Firstranker's choice
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GATE 2016
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Q. 1 – Q. 5 carry one mark each.
Q.1 The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit.
(A) least (B) less (C) lesser (D) low
Q.2 The unruly crowd demanded that the accused be ______ without trial.
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(A) hanged (B) hanging (C) hankering (D) hung
Q.3 Choose the statement(s) where the underlined word is used correctly:
(i) A prone is a dried plum.
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(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
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(A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only
Q.4 Fact: If it rains, then the field is wet.
Read the following statements:
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(i) It rains
(ii) The field is not wet
(iii) The field is wet
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(iv) It did not rain
Which one of the options given below is NOT logically possible, based on the given fact?
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(A) If (iii), then (iv). (B) If (ii), then (iv). (C) If (i), then (ii).
Q.5 A window is made up of a square portion and an equilateral triangle portion above it. The base of
the triangular portion coincides with the upper side of the square. If the perimeter of the window is
6 m, the area of the window in m2 is _______.
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(A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88
Q. 6 – Q. 10 carry two marks each.
Q.6 Students taking an exam are divided into two groups, P and Q such that each group has the same
number of students. The performance of each of the students in a test was evaluated out of 200
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marks. It was observed that the mean of group P was 105, while that of group Q was 85. Thestandard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were
distributed on a normal distribution, which of the following statements will have the highest
probability of being TRUE?
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(A) No student in group Q scored less marks than any student in group P.
(B) No student in group P scored less marks than any student in group Q.
(C) Most students of group Q scored marks in a narrower range than students in group P.
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(D) The median of the marks of group P is 100.
Q.7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of
resources. It also uses technology to ensure safety and security of the city, something which critics
argue, will lead to a surveillance state.
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Which of the following can be logically inferred from the above paragraph?
(i) All smart cities encourage the formation of surveillance states.
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(ii) Surveillance is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a smart city.
(iv) There is a perception that smart cities promote surveillance.
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(A) (i) and (iv) only (B) (ii) only (C) (iv) only (D) (i) only
Q.8 Find the missing sequence in the letter series. B, FH, LNP, _______
(A) SUWY (B) UVW (C) TVXZ (D) TWXZ
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Q.9 The binary operation ? is defined as a ? b = ab+(a+b), where a and b are any two real numbers.
The value of the identity element of this operation, defined as the number x such that a ? x = a, for
any a, is _______.
(A) 0 (B) 1 (C) 2 (D) 10
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Q.10 Which of the following curves represents the function y = ln(|ex|sin (|x|)|) for |x| < 2p?
Here, x represents the abscissa and y represents the ordinate.
(A) [Graph A] (B) [Graph B] (C) [Graph C] (D) [Graph D]
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END OF THE QUESTION PAPER
Chemical Engineering
Q. 1 – Q. 25 carry one mark each.
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Q.1 Which one of the following is an iterative technique for solving a system of simultaneous linear
algebraic equations?
(A) Gauss elimination (B) Gauss-Jordan (C) Gauss-Seidel (D) LU decomposition
Q.2 The Laplace transform of eat sin(bt) is ______.
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(A) b / ((s-a)2+b2) (B) (s-a) / ((s-a)2+b2) (C) (s-a) / ((s-a)2-b2) (D) b / ((s-a)2-b2)
Q.3 What are the modulus (r) and argument (?) of the complex number 3+4i ?
(A) r = v7, ? = tan-1(4/3) (B) r = v7, ? = tan-1(3/4) (C) r = 5, ? = tan-1(3/4) (D) r = 5, ? = tan-1(4/3)
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Q.4 A liquid mixture of ethanol and water is flowing as inlet stream P into a stream splitter. It is split
into two streams, Q and R, as shown in the figure below.
[Diagram of stream splitter]
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The flowrate of P, containing 30 mass% of ethanol, is 100 kg/h. What is the least number of
additional specification(s) required to determine the mass flowrates and compositions (mass%) of
the two exit streams?
(A) 0 (B) 1 (C) 2 (D) 3
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Q.5 The partial molar enthalpy (in kJ/mol) of species 1 in a binary mixture is given by
h1 = 2 - 60x2 + 100x1x2, where x1 and x2 are the mole fractions of species 1 and 2,
respectively. The partial molar enthalpy (in kJ/mol, rounded off to the first decimal place) of
species 1 at infinite dilution is _______.
Q.6 For a flow through a smooth pipe, the Fanning friction factor (f) is given by f = mRe-0.2 in the
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turbulent flow regime, where Re is the Reynolds number and m is a constant. Water flowingthrough a section of this pipe with a velocity 1 m/s results in a frictional pressure drop of 10 kPa.
What will be the pressure drop across this section (in kPa), when the velocity of water is 2 m/s?
(A) 11.5 (B) 20 (C) 34.8 (D) 40
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Q.7 In a cyclone separator used for separation of solid particles from a dust laden gas, the separation
factor is defined as the ratio of the centrifugal force to the gravitational force acting on the particle.
Sr denotes the separation factor at a location (near the wall) that is at a radial distance r from the
centre of the cyclone. Which one of the following statements is INCORRECT?
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(A) Sr depends on mass of the particle (B) Sr depends on the acceleration due to gravity
(C) Sr depends on tangential velocity of the particle (D) Sr depends on the radial location (r) of the particle
Q.8 A vertical cylindrical vessel has a layer of kerosene (of density 800 kg/m³) over a layer of water (of
density 1000 kg/m³). L-shaped glass tubes are connected to the column 30 cm apart. The interface
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between the two layers lies between the two points at which the L-tubes are connected. The levels(in cm) to which the liquids rise in the respective tubes are shown in the figure below.
[Diagram of the vessel with kerosene and water levels]
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The distance (x in cm, rounded off to the first decimal place) of the interface from the point at
which the lower L-tube is connected is _______.
Q.9 A composite wall is made of four different materials of construction in the fashion shown below.
The resistance (in K/W) of each of the sections of the wall is indicated in the diagram.
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[Diagram of composite wall with resistances]
The overall resistance (in K/W, rounded off to the first decimal place) of the composite wall, in the
direction of heat flow, is _______.
Q.10 Steam at 100°C is condensing on a vertical steel plate. The condensate flow is laminar. The average
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Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 10°C and 55°C, respectively.Assume the physical properties of the fluid and steel to remain constant within the temperature
range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio
Nu2 / Nu1?
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(A) 0.5 (B) 0.84 (C) 1.19 (D) 1.41
Q.11 A binary liquid mixture of benzene and toluene contains 20 mol% of benzene. At 350 K the vapour
pressures of pure benzene and pure toluene are 92 kPa and 35 kPa, respectively. The mixture
follows Raoult's law. The equilibrium vapour phase mole fraction (rounded off to the second
decimal place) of benzene in contact with this liquid mixture at 350 K is _______.
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Q.12 Match the dimensionless numbers in Group-1 with the ratios in Group-2.
Group-1 Group-2
P Biot number I viscous force / momentum diffusivity
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Q Schmidt number II buoyancy force / internal thermal resistance of a solid
R Grashof number III mass diffusivity / boundary layer thermal resistance
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(A) P-II, Q-I, R-III (B) P-I, Q-III, R-II (C) P-III, Q-I, R-II (D) P-I, Q-II, R-III
Q.13 For what value of Lewis number, the wet-bulb temperature and adiabatic saturation temperature are
nearly equal?
(A) 0.33 (B) 0.5 (C) 1 (D) 2
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Q.14 For a non-catalytic homogeneous reaction A ? B, the rate expression at 300 K is -rA (mol m-3s-1)
= 10CA / (1+5CA), where CA is the concentration of A (in mol/m³). Theoretically, the
upper limit for the magnitude of the reaction rate (-rA in mol m-3s-1, rounded off to the first
decimal place) at 300 K is _______.
Q.15 The variations of the concentrations (CA, CR and CS) for three species (A, R and S) with time, in an
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isothermal homogeneous batch reactor are shown in the figure below.[Graph of concentrations vs time]
Select the reaction scheme that correctly represents the above plot. The numbers in the reaction
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schemes shown below, represent the first order rate constants in unit of s-1.(A) A ? R ? S (rate constants 1 and 3) (B) A ? R ? S (rate constants 3 and 3)
(C) A ? R, A ? S (rate constants 1 and 3) (D) A ? S, A ? R (rate constants 3 and 3)
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Q.16 Hydrogen iodide decomposes through the reaction 2HI ? H2 + I2. The value of the universal gas
constant R is 8.314 J mol-1K-1. The activation energy for the forward reaction is 184000 J mol-1.
The ratio (rounded off to the first decimal place) of the forward reaction rate at 600 K to that at 550
K is _______.
Q.17 Match the instruments in Group-1 with process variables in Group-2.
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Group-1 Group-2
P Conductivity meter I Flow
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Q Turbine meter II Pressure
R Piezoresistivity element III Composition
(A) P-II, Q-I, R-III (B) P-II, Q-III, R-I (C) P-III, Q-II, R-I (D) P-III, Q-I, R-II
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Q.18 What is the order of response exhibited by a U-tube manometer?
(A) Zero order (B) First order (C) Second order (D) Third order
Q.19 A system exhibits inverse response for a unit step change in the input. Which one of the following
statement must necessarily be satisfied?
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(A) The transfer function of the system has at least one negative pole (B) The transfer function of the system has at least one positive pole
(C) The transfer function of the system has at least one negative zero (D) The transfer function of the system has at least one positive zero
Q.20 Two design options for a distillation system are being compared based on the total annual cost.
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Information available is as follows:Installed cost of the system (Rs in lakhs) Option P: 150, Option Q: 120
Cost of cooling water for condenser (Rs in lakhs/year) Option P: 16, Option Q: 6
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Cost of steam for reboiler (Rs in lakhs/year) Option P: 8, Option Q: 20
The annual fixed charge amounts to 12% of the installed cost. Based on the above information,
what is the total annual cost (Rs in lakhs /year) of the better option?
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(A) 40 (B) 42.4 (C) 92 (D) 128
Q.21 Standard pipes of different schedule numbers and standard tubes of different BWG numbers are
available in the market. For a pipe / tube of a given nominal diameter, which one of the following
statements is TRUE?
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(A) Wall thickness increases with increase in both the schedule number and the BWG number (B) Wall thickness increases with increase in the schedule number and decreases with increase in the BWG number
(C) Wall thickness decreases with increase in both the schedule number and the BWG number (D) Neither the schedule nor the BWG number has any relation to wall thickness
Q.22 Terms used in engineering economics have standard definitions and interpretations. Which one of
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the following statements is INCORRECT?(A) The profitability measure ‘return on investment' does not consider the time value of money (B) A cost index is an index value for a given time showing the cost at that time relative to a certain base time
(C) The 'six-tenths factor rule' is used to estimate the cost of an equipment from the cost of a similar equipment with a different capacity (D) Payback period is calculated based on the payback time for the sum of the fixed and the working capital investment
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Q.23 India has no elemental sulphur deposits that can be economically exploited. In India, which one of
the following industries produces elemental sulphur as a by-product?
(A) Coal carbonisation plants (B) Petroleum refineries (C) Paper and pulp industries (D) Iron and steel making plants
Q.24 Two paper pulp plants P and Q use the same quality of bamboo as a raw material. The chemicals
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used in their digester are as follows:Plant P Plant Q
NaOH Yes Yes
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Na2S No Yes
Na2CO3 Yes No
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NaHCO3 No Yes
Na2SO3 Yes Yes
Which one of the following statements is CORRECT?
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(A) Plant P and Plant Q both use the Sulfite process (B) Plant P and Plant Q both use the Kraft process
(C) Plant P uses Sulfite process (D) Plant P uses Kraft process
Q.25 Match the industrial processes in Group-1, with the catalyst materials in Group-2.
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Group-1 Group-2
P Ethylene polymerisation I Nickel
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Q Petroleum feedstock cracking II Vanadium pentoxide
R Oxidation of SO2 to SO3 III Zeolite
S Hydrogenation of oil IV Aluminium triethyl with titanium chloride promoter
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(A) P-IV, Q-III, R-II, S-I (B) P-II, Q-III, R-IV, S-I (C) P-I, Q-II, R-III, S-IV (D) P-I, Q-IV, R-III, S-II
Q. 26 – Q. 55 carry two marks each.
Q.26 A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.
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[Matrix equation: 0 0 0 4 1 | 3 x1 ... = 46 ...]
The value (rounded off to the nearest integer) of x1 is _______.
Q.27 What is the solution for the second order differential equation d2y/dx2 + y = 0, with the initial
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conditions y|x=0 = 5 and dy/dx|x=0 = 10?(A) y=5+10sin x (B) y = 5 cosx-5 sin x (C) y = 5 cosx+10x (D) y = 5 cosx+10sinx
Q.28 The model y = mx2 is to be fit to the data given below.
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x 1 v2 v3
y 2 5 8
Using linear regression, the value (rounded off to the second decimal place) of m is _______.
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Q.29 The Lagrange mean-value theorem is satisfied for f(x) = x3 - x2 +5, in the interval (1,4) at a value
(rounded off to the second decimal place) of x equal to _______.
Q.30 Values of f (x) in the interval [0, 4] are given below.
x 0 1 2 3 4
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f(x) 3 10 21 36 55
Using Simpson's 1/3 rule with a step size of 1, the numerical approximation (rounded off to the
second decimal place) of ?04 f (x) dx is _______.
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Q.31 A jacketed stirred tank with a provision for heat removal is used to mix sulphuric acid and water in
a steady state flow process. H2SO4 (l) enters at a rate of 4 kg/h at 25°C and H2O (l) enters at a rate
of 6 kg/h at 10°C. The following data are available:
Specific heat capacity of water = 4.2 kJ kg-1K-1.
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Specific heat capacity of aqueous solution of 40 mass% H2SO4 = 2.8 kJ (kg solution)-1 K-1.
Assume the specific heat capacities to be independent of temperature.
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Based on reference states of H2SO4 (l) and H2O (l) at 25°C, the heat of mixing for aqueous solution
of 40 mass% H2SO4 = -650 kJ (kg H2SO4)-1.
If the mixed stream leaves at 40°C, what is the rate of heat removal (in kJ/h)?
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(A) 1802 (B) 2558 (C) 5702 (D) 6458
Q.32 An ideal gas is adiabatically and irreversibly compressed from 3 bar and 300 K to 6 bar in a closed
system. The work required for the irreversible compression is 1.5 times the work that is required for
reversible compression from the same initial temperature and pressure to the same final pressure.
The molar heat capacity of the gas at constant volume is 30 J mol-1 K-1 (assumed to be independent
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of temperature); universal gas constant, R is 8.314 J mol-1 K-1; ratio of molar heat capacities is1.277. The temperature (in K, rounded off to the first decimal place) of the gas at the final state in
the irreversible compression case is _______.
Q.33 A gas obeying the Clausius equation of state is isothermally compressed from 5 MPa to 15 MPa in
a closed system at 400 K. The Clausius equation of state is P = RT / (v-b(T)) where P is the pressure, T is
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the temperature, v is the molar volume and R is the universal gas constant. The parameter b in theabove equation varies with temperature as b(T) = b0 + b1T with b0 = 4 × 10-5 m3mol-1 and
b1 = 1.35 × 10-7 m3mol-1K-1. The effect of pressure on the molar enthalpy (h) at a constant
temperature is given by (?h/?P)T = -(T(?v/?T)P-v).
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Let hi and hf denote the initial and final molar
enthalpies, respectively. The change in the molar enthalpy hf – hi (in J mol-1, rounded off to the
first decimal place) for this process is _______.
Q.34 A binary system at a constant pressure with species '1' and '2' is described by the two-suffix
Margules equation, gE/RT = 3x1x2, where gE is the molar excess Gibbs free energy, R is the universal
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gas constant, T is the temperature and x1, x2 are the mole fractions of species 1 and 2, respectively.At a temperature T, g1 = 1 and g2 = 2, where g1 and g2 are the molar Gibbs free energies of pure
species 1 and 2, respectively. At the same temperature, g represents the molar Gibbs free energy of
the mixture. For a binary mixture with 40 mole % of species 1, the value (rounded off to the
second decimal place) of g / RT is _______.
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Q.35 Water (density=1000 kg m-3) is pumped at a rate of 36 m³/h, from a tank 2 m below the pump, to an
overhead pressurized vessel 10 m above the pump. The pressure values at the point of suction from
the bottom tank and at the discharge point to the overhead vessel are 120 kPa and 240 kPa,
respectively. All pipes in the system have the same diameter. Take acceleration due to gravity,
g = 10 m s-2. Neglecting frictional losses, what is the power (in kW) required to deliver the fluid?
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(A) 1.2 (B) 2.4 (C) 3.6 (D) 4.8
Q.36 An agitated cylindrical vessel is with baffles and flat blade impellers. The power number for
this system is given by Np = P / (?n3D5) where P is the power consumed for the mixing, ? is the
density of the fluid, n is the speed of the impeller and D is the diameter of the impeller. The
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diameter of the impeller is 1/3rd the diameter of the tank and the height of liquid level is equal to thetank diameter. The impeller speed to achieve the desired degree of mixing is 4 rpm. In a scaled up
design, the linear dimensions of the equipment are to be doubled, holding the power input per unit
volume constant. Assuming the liquid to be Newtonian and Np to be independent of Reynolds
number, what is the impeller speed (in rpm) to achieve the same degree of mixing in the scaled up
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vessel?(A) 0.13 (B) 1.26 (C) 2.52 (D) 3.82
Q.37 Consider a rigid solid sphere falling with a constant velocity in a fluid. The following data are
known at the conditions of interest: viscosity of the fluid = 0.1 Pa s, acceleration due to gravity
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= 10 m s-2, density of the particle = 1180 kg m-3 and density of the fluid = 1000 kg m-3. The diameter(in mm, rounded off to the second decimal place) of the largest sphere that settles in the Stokes' law
regime (Reynolds number = 0.1), is _______.
Q.38 The characteristics curve (Head – Capacity relationship) of a centrifugal pump is represented by the
equation ?Hpump = 43.8 – 0.19Q, where ?Hpump is the head developed by the pump (in m) and
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Q is the flowrate (in m³/h) through the pump. This pump is to be used for pumping water through ahorizontal pipeline. The frictional head loss ?Hpiping (in m) is related to the water flowrate Q1 (in
m³/h) by the equation ?Hpiping = 0.0135Q12 + 0.045Q1. The flowrate (in m³/h, rounded off to the
first decimal place) of water pumped through the above pipeline, is _______.
Q.39 Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, the
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velocity varies linearly with the distance from the wall. The Fanning friction factor is defined as,f = tw / (?u2/2) where tw is the shear stress at the wall of the pipe, ? is the density of the fluid and u is
the average velocity in the pipe. Water (density = 1000 kg m-3, viscosity = 1×10-3 kg m-1 s-1) flows
at an average velocity of 1 m s-1 through the pipe. For this flow condition, the friction factor f is
0.005. At a distance of 0.05 mm from the wall of the pipe (in the viscous sub-layer), the velocity (in
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m s-1, rounded off to the third decimal place), is _______.Q.40 In a 1-1 pass shell and tube exchanger, steam is condensing in the shell side at a temperature (Ts) of
135°C and the cold fluid is heated from a temperature (T1) of 20°C to a temperature (T2) of 90°C.
The energy balance equation for this heat exchanger is
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UA = mcp ln((Ts-T1)/(Ts-T2)) where U is the overall heat transfer coefficient, A is the heat transfer area, m is the mass flow rate
of the cold fluid and cp is its specific heat. Tube side fluid is in a turbulent flow and the heat
transfer coefficient can be estimated from the following equation:
Nu = 0.023 (Re)0.8 (Pr)1/3
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where Nu is the Nusselt number, Re is the Reynolds number and Pr is the Prandtl number. The
condensing heat transfer coefficient in the shell side is significantly higher than the tube side heat
transfer coefficient. The resistance of the wall to heat transfer is negligible. If only the mass flow
rate of the cold fluid is doubled, what is the outlet temperature (in °C) of the cold fluid at steady
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state?(A) 80.2 (B) 84.2 (C) 87.4 (D) 88.6
Q.41 In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth
plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these
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temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil doesnot vary perceptibly in this temperature range. Consider four experiments at steady state under
different experimental conditions, as shown in the figure below. The figure shows plate
temperatures and the heat fluxes in the vertical direction.
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[Diagrams for Experiment 1, Experiment 2, Experiment 3, Experiment 4 with temperatures and heat fluxes]
What is the steady state heat flux (in W m-2) with the top plate at 70°C and the bottom plate at
40°C?
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(A) 26 (B) 39 (C) 42 (D) 63
Q.42 The space between two hollow concentric spheres of radii 0.1 m and 0.2 m is under vacuum.
Exchange of radiation (uniform in all directions) occurs only between the outer surface (S1) of the
smaller sphere and the inner surface (S2) of the larger sphere. The fraction (rounded off to the
second decimal place) of the radiation energy leaving S2, which reaches S1 is _______.
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Q.43 A binary distillation column is to be designed using McCabe Thiele method. The distillate contains
90 mol% of the more volatile component. The point of intersection of the q-line with the
equilibrium curve is (0.5, 0.7). The minimum reflux ratio (rounded off to the first decimal place) for
this operation is _______.
Q.44 Solute C is extracted in a batch process from its homogenous solution of A and C, using solvent B.
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The combined composition of the feed and the extracting solvent is shown in the figure below aspoint M, along with the tie line passing through it. The ends of the tie line are on the equilibrium
curve.
[Diagram of triangular diagram for extraction process]
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What is the selectivity for C?
(A) 3.5 (B) 7 (C) 10.5 (D) 21
Q.45 At 30°C, the amounts of acetone adsorbed at partial pressures of 10 and 100 mmHg are 0.1 and 0.4
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kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes the adsorptionof acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kg of activated
carbon) at a partial pressure of 50 mmHg and 30°C?
(A) 0.23 (B) 0.25 (C) 0.30 (D)0.35
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Q.46 Consider the following two cases for a binary mixture of ideal gases A and B under steady state
conditions. In Case 1, the diffusion of A occurs through non-diffusing B. In Case 2, equimolal
counter diffusion of A and B occurs. In both the cases, the total pressure is 100 kPa and the partial
pressures of A at two points separated by a distance of 10 mm are 10 kPa and 5 kPa. Assume that
the Fick's first law of diffusion is applicable. What is the ratio of molar flux of A in Case 1 to that
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in Case 2?(A) 0.58 (B) 1.08 (C) 1.58 (D) 2.18
Q.47 The liquid phase reversible reaction A ? B is carried out in an isothermal CSTR operating under
steady state conditions. The inlet stream does not contain B and the concentration of A in the inlet
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stream is 10 mol/lit. The concentrations of A at the reactor exit, for residence times of 1 s and 5 sare 8 mol/lit and 5 mol/lit, respectively. Assume the forward and backward reactions are
elementary following the first order rate law. Also assume that the system has constant molar
density. The rate constant of the forward reaction (in s-1, rounded off to the third decimal place)
is _______.
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Q.48 A liquid phase irreversible reaction A ? B is carried out in an adiabatic CSTR operating under
steady state conditions. The reaction is elementary and follows the first order rate law. For this
reaction, the figure below shows the conversion (XA) of A as a function of temperature (T) for
different values of the rate of reaction (-rA in mol m-3s-1 ) denoted by the numbers to the left of
each curve. This figure can be used to determine the rate of the reaction at a particular temperature,
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for a given conversion of A.[Graph of Conversion vs Temperature for different rates of reaction]
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