3) The system of linear equations Ax = 0, where A is an n � n matrix, has a non-trivial solution ONLY if
(A) rank of A > n
(B) rank of A = n
(C) rank of A < n.
(D) A is an identity matrix
4) A dehumidifier (shown below) is used to completely remove water vapor from air.
Which ONE of the following statements is TRUE ?
A. Water is the ONLY tie component
B. Air is the ONLY tie component,
C. BOTH water and air are the components
D. There are NO tie components
5) Dehydrogenation of ethane, C2H6 (g) �C2H4 (g) + H2 (g), is carried out in a continuous stirred tank reactor (CSTR). The feed is pure ethane. If the reactor exit stream contains unconverted ethane along with the products, then the number of degrees of freedom for the CSTR is
(A) 1,
(B) 2,
(C) 3,
(D) 4
6) An ideal gas at temperature T1 and pressure P1 is compressed isothermally to pressure P2 (> P1) in a closed system. Which ONE of the following is TRUE for internal energy (U) and Gibbs free energy (G) of the gas at the two states ?
(A) U1 = U2, G1 > G2
(B) U1 = U2, G1 < G2
(C) U1 > U2, G1 = G2
(D) U1 < U2, G1 = G2
7) Under fully turbulent flow conditions, the frictional pressure drop across a packed bed varies with the superficial velocity (V) of the fluid as
(A) V -1
(B) V
(C) V 3/2
(D) V 2
8) For a mixing tank operating in the laminar regime, the power number varies with the Reynolds number (Re) as
(A) Re �1/2
(B) Re 1/2
(C) Re
(D) Re -1
9) During the transient convective cooling of a solid object, Biot number�0 indicates.
A. Uniform temperature throughout the object
B. Negligible convection at the surface of the object
C. Significant thermal resistance within the object
D. Significant temperature gradient within the object
10) The Prandtl number of a fluid is the ratio of
A. Thermal diffusivity to momentum diffusivity
B. Momentum diffusivity to thermal diffusivity
C. Conductive resistance to convective resistance
D. Thermal diffusivity to kinematic diffusivity
11) According to the penetration theory of mass transfer, the mass transfer coefficient (k) varies with diffusion coefficient (D) of the diffusing species as
(A) D
(B) D -1/2
(C) D 1/2
(D) D 3/2
12) The ratio of the liquid to gas flow rate in a counter-current gas absorption column is increased at otherwise identical conditions. Which ONE of the following statements is TRUE ?
A. The operating line shifts towards the equilibrium curve
B. The operating line shifts away from the equilibrium curve
C. The concentration of the absorbed species increases in the exit liquid stream
D. The operating line dies not shift.
13) For a homogeneous reaction system, where
Cj is the concentration of j at time t
Nj is the number of moles of j at time t
V is the reaction volume at time t
t is the reaction time.
The rate of reaction for species j is defined as
(A) (B) (C) (D)
14) The half-life of a first order liquid phase reaction is 30 seconds. Then the rate constant, in min-1, is
(A) 0.0231
(B) 0.602
(C) 1.386
(D) 2.0
15) For a solid-catalyzed reaction, the Thiele modulus is proportional to
16) Which ONE of the following sensors is used for the measurement of temperature in a combustion process (T > 1800�C) ?
(A) Type J thermocouple,
(B) Thermistor
(C) Resistance temperature detector,
(D) Pyrometer.
18) The total fixed cost of a chemical plant is Rs. 10.0 lakhs; the internal rate of return is 15% and the annual operating cost is Rs. 2.0 lakhs. The annualized cost of the plant (in lakhs of Rs.) is
(A) 1.8
(B) 2.6
(C) 3.5
(D) 4.3
19) In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics is
(A) Catalytic reforming
(B) Catalytic cracking
(C) Hydrocarcking,
(D) Alkylation.
20) The active component of catalysts used in steam reforming of methane to produce synthesis gas is
(A) Nickel
(B) Iron
(C) Platinum
(D) Palladium
Q. 21 to Q. 60 carry two marks each.
21) The value of the limit �is
(A) �∞
(B) 0
(C) 1
(D) ∞
22) The general solution of the differential equation �
= 0,
with C1 and C2 as constants of integration, is
(A) C1 e-3x + C2 e-2x
(B) C1 e3x + C2 e-2x
(C) C1 e3x + C2 e2x
(D) C1 e-3x + C2 e2x
23) Using the residue theorem, the value of the integral (counter clockwise)
around a circle with center at z = 0 and radius = 8 (where z is a complex number and i = ), is
(A) � 20π i
(B) � 40π
(C) � 40π i
(D) 40π i
24) Consider the integral,
over the surface of a sphere of radius = 3 with center at the origin and surface unit normal n pointing away from the origin. Using the Gauss divergence theorem, the value of this integral is
(A) � 180π
(B) 0
(C) 90π
(D) 180π
25) Using the trapezoidal rule and 4 equal intervals (n = 4), the calculated value of the integral (rounded to the first place of decimal)
1 is
(A) 1.7
(B) 1.9
(C) 2.0
(D) 2.1
26) The eigenvalues of matrix are 5 and �1. Then the eigenvalues of �2A + 3I (I is a 2 x 2 identity matrix) are
(A) �7 and 5
(B) 7 and �5
(C) and (D)
27) A fair die is rolled. Let R denote the event of obtaining a number less than or equal to 5 and S denote the event of obtaining an odd number. Then which ONE of the following about the probability (P) is TRUE ?
(A) P(R/S) = 1
(B) P(R/S) = 0
(C) P(S/R) = 1
(D) P(S/R) = 0
28) Pure water (stream W) is to be obtained from a feed containing 5 wt % salt using a desalination unit as shown below:
Recycle (R)
Feed (F) Mixed feed Effluent
5 wt % salt 10 wt % salt Desalination
unit
a. Pure water (W)
b. 0 % salt
If the overall recovery of pure water (through stream W) is 0.75 kg/kg feed, then the recycle ratio (R/F is
(A) 0.25
(B) 0.5
C) 0.75
(D) 1.0
29) For a binary mixture at constant temperature and pressure, which ONE of the following relations between activity coefficient (γi) and mole fraction (xi) is thermodynamically consistent ?
(A) ln γ1 = �1 + 2 x1 , ln γ2 =
(B) ln γ1 = �1 + 2 x1 , ln γ2 =
(C) ln γ1 = �1 + 2 x1 , ln γ2 =
(D) ln γ1 = �1 + 2 x1 , ln γ2 =
30) Two identical reservoirs, open at the top, are drained through pipes attached to the bottom of the tanks as shown below. The two drain pipes are of the same length, but of different diameters (D1 > D2).
Assuming the flow to be steady and laminar in both drain pipes, if the volumetric flow rate in the larger pipe is 16 times of that in the smaller pipe, the ratio D1/D2 is
(A) 2
(B) 4
(C) 8
(D) 16
31) For an incompressible flow, the x- and y- components of the velocity vector are
νx = 2 (x + y); νy = 3 (y + z);
where x, y, z are in metres and velocities are in m/s. Then the z-component of the velocity vector (vz) of the flow for the boundary condition vz = 0 at z = 0 is
(A) 5 z
(B) �5 z
(C) 2x + 3z
(D) �2x�3z
32) The terminal settling velocity of a 6 mm diameter glass sphere (density: 2500 kg/m3) in a viscous Newtonian liquid (density: 1500 kg/m3) is 100 μm/s. If the particle Reynolds number is small and the value of acceleration due to gravity is 9.81 m/s2, then the viscosity of the liquid (in Pa.s) is
(A) 100
(B) 196.2
(C) 245.3
(D) 490.5
33) A well-insulted hemispherical furnace (radius = 1 m) is shown below:
The self-view factor of radiation for the curved surface 2 is
(A) 1/4
(B) 1/2
(C) 2/3
(D) 3/4
34) A double-pipe heat exchanger is to be designed to heat 4 kg/s of a cold feed from 20 to 40�C using a hot stream available at 160�C and a flow rate of 1 kg/s. The two streams have equal specific heat capacities and the overall heat transfer coefficient of the heat exchanger is 640 W/m2.K. Then the ratio of the heat transfer areas require for the co-current to counter-current modes of operations is
(A) 0.73
(B) 0.92
(C) 1.085
(D) 1.25
35) For the composite wall shown below (case 1), the steady state interface temperature is 180�C. If the thickness of layer P is doubled (Case 2), then the rate of heat transfer (assuming 1-D conduction) is reduction by
(A) 20%
(B) 40%
(C) 50%
(D) 70%
36) Species A is diffusing at steady state from the surface of a sphere (radius = 1 cm) into a stagnant fluid. If the diffusive flux at a distance r = 3 cm from the center of the sphere is 27 mol/cm2.s, the diffusive flux (in mol/cm2.s) at a distance r = 9 cm is
(A) 1
(B) 3
(C) 9
(D) 27
37) The feed to a binary distillation column has 40 mol % vapor and 60 mol % liquid. Then, the slope of the q-line in the McCabe-Thiele plot is
(A) �1.5
(B) �0.6
(C) 0.6
(D) 1.5
38) The equilibrium moisture curve for a solid is shown below :
The total moisture content of the solid is X and it is exposed to air of relative humidity H. In the table below, Group Ilists the types of moisture, and Group II represents the region in the graph above
Group I Group II
P. Equilibrium moisture 1
Q. Bound moisture 2
R. Unbound moisture 3
S. Free moisture 4
Which ONE of the following is the correct match ?
(A) P-1, Q-2, R-3, S-4
(B) P-1, Q-3, R-4, S-2
(C) P-1, Q-4, R-2, S-3
(D) P-1, Q-2, R-4, S-3
40) An isothermal pulse test is conducted on a reactor and the variation of the outlet tracer concentration with time is shown below :
The mean residence time of the fluid in the reactor (in minutes) is
(A) 5.0 (B) 7.5 (C) 10.0 (D) 15.0
41) The inverse Laplace transform of is
(A) e-t/2 � e-t
B) 2e-t/2 � e-t
(C) e-t � 2e-t/2
(D) e-t � e-t/2
42) The characteristic equation of a closed loop system using a proportional controller with gain Kc is
12 s3 + 19 s2 + 8 s + 1 + Kc = 0
At the onset of instability, the value of Kc is
(A) 35/3
(B) 10
(C) 25/3
(D) 20/3
43) The block diagram for a control system is shown below :
For a unit step change in the set point, R(s), the steady state offset in the output Y(s) is
(A) 0.2
(B) 0.3
(C) 0.4
(D) 0.5
45) A column costs Rs. 5.0 lakhs and has a useful life of 10 years. Using the double declining balance depreciation method, the book value of the unit at the end of five years (in lakhs of Rs.) is
(A) 1.21
(B) 1.31
(C) 1.64
(D) 2.05
46) An equi-molar mixture of four hydrocarbons (1, 2, 3, 4) is to be separated into high purity individual components using a sequence of simple distillation columns (one overhead and one bottom stream). Four possible schemes are shown below.
Scheme R Scheme S
Using the Ki (+ yi*/xi) values given above, the optimal scheme is
(A) P (B) Q (C) R (D) S
47) Match the equipment in Group I to the internals in Group II.
GROUP I GROUP II
P. Centrifugal pump 1. Baffle
Q. Distillation column 2. Impeller
R. Heat exchanger 3. Tray
4. Volute
(A) P-2, Q-1, R-4
(B) P-2, Q-4, R-3
(C) P-1, Q-3, R-4
(D) P-4, Q-3, R-1
48) Match the product in Group I with the name of the process in Group II.
1 GROUP I GROUP II
2 P. Sodium carbonate 1. Haber
3 Q. Ammonia 2. Solvay
4 R. Sulphuric acid 3. Fischer-Tropsch
4. Contact
(A) P-2, Q-1, R-4
(B) P-4, Q-1, R-2
(C) P-3, Q-4, R-2
(D) P-2, Q-1, R-3
49) Match the product in Group I to the raw material in Group II.
1 GROUP I GROUP II
2 P. Ethylene 1. Natural gas
3 Q. Methanol 2. Synthesis gas
4 R. Phthalic anhydride 3. Naphtha
4. Naphthalene
(A) P-1, Q-2, R-3
(B) P-2, Q-1, R-4
(C) P-3, Q-1, R-4
(D) P-3, Q-2, R-4
50) Match the unit process in Group I with the industry in Group II
GROUP I GROUP II
P. Steam cracking 1. Petroleum refining
Q. Hydrocracking 2. Petrochemicals
R. Condensation 3. Polymers
4 Soaps and Detergents
(A) P-1, Q-2, R-3
(B) P-2, Q-3, R-3
(C) P-1, Q-2, R-4
(D) P-2, Q-1, R-3
51) The work required for compression (in kJ/mol) is
(A) 3.74 (B) 6.24 (C) 7.48 (D) 12.48
52) The final pressure P2 (in bar) is
(A) 23/4
B) 25/4
(C) 23/2
(D) 25/2
53) The maximum temperature in the slab occurs at x equal to
(A) 0
(B) L/4
(C) L/2
(D) L
54) The heat flux at x = L is
(A) 0
(B) S L/4
(C) S L/2
(D) S L
55) The mole fraction of methanol in the distillate is
(A) 0.2
(B) 0.7
(C) 0.8
(D) 0.9
56) If the enthalpy of the distillate with reference to the feed is 3000 kJ/kmol, and the enthalpy of the bottoms with reference to the feed is �1000 kJ/kmol, the heat duty of the preheater (Qh in kJ/hr) is
(A) �2�106
(B) �1�106
(C) 1�106
(D) 2�106
57) The velocity of water at the tip of the nozzle (in m/s) is
(A) 13.4
(B) 18.0
C) 23.2
(D) 27.1
58) The gauge pressure (in kPa) at point B is
(A) 80.0
(B) 100.0
(C) 239.3
(D) 367.6
59) The rate constant (k) for this reaction at 50�C is
(A) 0.2
(B) 0.2
(C) 0.4
(D) 0.4
60) The concentration of A (in gmol/liter) at the exit of the plug flow reactor is
(A) 0.5
(B) 1.0
(C) 2.0
(D) 2.5
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