of species 1 and 2 in the liquid, respectively. Which one of the following is the CORRECT value of the partial molar enthalpy of species 1 at infinite dilution,

(A) 100

(B) 42

(C) 64

(D) 40

42. Which one of the following represents the CORRECT effects of concentration polarization in a reverse osmosis process?

(A) Reduced water flux and reduced solute rejection

(B) Increased water flux and increased solute rejection

(C) Reduced water flux and increased solute rejection

(D) Increased water flux and reduced solute rejection

43. CO and H_{2} participate in a catalytic reaction. The partial pressures (in atm) of the reacting species CO and H_{2} in the feed stream are p_{CO} and p_{H2}, respectively. While CO undergoes molecular adsorption, H_{2} adsorbs via dissociative adsorption, that is, as hydrogen atoms. The equilibrium constants (in atm^{−1}) corresponding to adsorption of CO and H_{2} to the catalyst sites are KCO and KH_{2}, respectively. Total molar concentration of active sites per unit mass of the catalyst is Ct (in mol.(g cat)^{−1}). Both the adsorption steps are at equilibrium. Which one of the following expressions is the CORRECT ratio of the concentration of catalyst sites occupied by CO to that by hydrogen atoms?

44. A cascade control strategy is shown in the figure below. The transfer function between the output (y) and the secondary disturbance (d_{2}) is defined as

Which one of the following is the CORRECT expression for the transfer function G_{d2}(s)?

45. Level (h) in a steam boiler is controlled by manipulating the flow rate (F) of the make-up (fresh) water using a proportional (P) controller. The transfer function between the output and the manipulated input is

The measurement and valve transfer functions are both equal to 1. A process engineer wants to tune the controller so that the closed-loop response gives decaying oscillations under servo mode. Which one of the following is the CORRECT value of the controller gain to be used by the engineer?

(A) 0.25

(B) 2

(C) 4

(D) 6

46. Which of the following statements is/are CORRECT?

(A) Bond number includes surface tension.

(B) Jakob number includes latent heat.

(C) Prandtl number includes liquid-vapor density difference.

(D) Biot number includes gravity.

47. If a matrix M is defined as the sum of all the eigenvalues of M^{3} is equal to ________ (in integer).

48. The first derivative of the function evaluated at r = 1 is ________ (in integer).

49. Wet air containing 10 mole percent water vapor is dried by continuously passing it through a column of CaCl_{2} The pellets remove 50 percent of water from wet air entering the column. The mole percent of water vapor in the product stream exiting the column is ___________ (rounded off to two decimal places).

50. Orsat analysis showing the composition (in mol %, on a dry basis) of a stack gas is given in the table below. The humidity measurement reveals that the mole fraction of H_{2}O in the stack gas is 0.07. The mole fraction of N_{2} calculated on a wet basis is ________ (rounded off to two decimal places).

51. A pump draws water (density =1000 kg.m^{−3}) at a steady rate of 10 kg.s^{−1}. The pressures at the suction and discharge sides of the pump are −20 kPa (gauge) and 350 kPa (gauge), respectively. The pipe diameters at the suction and discharge side are 70 mm and 50 mm, respectively. The suction and discharge lines are at the same elevation, and the pump operates at an efficiency of 80 %. Neglecting frictional losses in the system, the power (in kW) required to drive the pump is ______ (rounded off to two decimal places).

52. A cylindrical tank with a diameter of 500 mm contains water (density =1 g.cm^{−3}) upto a height ℎ. A 5 mm diameter round nozzle, whose center is 1 cm above the base of the tank, has its exit open to the atmosphere as shown in the schematic below. The pressure above the water level in the tank is maintained at 2 bar (absolute). Neglect all frictional and entry/exit losses. Use acceleration due to gravity as 10 m.s^{−2} and atmospheric pressure as 1 bar. The absolute value of initial when h = 51 cm is equal to _______ (round off to two decimal places).

53. A large tank is filled with water (density =1 g.cm^{−3}) upto a height of 5 m. A 100 μm diameter solid spherical particle (density =0.8 g.cm^{−3}) is released at the bottom of the tank. The particle attains its terminal velocity (v_{t}) after traveling to a certain height in the tank. Use acceleration due to gravity as 10 m.s^{−2} and water viscosity as 10^{−3}s . Neglect wall effects on the particle. If Stokes law is applicable, the absolute value of v_{t} (in mm.s^{−1}) is ____________ (rounded off to two decimal places).

54. A fluid is flowing steadily under laminar conditions over a thin rectangular plate at temperature T_{s} as shown in the figure below. The velocity and temperature of the free stream are u_{∞} and T_{∞}, respectively. When the fluid flow is only in the x- direction, h_{x} is the local heat transfer coefficient. Similarly, when the fluid flow is only in the y-direction, h_{y} is the corresponding local heat transfer coefficient. Use the correlation Nu = 0.332 (Re)^{1/2} (Pr)^{1/3} for the local heat transfer coefficient, where, Nu, Re, and Pr, respectively are the appropriate Nusselt, Reynolds and Prandtl numbers. The average heat transfer coefficients are defined as and If w = 1 m and l = 4 m, the value of the ratio of is ________ (in integer).

55. A perfectly insulated, concentric tube countercurrent heat exchanger is used to cool lubricating oil using water as a coolant (see figure below). Oil enters the outer annulus at a mass flow rate of 2 kg.s^{−1} with a temperature of 100°C and leaves at 40° Water enters the inner tube at a mass flow rate of 1 kg.s−1 with a temperature of 20°C and leaves at 80°C. Use specific heats of oil and water as 2089 J.kg^{−1}K^{−1} and 4178 J.kg^{−1}K^{−1}, respectively. There is no phase change in both the streams. Under steady-state conditions, the number of transfer units (NTU) is _______ (in integer).

56. Partially saturated air at 1 bar and 50°C is contacted with water in an adiabatic saturator. The air is cooled and humidified to saturation, and exits at 25°C with an absolute humidity of 0.02 kg water per kg dry air. Use latent heat of vaporization of water as 2450 kJ.kg^{−1}, and average specific heat capacity for dry air and water, respectively as 1.01 kJ.kg^{−1}K^{−1} and 4.18 kJ.kg^{−1}K^{−1}. If the absolute humidity of air entering the adiabatic saturator is H × 10^{−}^{3} kg water per kg dry air, the value of H is __________ (rounded off to two decimal places).

57. Distillation of a non-reactive binary mixture with components A and B is carried out in a batch still as shown in the figure below. The initial charge of the mixture in the still is 1 kmol. The initial and final amounts of 𝐴 in the still are 0.1 kmol and 0.01 kmol, respectively. Use a constant relative volatility of 4.5. The mole fraction of 𝐵 remaining in the vessel is _______ (rounded off to three decimal places).

58. Fresh catalyst is loaded into a reactor before the start of the following catalytic reaction.

**A ****→**** products**

The catalyst gets deactivated over time. The instantaneous activity a(t), at time t, is defined as the ratio of the rate of reaction −rꞌ_{A}(t) (mol.(g cat)^{−}^{1}hr^{−}^{1}) to the rate of reaction with fresh catalyst. Controlled experimental measurements led to an empirical correlation

−rꞌ_{A}(t) = −0.5t + 10

where t is in hours. The activity of the catalyst at t = 10 hr is _______ (rounded off to one decimal place).

59. A unimolecular, irreversible liquid-phase reaction

**A ****→ ****P**

was carried out in an ideal batch reactor at temperature T. The rate of the reaction (−r_{A}) measured at different conversions X_{A} is given in the table below. This reaction is also carried out in an ideal continuous stirred tank reactor (CSTR) at the same temperature T with a feed concentration of 1 mol.m^{−3}, under steady-state conditions. For a conversion of 0.8, the space time (in s) of the CSTR is __________ (in integer).

60. An irreversible liquid-phase second-order reaction with rate constant k = 0.2 liter.mol^{−1}min^{−1}, is carried out in an isothermal non-ideal reactor. A tracer experiment conducted on this reactor resulted in a residence time distribution (𝐸-curve) as shown in the figure below. The areas of the rectangles (i), (ii), and (iii) are equal. Pure A at a concentration of 1.5 mol.liter^{−1} is fed to the reactor. The segregated model mimics the nonideality of this reactor. The percentage conversion of A at the exit of the reactor is ______ (rounded off to the nearest integer).

61. The outlet concentration C_{A} of a plug flow reactor (PFR) is controlled by manipulating the inlet concentration C_{A0}. The following transfer function describes the dynamics of this PFR.

In the above equation, V = 1 m^{3}, F = 0.1 m^{3}min^{−}^{1} and k = 0.5 min^{−}^{1}. The measurement and valve transfer functions are both equal to 1. The ultimate gain, defined as the proportional controller gain that produces sustained oscillations, for this system is _______ (rounded off to one decimal place).

62. The transfer function of a measuring instrument is

At time t = 0, a step change of +1 unit is introduced in the input of this instrument. The time taken by the instrument to show an increase of 1 unit in its output is _____ (rounded off to two decimal places).

63. A design engineer needs to purchase a membrane module (M) for a plant. Details about the two available options, M1 and M2, are given in the table below. The overall plant has an expected life of 7 years. If the interest rate is 8 % per annum, compounded annually, the difference in the net present value (NPV) of these two options, in lakhs of rupees, is ______ (rounded off to one decimal place).

64. The purchase cost of a new distillation column is Rs.10 lakhs with an installation factor of 5.8. The cost of the capital is to be annualized over a period of 6 years at a fixed rate of interest of 5 % per annum, compounded annually. The annual cost (in lakhs of rupees) of the installed capital is _______ (rounded off to one decimal place).

65. Pumps A and B are being considered for purchase in a chemical plant. Cost details for these two pumps are given in the table below. The interest rate is 10 % per annum, compounded annually. For both the pumps to have the same capitalized cost, the salvage value (in Rs.) of pump B should be ______ (rounded off to the nearest integer).

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