Firstranker's choice
GATE 2015
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Q. 1 – Q. 25 carry one mark each.
Q.1 The following set of three vectors
and is linearly dependent when x is equal to
(A) 0 (B) 1 (C) 2 (D) 3
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Q.2 For the matrix , if is an eigenvector, the corresponding eigenvalue is
Q.3 Consider a linear ordinary differential equation: dy/dx + p(x)y = r(x). Functions p(x) and r(x) are
defined and have a continuous first derivative. The integrating factor of this equation is non-zero.
Multiplying this equation by its integrating factor converts this into a:
(A) Homogeneous differential equation (B) Non-linear differential equation
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(C) Second order differential equation (D) Exact differential equationQ.4 A complex-valued function, f(z), given below is analytic in domain D:
f(z) = u(x, y)+iv(x, y)
z = x+iy
Which of the following is NOT correct?
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(A) df/dz = du/dy + i dv/dy
(B) df/dz = dv/dy - i du/dy
(C) df/dz = du/dx + i dv/dx
(D) df/dz = dv/dy + i du/dx
Q.5 A scalar function in the xy-plane is given by (x,y) = x² + y². If i and j are unit vectors in the
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x and y directions, the direction of maximum increase in the value of 6 at (1,1) is along:(A) -2i + 2j (B) 2i + 2j
(C)-2i – 2j (D) 2i – 2j
Q.6 For a pure liquid, the rate of change of vapour pressure with temperature is 0.1 bar/K in the
temperature range of 300 to 350 K. If the boiling point of the liquid at 2 bar is 320 K, the
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temperature (in K) at which it will boil at 1 bar (up to one decimal place) isQ.7 Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T1,
P1) to a final state (T2, P2), each by a different path. Which of the following is ALWAYS TRUE for
the three systems? (? represents the change between the initial and final states; U, S, G, Q and W
are internal energy, entropy, Gibbs free energy, heat added and work done, respectively.)
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(A) ?U, ?S, Q are same (B) W, ?U, ?G are same
(C) ?S, W, Q are same (D) ?G, ?U, ?S are same
Firstranker's choice
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GATE 2015
Q.8 For a gas phase cracking reaction A ? B + C at 300°C, the Gibbs free energy of the reaction
at this temperature is ?G° = -2750 J/mol. The pressure is 1 bar and the gas phase can be assumed
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to be ideal. The universal gas constant R = 8.314 J/mol.K. The fractional molar conversion of A atequilibrium is:
(A) 0.44 (B) 0.50 (C) 0.64 (D) 0.80
Q.9 If v, u, s and g represent respectively the molar volume, molar internal energy, molar entropy
and molar Gibbs free energy, then match the entries in the left and right columns below and choose
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the correct option.P. (du/dv)s I. Temperature
Q. (?g/?p)T II. Pressure
R. - (?g/?T)P III. V
S. (du/ds)v IV. S
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(A) P-II, Q-III, R-IV, S-I (B) P-II, Q-IV, R-III, S-I
(C) P-I, Q-IV, R-II, S-III (D) P-III, Q-II, R-IV, S-I
Q.10 Two different liquids are flowing through different pipes of the same diameter. In the first pipe,
the flow is laminar with centerline velocity, Vmax,1, whereas in the second pipe, the flow is
turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, Vmax,2-
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For equal volumetric flow rates in both the pipes, the ratio Vmax,1/Vmax,2 (up to two decimalplaces) is
Q.11 For uniform laminar flow over a flat plate, the thickness of the boundary layer, d, at a distance x
from the leading edge of the plate follows the relation:
(A) d(x) ? x-1 (B) d(x) ? x
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(C) d(x) ? x1/2 (D) d(x) ? x-1/2Q.12 A cylindrical packed bed of height 1 m is filled with equal sized spherical particles. The particles
are nonporous and have a density of 1500 kg/m³. The void fraction of the bed is 0.45. The bed is
fluidized using air (density 1 kg/m³). If the acceleration due to gravity is 9.8 m/s², the pressure
drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is
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Q.13 Two infinitely large parallel plates (I and II ) are held at temperatures T1 and T? (T1 > Tm)
respectively, and placed at a distance 2d apart in vacuum. An infinitely large flat radiation shield
(III) is placed in parallel in between I and II. The emissivities of all the plates are equal. The ratio
of the steady state radiative heat fluxes with and without the shield is:
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(A) 0.5 (B) 0.75 (C) 0.25 (D) 0
Q.14 For a binary mixture of components A and B, NA and NB denote the total molar fluxes of
components A and B, respectively. JA and JB are the corresponding molar diffusive fluxes.
Which of the following is true for equimolar counter-diffusion in the binary mixture?
(A) NA+NB = 0 and JA+JB ? 0 (B) NA+NB ? 0 and JA + JB = 0
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(C) NA + NB ? 0 and JA + JB ? 0 (D) NA+NB = 0 and JA + JB = 0Q.15 Benzene is removed from air by absorbing it in a non-volatile wash-oil at 100 kPa in a counter-
current gas absorber. Gas flow rate is 100 mol/min, which includes 2 mol/min of benzene. The
flow rate of wash-oil is 50 mol/min. Vapor pressure of benzene at the column conditions is
50 kPa. Benzene forms an ideal solution with the wash-oil and the column is operating at steady
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state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates ofliquid and gas phases inside the column.
Q.16 A spherical naphthalene ball of 2 mm diameter is subliming very slowly in stagnant air at 25°C.
The change in the size of the ball during the sublimation can be neglected. The diffusivity of
naphthalene in air at 25°C is 1.1×106 m²/s.
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The value of mass transfer coefficient is B × 10³ m/s, where B (up to one decimal place) isQ.17 Which of the following can change if only the catalyst is changed for a reaction system?
(A) Enthalpy of reaction (B) Activation energy
(C) Free energy of the reaction (D) Equilibrium constant.
Q.18 For which reaction order, the half-life of the reactant is half of the full lifetime (time for 100%
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conversion) of the reactant ?(A) Zero order (B) Half order
(C) First order (D) Second order
Q.19 An irreversible, homogeneous reaction A ? products, has the rate expression:
Rate = 2CA2+0.1CA / 1+50CA
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where CA is the concentration of A.Ca varies in the range 0.5 - 50 mol/m³.
For very high concentrations of A, the reaction order tends to:
(A) 0 (B) 1 (C) 1.5 (D) 2
Q.20 Match the output signals as obtained from four measuring devices in response to a unit step
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change in the input signal.P: Gas chromatograph, with a long capillary tube
Q: Venturi tube
R: Thermocouple
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S: Pressure transducer with second order dynamics(A) P-IV, Q-III, R-II, S-I
(B) P-I, Q-II, R-III, S-IV
(C) P-IV, Q-I, R-II, S-III
(D) P-III, Q-I, R-II, S-IV
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Q.21 The transfer function for the disturbance response in an open-loop process is given by Gopen (s).
The corresponding transfer function for the disturbance response in a closed-loop feedback
control system with proportional controller is given by Gclosed (s). Select the option that is
ALWAYS correct {O[G(s)] represents order of transfer function G(s)}:
(A) O[Gopen(s)] = 0[Gclosed (s)]
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(B) O[Gopen(s)] < 0[Gclosed (s)](C) O[Gopen (s)] = O[Gclosed (s)]
(D) O[Gopen (s)] > O[Gclosed (s)]
Q.22 Identify the WRONG statement amongst the following:
(A) Steam distillation is used for mixtures that are immiscible with water.
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(B) Vacuum distillation is used for mixtures that are miscible with water.(C) Steam distillation is used for mixtures that are miscible with water.
(D) Vacuum distillation columns have larger diameters as compared to atmospheric columns for
the same throughput.
Q.23 Match the polymer mentioned on the left with the catalyst used for its manufacture given on the
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right.(I) Low density Polyethylene (P) Ziegler-Natta catalyst
(II) High density Polyethylene (Q) Traces of Oxygen
(III) Polyethylene Terephthalate (R) Butyl Lithium
(IV) Polyvinyl Chloride (S) Antimony
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(A) I-Q, II-R, III-S, IV-P (B) I-S, II-P, III-Q, IV-R
(C) I-Q, II-P, III-S, IV-R (D) I-S, II-R, III-P, IV-Q
Q.24 Match the technologies in Group 1 with the entries in Group 2:
Group 1 Group 2
P. Urea manufacture I. Microencapsulation
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Q. Coal gasification II. Ultra-low sulphur dieselR. Controlled release of chemicals III. Shale oil
S. Deep hydrodesulphurization IV. Prilling tower
V. Gas hydrates
VI. Gas-solid non-catalytic reaction
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(A) P-I, Q-V, R-II, S-VI (B) P-IV, Q-VI, R-I, S-II
(C) P-IV, Q-I, R-III, S-II (D) P-V, Q-VI, R-IV, S-II
Q.25 Match the chemicals written on the left with the raw materials required to produce them
mentioned on the right.
(I) Single Superphosphate (SSP) (P) Rock phosphate + Sulfuric Acid + Ammonia
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(II) Triple Superphosphate (TSP) (Q) Brine(III) Diammonium Phosphate (DAP) (R) Rock phosphate + Sulfuric Acid
(IV) Caustic soda (S) Rock phosphate + Phosphoric Acid
(A) I-Q, II-R, III-S, IV-P (B) I-S, II-P, III-Q, IV-R
(C) I-R, II-S, III-P, IV-Q (D) I-S, II-R, III-P, IV-Q
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Q. 26 – Q. 55 carry two marks each.
Q.26 The diameters of sand particles in a sample range from 50 to 150 microns. The number of
particles of diameter x in the sample is proportional to 1/(50+x). The average diameter, in microns,
(up to one decimal place) is
Q.27 A vector u = -2 y î + 2 x j, where î and j are unit vectors in x and y directions, respectively.
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Evaluate the line integralI = ? u·dr
C
where C is a closed loop formed by connecting points (1,1), (3,1), (3,2) and (1,2) in that order.
The value of I is
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Q.28 The solution of the non-linear equation
x³ - x = 0
is to be obtained using Newton-Raphson method. If the initial guess is x = 0.5, the method
converges to which one of the following values:
(A) -1 (B) 0 (C) 1 (D) 2
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Q.29 For complex variable z, the value of the contour integral ? e-2z/(2piz(z-3)) dz along the clockwise
contour C: |z|= 2(up to two decimal places)
Q.30 The schematic diagram of a steady state process is shown below. The fresh feed (F) to the reactor
consists of 96 mol% reactant A and 4 mol% inert I. The stoichiometry of the reaction is A ? ?.
A part of the reactor effluent is recycled. The molar flow rate of the recycle stream is 0.3 F. The
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product stream P contains 50 mol% C. The percentage conversion of A in the reactor based on Aentering the reactor at point 1 in the figure (up to one decimal place) is
Q.31 An ideal gas is initially at a pressure of 0.1 MPa and a total volume of 2 m³. It is first
compressed to 1 MPa by a reversible adiabatic process and then cooled at constant pressure to a
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final volume of 0.2 m³. The total work done (in kJ) on the gas for the entire process (up to onedecimal place) is
Data: R = 8.314 J/mol.K; heat capacity at constant pressure (Cp) = 2.5R
Q.32 Given that molar residual Gibbs free energy, gR, and molar residual volume, vR, are related as
gR = ?vR dP/RT, find gR at T = 27°C and P = 0.2 MPa. The gas may be assumed to follow the virial
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equation of state, z= 1 + BP/RT, where B = -10-4 m³/mol at the given conditions(R = 8.314 J/mol.K). The value of gk in J/mol is:
(A) 0.008 (B) -2.4 (C) 20 (D) -20
Q.33 A binary mixture of components (1) and (2) forms an azeotrope at 130°C and x1 = 0.3. The liquid
phase non-ideality is described by In ?1 = Ax2² and ln ?2 = Ax1², where ?1, ?2 are the activity
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coefficients, and x1, x2 are the liquid phase mole fractions. For both components, the fugacitycoefficients are 0.9 at the azeotropic composition. Saturated vapor pressures at 130°C are P1sat =
70 bar and P2sat = 30 bar.
The total pressure in bars for the above azeotropic system (up to two decimal places) is
Q.34 For Fanning friction factor f (for flow in pipes) and drag coefficient CD (for flow over
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immersed bodies), which of the following statements are true?P: faccounts only for the skin friction
Q: CD accounts only for the form friction
R: CD accounts for both skin friction and form friction
S: Both fand CD depend on the Reynolds number
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T: For laminar flow through a pipe, f doubles on doubling the volumetric flow rate.(A) R, S, T (B) P, Q, S (C) P, R, S (D) P, Q, S, T
Q.35 A centrifugal pump delivers water at the rate of 0.22 m³/s from a reservoir at ground level to
another reservoir at a height H, through a vertical pipe of 0.2 m diameter. Both the reservoirs are
open to atmosphere. The power input to the pump is 90 kW and it operates with an efficiency of
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75%.Data:
Fanning friction factor for pipe flow is f= 0.004. Neglect other head losses.
Take gravitational acceleration, g = 9.8 m/s² and density of water is 1000 kg/m³.
The height H, in meters, to which the water can be delivered (up to one decimal place) is
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Q.36 A typical batch filtration cycle consists of filtration followed by washing. One such filtration unit
operating at constant pressure difference first filters a slurry during which 5 liters of filtrate is
collected in 100 s. This is followed by washing, which is done for tw seconds and uses 1 liter of
wash water. Assume the following relation to be applicable between the applied pressure drop ?P,
cake thickness L at time t, and volume of liquid V collected in time t:
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?P/L = k1 dV/dt ; L = k2 V, if L is changing.k1 and k2 can be taken to be constant during filtration and washing. The wash time tw, in seconds
(up to one decimal place), is
Q.37 A spherical solid particle of 1 mm diameter is falling with a downward velocity of 1.7 mm/s
through a liquid (viscosity 0.04 Pa.s) at a low Reynolds number (Stokes regime). The liquid is
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flowing upward at a velocity of 1 mm/s. All velocities are with respect to a stationary referenceframe. Neglecting the wall effects, the drag force per unit projected area of the particle, in Pa,
(up to two decimal places) is
Q.38 In the figure below, the temperature profiles of cold and hot fluids in counter current double
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pipe heat exchangers (in different modes of operation) are shown on the left. For each case,match the heat exchange process for the fluid represented by the bold curve with the options
given on the right.
(P) Heating of sub-cooled feed to super heated vapour .
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(Q) Condensation of super heated vapour(R) Boiling of sub-cooled liquid. followed by sub-cooling
(A) I-P, II-Q, III-R, IV-S (B) I-P, II-Q, III-S, IV-R
(C) I-Q, II-P, III-S, IV-R (D) I-Q, II-S, III-P, IV-R
Q.39 A heated solid copper sphere (of surface area A and volume V) is immersed in a large body of cold
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fluid. Assume the resistance to heat transfer inside the sphere to be negligible and heat transfercoefficient (h), density (?), heat capacity (C), and thermal conductivity (k) to be constant.
Then, at time t, the temperature difference between the sphere and the fluid is proportional to:
(A) exp[ -hA/?VC t] (B) exp[ -hA/?VC t]
(C) exp[ -4pk/ ?CA t] (D) exp[-P/ PCA t]
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Q.40 Air is flowing at a velocity of 3 m/s perpendicular to a long pipe as shown in the figure below.
The outer diameter of the pipe is d = 6 cm and temperature at the outside surface of the pipe is
maintained at 100 °C. The temperature of the air far from the tube is 30 °C.
Data for air: Kinematic viscosity, v = 18×10¯º m²/s; Thermal conductivity, k = 0.03 W/(m.K)
Using the Nusselt number correlation: Nu = hd/k = 0.024×Re0.8, the rate of heat loss per unit
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length (W/m) from the pipe to air (up to one decimal place) isQ.41 Consider a solid block of unit thickness for which the thermal conductivity
decreases with an increase in temperature. The opposite faces of the block are
maintained at constant but different temperatures: T(x = 0)> T(x = 1). Heat
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transfer is by steady state conduction in x-direction only. There is no source orsink of heat inside the block. In the figure identify the correct temperature
profile in the block.
(A) I (B) II (C) III (D) IV
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Q.42 A multi-stage, counter-current liquid-liquid extractor is used to separate solute C from a binary
mixture (F) of A and C using solvent B. Pure solvent B is recovered from the raffinate R by
distillation, as shown in the schematic diagram below.
Locations of different mixtures for this process are indicated on the triangular diagram below.
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P is the solvent-free raffinate, E is the extract, F is the feed and A is the difference point fromwhich the mass balance lines originate. The line PB intersects the binodal curve at U and T.
The lines PA and FB intersect the binodal at V and W respectively.
The raffinate coming out of the extractor is represented in the diagram by the point:
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(A) T (B) U (C) V (D) WQ.43 A binary feed consisting of 25 mol% liquid and 75 mol% vapour is separated in a staged
distillation column. The mole fraction of the more volatile component in the distillate product is
0.95. The molar flow rate of distillate is 50% of the feed flow rate and the McCabe-Thiele method
can be used to analyze the column. The q-line intersects the operating line of the enriching section
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at (0.35, 0.5) on the x-y diagram. The slope of the stripping section operating line (up to onedecimal place) is
Q.44 Consider a steady state mass transfer process between well-mixed liquid and vapour phases of a
binary mixture comprising of components A and B. The mole fractions of component A in the bulk
liquid (xA) and bulk vapour (ya) phases are 0.36 and 0.16, respectively. The mass transfer
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coefficients for component A in liquid and vapour phases are 0.1 mol/(m².s) and 0.05 mol/(m².s),respectively. The vapour-liquid equilibrium can be approximated as yA = 2xA, for xA less than 0.4.
The mole fraction of A in the liquid at the interface (up to two decimal places) is
Q.45 Adsorption on activated carbon is to be used for reducing phenol concentration in wastewater
from 0.04 mol/l to 0.008 mol/l. The adsorption isotherm at the operating temperature can be
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expressed as q = 0.025C1/3 ; where q is the phenol concentration in solid (mol/g solid) and C is thephenol concentration in water (mol/l). The minimum amount of solid (in grams) required per liter
of wastewater (up to one decimal place) is
Q.46 Consider two steady isothermal flow configurations shown schematically as Case I and Case II
below. In Case I, a CSTR of volume V1 is followed by a PFR of volume V2, while in Case II a
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PFR of volume V2 is followed by a CSTR of volume V1. In each case, a volumetric flow rate Q ofliquid reactant is flowing through the two units in series. An irreversible reaction A ? products
(order n) takes place in both cases, with a reactant concentration CA0 being fed into the first unit.
Choose the correct option:
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(A) CAI/CAII> 1 for n=1(B) CAI/CAII<1 for n=1
(C) CAI/CAII= 1 for n=1
(D) CAI/CAII= 1 for n > 0
Q.47 A catalyst slab of half-thickness L (the width and length of the slab >> L)is used to conduct the
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first order reaction A ? B. At 450 K, the Thiele modulus for this system is 0.5. The activationenergy for the first order rate constant is 100 kJ/mol. The effective diffusivity of the reactant in
the slab can be assumed to be independent of temperature, and external mass transfer resistance
can be neglected. If the temperature of the reaction is increased to 470 K, then the effectiveness
factor at 470 K (up to two decimal places) will be
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Value of universal gas constant = 8.314 J/mol. K.Q.48 The impulse response to a tracer pulse experiment for a flow reactor is given below:
In the above figure, C is the exit tracer concentration. The corresponding E or Eo (normalized E)
curve is correctly represented by which of the following choices? Here, 0 is dimensionless time.
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(A)
(B)
(C)
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(D)
Q.49 An isothermal steady state mixed flow reactor (CSTR) of 1 m³ volume is used to carry out the
first order liquid-phase reaction A ? products. Fresh feed at a volumetric flow rate of Q
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containing reactant A at a concentration CAO mixes with the recycle stream at a volumetric flowrate RQ as shown in the figure below.
It is observed that when the recycle ratio R = 0.5, the exit conversion XAf= 50%. When the
recycle ratio is increased to R = 2, the new exit conversion (in percent) will be:
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(A) 50.0 (B) 54.3 (C) 58.7 (D) 63.2
Q.50 Which one of the following transfer functions, upon a unit step change in disturbance at t = 0,
will show a stable time domain response with a negative initial slope (i.e., slope at t = 0):
(A) G(s)= 1/(s+1) + 2/(s+4)
(B) G(s)= -1/(s+1) + 2/(s+4)
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(C) G(s)= 1/(s+1) + 2/(s-4)(D) G(s)= -1/(s-1) + 2/(s-4)
Q.51 The block diagram for a process with feedback control for output deviation variable h is shown in
the figure below. All transfer functions are given with pre-factor of s in minutes. A unit step change
is made in the set-point at t = 0. The time required for h to reach 50% of its ultimate value, in
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minutes (up to two decimal places), is:Q.52 Consider a control system with the open loop transfer function given by:
GOL(s) = Ke-0.3s / (1.5s +1)
In the above function, pre-factor of s is in minutes and Kis the gain of proportional controller.
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The frequency for phase margin of 30° is 4.04 rad/min. The value of K for a gain margin of 1.7(up to one decimal place) is
Q.53 The cost of two independent process variables f1 and f2 affects the total cost Cr (in lakhs
of rupees) of the process as per the following function:
CT =100 f1 +1000+20f2² +50 f1/f2
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The lowest total cost Cr, in lakhs of rupees (up to one decimal place), isQ.54 A proposed chemical plant is estimated to have a fixed capital (FC) of Rs. 24 crores. Assuming
other costs to be small, the total investment may be taken to be same as FC. After commissioning
(at t = 0 years), the annual profit before tax is Rs. 10 crores /year (at the end of each year) and the
expected life of the plant is 10 years. The tax rate is 40% per year and a linear depreciation is
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allowed at 10% per year. The salvage value is zero. If the annual interest rate is 12%, the NPV (netpresent value or worth) of the project in crores of rupees (up to one decimal place) is
Q.55 Select the WRONG statement regarding water gas shift converters from the list below.
(A) Inter-stage cooling is provided between the stages of shift converters.
(B) Usually high temperature shift (HTS) reactor has a iron-based catalyst and low
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temperature shift (LTS) reactor has a copper-based catalyst.(C) HTS reactor is followed by LTS reactor .
(D) LTS reactor is followed by HTS reactor .
END OF THE QUESTION PAPER
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