GATE 2014 Chemical Engineering- Answer Key
Content
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Q. No. 1 – 25 Carry One Mark Each
1. A random variable X has a pdf ( )
¦ ¹ ( − <
¦ ¦
¸ ¸
=
´ `
¦ ¦
¹ )
4
X
C 1 x if x 1
f x
0 otherwise
. Then
1
P X
2
¦ ¹
<
´ `
¹ )
is
(A) 0.617 (B) 0.325 (C) 0.513 (D) 0.217
2. The Characteristic Equation of a matrix A is
2
1 0 λ − λ − = . Then
(A)
1
A does not exist
−
(B)
1
A A I
−
= +
(C)
1
A A I
−
= −
(D)
1
A
−
exists but cannot be determined from the data given
3. The Eigen values of a Skew – Symmetric matrix are
(A) Negative (B) Real
(C) Absolute value of one (D) Purely Imaginary or zero
4. The rank of a 7 x 5 Matrix A is 5 and the rank of 5 x 7 Matrix B is 3. Then
minimum rank of the product of the two matrices A and B is
(A) 5 (B) 3 (C) 4 (D) 2
5. ( ) f z u iv = + and z is analytic function. Given that
3 2
u x 3xy = − . The analytic
function f(z) is (where ‘c’ is a constant)
(A)
3
z c − + (B)
3
z c + (C)
3
2z c − + (D)
3
2z c +
6. A natural draft cooling tower is filled with wooden grids, which cover about
.......... percent of the tower height.
(A) 10-15 (B) 30-40 (C) 70-80 (D) 90-100
7. The change in enthalpy, when a unit quantity of gas is absorbed by relatively
large quantity of adsorbent (on which a definite concentration of the adsorbed
gas already exists) is termed as the
(A) Differential heat of adsorption (B) Heat of wetting
(C) Integral heat of adsorption (D) None of these
8. The kinematic viscosity (in stoke) and the absolute/dynamic viscosity (in poise)
are the same for __________ at room temperature.
(A) Air (B) Water (C) Mercury (D) Alcohol
9. In a heat exchanger, the rate of heat transfer from the hot fluid to the cold fluid
(A) Varies directly as the area and the LMTD
(B) Directly proportional to LMTD and inversely proportional to the area
(C) Varies as square of the area (D) None of these
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10. A single pass air heater is connected to a two pass unit. For the air flow rate and
other conditions remaining the same, the film heat transfer co-efficient for air will
vary in the ratio of
(A) 2 (B) 2
0.8
(C) 2
0.2
(D) 2
0.5
11. Friction factor for fluid flow in pipe does not depend upon the...........
(A) Pipe length (B) Pipe roughness
(C) Fluid density & viscosity (D) Mass flow rate of fluid
12. In the free convection regime of pool boiling, the heat flux is proportional to
(A) ∆t
1/2
(B) ∆t
2
(C) ∆t
5/4
(D) ∆t
13. Power required to drive a ball mill with a particular ball load is proportional to
________. (where, D = diameter of ball mill)
(A) D (B) 1/D (C) D
2.5
(D) 1/D
2.5
14. Range of compressibility co-efficient of the commercial compressible cake
obtained in filtration operation is
(A) 0.01 to 0.1 (B) 0.1 to 0.3 (C) 0.2 to 0.8 (D) 0.2 to 0.4
15. Balls for ball mills are never made of
(A) Forged/cast steel (B) Lead
(C) Cast iron (D) Alloy steel
16. Reaction of orthophosphoric acid with soda ash produces
(A) Sodium Triolyphosphate (STPP) (B) Tricresyl phosphate
(C) Tributyl phosphate (D) Nitrophosphate
17. Raw materials for nitric acid manufacture are
(A) Hydrogen peroxide, air and water
(B) Anhydrous ammonia and air
(C) Anhydrous ammonia, air and water
(D) Wet ammonia, air and water
Q.No. 18 to 22 are Numerical Answer Type Questions and Carry One Mark
Each. Enter a number as the answer using virtual keyboard.
18. Consider the following arrangement.
The water pressure at a depth of 35ft will be_____________ psig
Water
T 50ºF =
( ) 1
( ) 2
Elevation 250ft =
Elevation 200ft =
35ft
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19. Based on the following data
H
2
(g) + I
2
(s) → 2 HI(g) ∆H
R
= 51.9 kJ
H
2
(g) + I
2
(g) → 2 HI(g) ∆H
R
= -9.2 kJ
The enthalpy of sublimation of I
2
_____________
20. If the equivalent head is measured as 400mm of mercury (γ) =13.6, then the
pressure in KN/m
2
will be ___________.
21. Force required to hold a circular disc at rest, if the diameter of the disc is 5m and
is held normal to a 24.7 m/s wind of density 0.001 g/cc, is______. [
D
C 1.2 = ]
22. A radiator which behaves as a black body operates at a surface temperature of
o
50 C. Heat flux at the surface of the radiator is_______________
2
W/ m
23. A solution with reasonably permanent pH is called a/an ........... solution.
(A) ideal (B) non-ideal (C) buffer (D) colloidal
24. Which of the following gases is the most soluble in water?
(A) NH
3
(B) CO
2
(C) H
2
S (D) CH
4
25. Stokes equation is valid in the Reynolds number range of
(A) 0.01- 0.1
(B) 0.1-2 (C) 2-10 (D) 10-100
Q. No. 26 – 51 Carry Two Marks Each
26. Consider the following statements.
1. If a particle has a constant acceleration, then its position function is a cubic
polynomial.
2. If f(x) is differentiable on the open interval (a, b) then by mean value theorem
there is a number c in (a, b) such that ( ) ( ) ( ) ( ) − = − b a f ' c f b f a .
3. If
x
lim
→∞
( )
k
0
f x
= for every number k, then ( )
x
lim f x
→∞
= ∞
4. If f(x) has an absolute or local minimum at x = c, then f’(C) = 0
The correct statements are
(A) 1,2,3,4 (B) 1 and 3 (C) 1 and 2 (D) 2, 3 and 4
27. What height would a water barometer need to be to measure atmospheric
pressure?
(A) 10.19 (B) 1.29 (C) 20.29
(D) 9.89
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28. The second order system with the transfer function of
2
4
(s +2s+4)
has a
damping ratio of
(A) 2.0 (B) 0.5 (C) 1.0 (D) 4.0
29. The average heat transfer co-efficient over the entire length of the plate (h
a
) and
the local heat transfer co-efficient (h
L
) in case of heat transfer over a flat plate in
laminar zone is related as
(A) h
a
= 0.8h
L
(B) h
a
= 2h
L
(C) h
a
= h
L
(D) h
a
= 5h
L
30. ( ) ( ) { } ( ) ( )
2
If F x f g x , g 1 2, g' 1 3, = = =
( ) ( ) = = f 2 4, f ' 2 5, Then ( ) F ' 1 will be
is _____________
(A) 60 (B) 120 (C) 30 (D) Data insufficient
31. A home thermo state for on–off control of room temperature produces a cycle
with 30 minutes period and 3
0
F amplitude. If a thermometer with a time constant
of 4.0 minute placed beside it, then which of the following cycle will it indicate?
Assume that the thermometer has first order lag.
(A) ( ) ( ) 0 t 1.34sin 0.8t 0.8 = − (B) ( ) ( ) 0 t 2.28sin 0.076t 0.34 = −
(C) ( ) ( ) = − 0 t 2.34sin 0.2089t 0.9 (D) ( ) ( ) 0 t 3.38sin 0.076t 0.34 = −
32. The value of ‘b’ such that
2
2
x 2
bx 15x 15 b
lim exists is
x x 2
→−
+ + +
+ −
(A) 1 (B) 2 (C) 3 (D) None of these
33.
( )
2
x
lim x x x
→∞
+ − =
(A)
1
2
(B)
1
2
−
(C) 1 (D) ∞
Q.No. 34 to 38 are Numerical Answer Type Questions and Carry Two
Marks Each. Enter a number as the answer using virtual keyboard.
34. In a ball mill of diameter 2000 mm, 100 mm diameter steel balls are being used
for grinding. Presently, for the material being ground, the mill is running at 15
rpm. If the 100 mm balls are replaced by
50 mm balls, all the other conditions remaining the same, the speed that the mill
have to run, will be ________.
35. Consider a 3 mm diameter vertical tube. If the liquid rises 6 mm above the liquid
outside the tube, then the contact angle for the above will be ___________
degrees. Water has a surface tension of 0.4 N/m.
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36. Most chemical plants use an initial working capital amounting to 10-20% of the
total capital investment. But this percentage may increase to ........ percent in
case of seasonal products manufacturing plant.
37. Air is introduced through a nozzle into a tank of water to form a stream of
bubbles. If the bubbles are intended to have a diameter of 2 mm, the pressure of
the air at the tip of the nozzle must exceed that of the surrounding water and will
be ________ N/m
2
. Assume that the value of surface tension between air and
water as 72.7 x 10
-3
N/m.
38. An elementary liquid phase reaction (irreversible first order) A → R takes place in
a PFR and the conversion is 96%. If a mixed flow reactor of 10 times as large as
the PFR is hooked up in parallel with the existing unit, then the fraction that the
production be increased for the same 96% conversion would be _______.
39. Acetic acid is hydrolysed in three stirred tank reactors operated in series. The
feed flows to the first reactor (V = 1 lit) at a rate of 400 cm
3
/min. The second
and third reactors have volumes of 2 and 1.5 litres respectively. The first order
irreversible rate constant is 0.158 min
-1
. . Calculate the fraction hydrolysed in the
effluent from the third reactor.
(A) 0.749 (B) 0.618 (C) 0.283 (D) 0.148
40. For increased speed of response of an expansion pressure spring thermometer,
the thermometer bulb should have a
(A) Large area but small mass (B) High thermal conductivity
(C) Small specific heat (D) All of these
41. The inventory of raw materials included in the working capital is usually about
............... month’s supply of raw materials valued at delivery prices.
(A) 1 (B) 6 (C) 12 (D) 3
42. The thermal decomposition of nitrous oxide (N
2
O) in the gas phase at 1030
o
K is
studied in a constant volume vessel at various initial pressures of N
2
O. The half-
life data so obtained are as follows:
p
o
(mm Hg) 52.5 139 290 360
t
1/2
(sec) 860 470 255 212
2N
2
O → 2N
2
+ O
2
Order of the reaction (n) = 1.75.
Determine the rate equation that fits the data.
(A)
2 2
1.75
N O N O
-r = 0.20 (C ) (B)
2 2
0.75
N O N O
-r = 0.14 (C )
(C)
2 2
1.75
N O N O
-r = 0.36 (C ) (D)
2 2
0.75
N O N O
-r = 0.44 (C )
43. A reservoir of oil has a mass of 825 kg. The reservoir has a volume of 0.917 m
3
.
Compute the density, specific weight, and specific gravity of the oil.
(A) 900 kg/m
3
, 8829 N/m
3
, 0.9 (B) 1000 kg/m
3
, 9829 N/m
3
, 1.0
(C) 917 kg/m
3
, 9829 N/m
3
, 0.8 (D) 990 kg/m
3
, 7829 N/m
3
, 0.9
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44. A manometer connected to a pipe indicates a negative gauge pressure of 50mm
of mercury. What is the absolute pressure in the pipe if the atmospheric pressure
is 1 bar?
(A) 93.3 kN/m
2
(B) 73.3 kN/m
2
(C) 63.3 kN/m
2
(D) 53.3 kN/m
2
45. A first order thermometer having a time constant of 5 seconds is used to
measure a temperature oscillating between
o o
120 C to 140 C with a period of 2
minutes. What is the temperature indicated by the thermometer?
(A) 139
o
C (B) 149
o
C (C) 159
o
C (D) None of these
46. The value of the integral
2
0
d
3cos 5
π
θ
θ +
∫
is__________
47. Water flows through a horizontal coil heated from outside. During its passage, it
changes state from liquid at 200 kPa and 80
o
C to vapour at 100 kPa and 125
o
C.
The entering and exit velocities are 3 m/s and 200 m/s respectively. The heat
transferred through the coil per unit mass of water is ___________ (kJ/kg)
(H
inlet
= 334.9 kJ/kg; H
outlet
= 2726 kJ/kg).
Common Data Questions: 48 & 49
Oil at 160°C enters a 22m
2
single pass counter-current heat exchanger and exits
at 80°C. Cooling water enters at 20°C at a flow rate of 3kg/sec and leaves at
70°C. (The specific heat of water at the mean temperature of 45°C is
4180 J/kg° C.)
48. Calculate the heat transfer rate for the given data is __________ (W)
Oil at 160°C enters a 22m
2
single pass counter-current heat exchanger and exits
at 80°C. Cooling water enters at 20°C at a flow rate of 3kg/sec and leaves at
70°C. (The specific heat of water at the mean temperature of 45°C is
4180 J/kg° C.)
49. Calculate the overall heat transfer coefficient U. is _____________( W/m
2 o
C )
Common Data Questions: 50 & 51
An irreversible exothermic reaction which generates 4700 kcal/mole reagent "Z"
is to be run at 25°C (77°F) in a reactor with HTC (U) = 55 BTU/hr ft
2
°F and heat
transfer area (A) of 16.5
2
ft by controlled addition of reagent "Z". Jacket
temperature is 0°C (32°F).
50. Calculate the heat removal rate.
(A) 10,300 BTU/hr (B) 50,100 BTU/hr
(C) 90,120 BTU/hr (D) 40,800 BTU/hr
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An irreversible exothermic reaction which generates 4700 kcal/mole reagent "Z"
is to be run at 25°C (77°F) in a reactor with HTC (U) = 55 BTU/hr ft
2
°F and heat
transfer area (A) of 16.5
2
ft by controlled addition of reagent "Z". Jacket
temperature is 0°C (32°F).
51. Calculate the maximum allowable addition rate of a 5M solution of reagent "Z".
(Here ∆H=18600 BTU/mol)
(A) 0.44 ml/min (B) 7.3 ml/min (C) 5.24 ml/min (D) 9.98 ml/min
Linked Answer Questions: Q.52 to Q.55 Carry Two Marks Each
Statement for Linked Answer Questions: 52 & 53
A solution of ethyl alcohol containing 8.6% alcohol by weight is fed at the rate of
5000 kg/hr to a continuous fractionating column operating at atmospheric pressure.
The distillate which is the desired product contains 95.4% alcohol by weight and the
residue from the bottom of the column contains 0.1% alcohol by weight.
52. Calculate the mass flow rate of the distillate in kg/hr.
(A) 446 (B) 425 (C) 495 (D) 585
A solution of ethyl alcohol containing 8.6% alcohol by weight is fed at the rate of
5000 kg/hr to a continuous fractionating column operating at atmospheric
pressure. The distillate which is the desired product contains 95.4% alcohol by
weight and the residue from the bottom of the column contains 0.1% alcohol by
weight.
53. Calculate the residue flow rate in kg/hr.
(A) 4443 (B) 4554 (C) 4745 (D) 4221
Statement for Linked Answer Questions: 54 & 55
A liquid containing 47.5% acetic acid and 52.5% water is to be separated by
solvent extraction using isopropanol. The solvent used is 1.3 kg per kg of feed.
The final extract is found to contain 82% acid on solvent free basis. The residue
has 14% acid on solvent free basis.
54. Find the amount of acetic acid in the extract.
(A) 0.40Kg (B) 0.55Kg (C) 0.66Kg (D) 0.75Kg
A liquid containing 47.5% acetic acid and 52.5% water is to be separated by
solvent extraction using isopropanol. The solvent used is 1.3 kg per kg of feed.
The final extract is found to contain 82% acid on solvent free basis. The residue
has 14% acid on solvent free basis.
55. Find the percentage extraction of acid from the feed.
(A) 45.12 (B) 75.74 (C) 85.12 (D) 65.78
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Q. No. 56 – 60 Carry One Mark Each
56. Which of the following is closest in meaning to “appease”?
(A) Aggravate (B) Incite (C) Tease (D) Pacify
57. Pick up the statement which is the best way to express the underlined part of the
statement.
As the world’s major economies continue to lose steam, the odds of a recovery
led by a rejuvenated US look increasingly remote.
(A) Look increasing remote (B) looks more remote
(C) Is remotely increasing (D) Is increasing remotely
Fill in the Blanks
58. Scientists at Tel Aviv University tracked pollution trends for 189 megacities,
_______ Mumbai, New York City and Tokyo, by analyzing eight years' worth of
data from three of NASA's high-tech aerosol monitoring satellites.
(A) Between (B) Including (C) From (D) In
59. Pick the odd one out from following words.
Bluster Noise Rant Storm Bully Calm
(A) Noise (B) Rant (C) Storm (D) Calm
60. A man jogging inside a railway tunnel at a constant speed hears a train
approaching the tunnel from behind at a speed of 60 Km/hr, when he is one third
of the way inside the tunnel. Whether he keeps running forward or turns back, he
will reach the end of the tunnel at the same time the train reaches that end. The
speed at which the man is running is
(A) 12 Km/hr (B) 16 Km/hr (C) 20 Km/hr (D) 24 Km/hr
Q. No. 61 – 65 Carry Two Marks Each
61. The product of 3 positive integers is 36. If Riya knows the sum of the 3 numbers,
but is not able to uniquely identify the numbers, then the sum of the 3 numbers
is
(A) 13 (B) 12 (C) 10 (D) 11
62. The mean monthly salary paid to graduating MTech class of 2011 of an
engineering college is Rs. 75,000. The mean monthly salary paid to students with
a B.Tech as their graduation qualification is Rs. 81,000. The corresponding figure
for the student with M. Sc as their graduation qualification is Rs. 45,000. What is
the percentage of students with B.Tech and M.Sc as their graduation
qualifications in the class of 2011?
(A) 16.67% with B.Tech, 83.33% with M.Sc
(B) 86.33% with B.Tech, 16.67% with M.Sc
(C) 20% with B.Tech, 80% with M.Sc
(D) 80% with B.Tech, 20% with M.Sc
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63. The following graph shows the FDI in India and China from US for the year 2001
to 2006
Which of the following is closest to the percentage change in growth rate of India
in 2005 (over 2004) and the growth rate in 2003 (over 2002)?
(A) 0 (B) 10 (C) 20 (D) Data Insufficient
64. A survey was conducted of 100 people to find out of their newspaper choice
among TOI, Hindu and ET. The summarized information is given below
Only TOI 18; TOI but not Hindu 23;
TOI and ET 8; TOI 28; ET 48
ET and Hindu 10; None of these three 24
− −
− − −
− −
What is the number of people who read all three newspapers?
(A) 5 (B) 9 (C) 3 (D) 8
65. Swedish researchers found men who drank 300ml of a fizzy drink a day - slightly
less than a standard can - were 40 per cent more likely to develop prostate
cancer than those who never consumed the drinks. Worryingly, the risk applied
not to early-stage disease that was spotted via blood tests but to cancers that
had progressed enough to cause symptoms, the 'Daily Mail' reported.
Which of the following is supported by the information given above?
(A) Experts believe that sugar triggers the release of the hormone insulin, which
feeds tumours.
(B) The study, published in the American Journal of Clinical Nutrition, is far from
the first to link the sugary soft drinks to poor health.
(C) Previous research has flagged up heart attacks, diabetes, weight gain, brittle
bones, pancreatic cancer, muscle weakness and paralysis as potential risks.
(D) People who consume a standard can of fizzy drink a day are at a higher risk
of developing cancer as compared to people who don’t.
1000
900
800
700
600
500
400
300
200
100
0
2001 2002 2003 2004 2005 2006
India China
