Gate Question paper 2009 : Chemical Engineering , Chemistry PDF Download

 Page 1


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GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 1 of 11 
GATE question papers: Chemical Engineering 2009 (CH) 
Q. 1 ? Q. 20 carry one mark each. 
1. The direction of largest increase of the function xy
3
 ? x
2
 at the point (1, 1) is 
 (A)   (B)    (C)   (D)  j
ˆ
i
ˆ
3 ? j
ˆ
3 i
ˆ
? j
ˆ
3 i
ˆ
? ? j
ˆ
3 i
ˆ
? ?
 
2. The modulus of the complex number 
2
i 1 ?
 is 
 (A) 
2
1
  (B) 
2
1
  (C) 1  (D) 2 
 
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 statement is TRUE? 
 (A) Water is the ONLY tie component 
 (B) Air is the ONLY tie component 
 (C) BOTH water and air are tie components 
 (D) There are no tie components 
 
5. Dehydrogenation of ethane, C
2
H
6
 (g) ? C
2
H
4
 (g) + H
2
 (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 product, 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 T
1
 and pressure P
1
 is compressed isothermally to pressure P
2
 (> P
1
( 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) U
1
 = U
2
, G
1
 > G
2
   (B) U
1
 = U
2
, G
1
 < G
2
 
 (C) U
1
 > U
2
, G
1
 = G
2
   (D) U
1
 < U
2
, G
1
 = G
2 
 
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 
 
Wet air Dry air
Water
Dehumidifier
Page 2


http://www.questionpapers.net.in/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 1 of 11 
GATE question papers: Chemical Engineering 2009 (CH) 
Q. 1 ? Q. 20 carry one mark each. 
1. The direction of largest increase of the function xy
3
 ? x
2
 at the point (1, 1) is 
 (A)   (B)    (C)   (D)  j
ˆ
i
ˆ
3 ? j
ˆ
3 i
ˆ
? j
ˆ
3 i
ˆ
? ? j
ˆ
3 i
ˆ
? ?
 
2. The modulus of the complex number 
2
i 1 ?
 is 
 (A) 
2
1
  (B) 
2
1
  (C) 1  (D) 2 
 
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 statement is TRUE? 
 (A) Water is the ONLY tie component 
 (B) Air is the ONLY tie component 
 (C) BOTH water and air are tie components 
 (D) There are no tie components 
 
5. Dehydrogenation of ethane, C
2
H
6
 (g) ? C
2
H
4
 (g) + H
2
 (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 product, 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 T
1
 and pressure P
1
 is compressed isothermally to pressure P
2
 (> P
1
( 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) U
1
 = U
2
, G
1
 > G
2
   (B) U
1
 = U
2
, G
1
 < G
2
 
 (C) U
1
 > U
2
, G
1
 = G
2
   (D) U
1
 < U
2
, G
1
 = G
2 
 
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 
 
Wet air Dry air
Water
Dehumidifier
h p: ww. es i p r i tt //w qu t on ape s.net. n/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 2 of 11 
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 viscosity 
 
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 does not shift 
 
13. For a homogenous reaction system, where 
  C
j
 is the concentration of j at time t 
  N
j
 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) 
dt
dC
j
  (B) 
?
?
?
?
?
?
?
?
?
dt
dC
j
 (C) 
dt
dN
V
1
j
  (D) 
?
?
?
?
?
?
?
?
?
dt
dN
V
1
j
 
 
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 
 (A) 
rate diffusion
rate reaction rinsic int
   (B) 
rate reaction rinsic int
rate diffusion
 
 (C) 
rate diffusion
rate reaction rinsic int
   (D) 
rate reaction rinsic int
rate diffusion
 
 
16. Which ONE of the following sensors is used for the measurement of temperature in combustion 
process (T > 1800 ?C)? 
 (A) Type J thermocouple   (B) Thermistor 
 (C) Resistance temperature detector  (D) Pyrometer 
 
17. The roots of the characteristic equation of an underdamped second order system are 
 (A) real, negative and equal   (B) real, negative and unequal 
 (C) real, positive and unequal  (D) complex conjugates 
 
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 
 
Page 3


http://www.questionpapers.net.in/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 1 of 11 
GATE question papers: Chemical Engineering 2009 (CH) 
Q. 1 ? Q. 20 carry one mark each. 
1. The direction of largest increase of the function xy
3
 ? x
2
 at the point (1, 1) is 
 (A)   (B)    (C)   (D)  j
ˆ
i
ˆ
3 ? j
ˆ
3 i
ˆ
? j
ˆ
3 i
ˆ
? ? j
ˆ
3 i
ˆ
? ?
 
2. The modulus of the complex number 
2
i 1 ?
 is 
 (A) 
2
1
  (B) 
2
1
  (C) 1  (D) 2 
 
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 statement is TRUE? 
 (A) Water is the ONLY tie component 
 (B) Air is the ONLY tie component 
 (C) BOTH water and air are tie components 
 (D) There are no tie components 
 
5. Dehydrogenation of ethane, C
2
H
6
 (g) ? C
2
H
4
 (g) + H
2
 (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 product, 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 T
1
 and pressure P
1
 is compressed isothermally to pressure P
2
 (> P
1
( 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) U
1
 = U
2
, G
1
 > G
2
   (B) U
1
 = U
2
, G
1
 < G
2
 
 (C) U
1
 > U
2
, G
1
 = G
2
   (D) U
1
 < U
2
, G
1
 = G
2 
 
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 
 
Wet air Dry air
Water
Dehumidifier
h p: ww. es i p r i tt //w qu t on ape s.net. n/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 2 of 11 
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 viscosity 
 
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 does not shift 
 
13. For a homogenous reaction system, where 
  C
j
 is the concentration of j at time t 
  N
j
 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) 
dt
dC
j
  (B) 
?
?
?
?
?
?
?
?
?
dt
dC
j
 (C) 
dt
dN
V
1
j
  (D) 
?
?
?
?
?
?
?
?
?
dt
dN
V
1
j
 
 
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 
 (A) 
rate diffusion
rate reaction rinsic int
   (B) 
rate reaction rinsic int
rate diffusion
 
 (C) 
rate diffusion
rate reaction rinsic int
   (D) 
rate reaction rinsic int
rate diffusion
 
 
16. Which ONE of the following sensors is used for the measurement of temperature in combustion 
process (T > 1800 ?C)? 
 (A) Type J thermocouple   (B) Thermistor 
 (C) Resistance temperature detector  (D) Pyrometer 
 
17. The roots of the characteristic equation of an underdamped second order system are 
 (A) real, negative and equal   (B) real, negative and unequal 
 (C) real, positive and unequal  (D) complex conjugates 
 
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 
 
http://www.questionpapers.net.in/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 3 of 11 
19. In petroleum refining operations, the process used for converting paraffins and naphthenes to 
aromatics is 
 (A) catalytic reforming   (B) catalytic cracking 
 (C) hydrocracking    (D) alkylation 
 
20. The active component of catalysts use in steam reforming of methane to produce synthesis gas is 
 (A) Nickel  (B) Iron  (C) Platinum (D) Palladium 
 
Q. 2    1 to Q. 60 carry two marks each. 
 
21. The value of the limit 
3
) 2 / x (
x cos
? ?
 is 
 (A) ??  (B) 0  (C) 1  (D) ? 
 
22. The general solution of the differential equation 
  
dx
dy
dx
y d
2
2
? ?6y = 0, 
 with C
1
 and C
2
 as constants of integration, is 
 (A) C
1
 e
?3x
 + C
2
 e
?2x   
(B) C
1
 e
3x
 + C
2
 e
?2x 
 
(C) C
1
 e
3x
 + C
2
 e
2x    
(D) C
1
 e
?3x
 + C
2
 e
2x 
 
23. Using the residue theorem, the value of the integral (counterclockwise)  
  dz
4 z
z 7 8
?
?
?
 
 around a circle with center at z = 0 and radius = 8 (where z is a complex number and i = 1 ? , is 
 (A) ?20 ? i  (B) ?40 ?  (C) ?40 ?i  (D) 40 ?i 
 
24. Consider the integral 
  
??
? ? ? dS n ˆ ) k
ˆ
z 5 j
ˆ
y 2 i
ˆ
x 2 (
 over the surface a sphere of radius = 3 with center at the origin, and surface unit normal n ˆ pointing 
away from the origin. Using the Gauss divergence theorem, the value of this integral is 
 (A) ?180 ?  (B) 0  (C) 90 ?  (D) 180 ? 
 
25. Using the trapezoidal rule and 4 equal intervals (n = 4), the calculated value of the integral (rounded 
to the first place of decimal)  is 
?
?
?
0
d sin
 (A) 1.7  (B) 1.9  (C) 2.0  (D) 2.1 
 
26. The eigenvalues of matrix A =  and 5 and ?1. Then the eigenvalues of ?2A + 3I (I is a 2 ? 2 
identity matrix) are 
?
?
?
?
?
?
3 4
2 1
 (A) ?7 and 5 (B) 7 and ?5 (C) ?
7
1
 and 
5
1
 (D) 
7
1
 and ?
5
1
 
 
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 
 
 
 
Page 4


http://www.questionpapers.net.in/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 1 of 11 
GATE question papers: Chemical Engineering 2009 (CH) 
Q. 1 ? Q. 20 carry one mark each. 
1. The direction of largest increase of the function xy
3
 ? x
2
 at the point (1, 1) is 
 (A)   (B)    (C)   (D)  j
ˆ
i
ˆ
3 ? j
ˆ
3 i
ˆ
? j
ˆ
3 i
ˆ
? ? j
ˆ
3 i
ˆ
? ?
 
2. The modulus of the complex number 
2
i 1 ?
 is 
 (A) 
2
1
  (B) 
2
1
  (C) 1  (D) 2 
 
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 statement is TRUE? 
 (A) Water is the ONLY tie component 
 (B) Air is the ONLY tie component 
 (C) BOTH water and air are tie components 
 (D) There are no tie components 
 
5. Dehydrogenation of ethane, C
2
H
6
 (g) ? C
2
H
4
 (g) + H
2
 (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 product, 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 T
1
 and pressure P
1
 is compressed isothermally to pressure P
2
 (> P
1
( 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) U
1
 = U
2
, G
1
 > G
2
   (B) U
1
 = U
2
, G
1
 < G
2
 
 (C) U
1
 > U
2
, G
1
 = G
2
   (D) U
1
 < U
2
, G
1
 = G
2 
 
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 
 
Wet air Dry air
Water
Dehumidifier
h p: ww. es i p r i tt //w qu t on ape s.net. n/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 2 of 11 
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 viscosity 
 
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 does not shift 
 
13. For a homogenous reaction system, where 
  C
j
 is the concentration of j at time t 
  N
j
 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) 
dt
dC
j
  (B) 
?
?
?
?
?
?
?
?
?
dt
dC
j
 (C) 
dt
dN
V
1
j
  (D) 
?
?
?
?
?
?
?
?
?
dt
dN
V
1
j
 
 
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 
 (A) 
rate diffusion
rate reaction rinsic int
   (B) 
rate reaction rinsic int
rate diffusion
 
 (C) 
rate diffusion
rate reaction rinsic int
   (D) 
rate reaction rinsic int
rate diffusion
 
 
16. Which ONE of the following sensors is used for the measurement of temperature in combustion 
process (T > 1800 ?C)? 
 (A) Type J thermocouple   (B) Thermistor 
 (C) Resistance temperature detector  (D) Pyrometer 
 
17. The roots of the characteristic equation of an underdamped second order system are 
 (A) real, negative and equal   (B) real, negative and unequal 
 (C) real, positive and unequal  (D) complex conjugates 
 
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 
 
http://www.questionpapers.net.in/ 
GATE question papers: Chemical Engineering 2009 (CH) 
Published by: http://www.questionpapers.net.in/ 
 
Page 3 of 11 
19. In petroleum refining operations, the process used for converting paraffins and naphthenes to 
aromatics is 
 (A) catalytic reforming   (B) catalytic cracking 
 (C) hydrocracking    (D) alkylation 
 
20. The active component of catalysts use in steam reforming of methane to produce synthesis gas is 
 (A) Nickel  (B) Iron  (C) Platinum (D) Palladium 
 
Q. 2    1 to Q. 60 carry two marks each. 
 
21. The value of the limit 
3
) 2 / x (
x cos
? ?
 is 
 (A) ??  (B) 0  (C) 1  (D) ? 
 
22. The general solution of the differential equation 
  
dx
dy
dx
y d
2
2
? ?6y = 0, 
 with C
1
 and C
2
 as constants of integration, is 
 (A) C
1
 e
?3x
 + C
2
 e
?2x   
(B) C
1
 e
3x
 + C
2
 e
?2x 
 
(C) C
1
 e
3x
 + C
2
 e
2x    
(D) C
1
 e
?3x
 + C
2
 e
2x 
 
23. Using the residue theorem, the value of the integral (counterclockwise)  
  dz
4 z
z 7 8
?
?
?
 
 around a circle with center at z = 0 and radius = 8 (where z is a complex number and i = 1 ? , is 
 (A) ?20 ? i  (B) ?40 ?  (C) ?40 ?i  (D) 40 ?i 
 
24. Consider the integral 
  
??
? ? ? dS n ˆ ) k
ˆ
z 5 j
ˆ
y 2 i
ˆ
x 2 (
 over the surface a sphere of radius = 3 with center at the origin, and surface unit normal n ˆ pointing 
away from the origin. Using the Gauss divergence theorem, the value of this integral is 
 (A) ?180 ?  (B) 0  (C) 90 ?  (D) 180 ? 
 
25. Using the trapezoidal rule and 4 equal intervals (n = 4), the calculated value of the integral (rounded 
to the first place of decimal)  is 
?
?
?
0
d sin
 (A) 1.7  (B) 1.9  (C) 2.0  (D) 2.1 
 
26. The eigenvalues of matrix A =  and 5 and ?1. Then the eigenvalues of ?2A + 3I (I is a 2 ? 2 
identity matrix) are 
?
?
?
?
?
?
3 4
2 1
 (A) ?7 and 5 (B) 7 and ?5 (C) ?
7
1
 and 
5
1
 (D) 
7
1
 and ?
5
1
 
 
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 
 
 
 
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28. Pure water (stream W) is to be obtained from a feed containing 5 wt % salt using a desalination unit 
as shown below 
 
 
 
 
 
 
 
 
 
 
 
 
 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 ( ?
i
) and mole fraction (x
i
) is thermodynamically consistent? 
 (A) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 = 
2
1
x
2
1
2
1
x (B) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 =  
2
1
x
2
1
x
 (C) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 = ?
2
1
x
2
1
2
1
x (D) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 = ? 
2
1
x
2
1
x
 
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 (D
1
 > 
D
2
) 
  
 
 
 
 
 
 
 
 
 
 
 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 D
1
/D
2
 is 
 (A) 2  (B) 4  (C) 8  (D) 16 
 
31. For an incompressible flow, the x- and y-components of the velocity vector are 
 v
x
 = 2(x + y); v
y
 = 3 (y + z) 
 where x, y, z are in metres and velocities are in m/s. Then the z-component of the velocity vector (v
z
) 
of the flow for the boundary condition v
z
 = 0 at z = 0 is 
 (A) 5z   (B) ?5z  (C) 2x + 3z  (D) ?2x ? 3z 
 
32. The terminal settling velocity of a 6 mm diameter glass sphere (density: 2500 kg/m
3
) in a viscous 
Newtonian liquid (density: 1500 kg/m
3
) is 100 ?m/s. If the particle Reynolds number is small and the 
value of acceleration due to gravity is 9.81 m/s
2
, then the viscosity of the liquid (in Pa ?s) is 
 (A) 100  (B) 196.2  (C) 245.3  (D) 490.5 
 
 
 
Feed (F) 
5 wt % salt 
Mixed feed 
10 wt % salt
Desalination 
unit 
Pure water (W)
0% salt 
Recycle (R)
Effluent 
L 
D
1 
L
D
2
Page 5


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Page 1 of 11 
GATE question papers: Chemical Engineering 2009 (CH) 
Q. 1 ? Q. 20 carry one mark each. 
1. The direction of largest increase of the function xy
3
 ? x
2
 at the point (1, 1) is 
 (A)   (B)    (C)   (D)  j
ˆ
i
ˆ
3 ? j
ˆ
3 i
ˆ
? j
ˆ
3 i
ˆ
? ? j
ˆ
3 i
ˆ
? ?
 
2. The modulus of the complex number 
2
i 1 ?
 is 
 (A) 
2
1
  (B) 
2
1
  (C) 1  (D) 2 
 
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 statement is TRUE? 
 (A) Water is the ONLY tie component 
 (B) Air is the ONLY tie component 
 (C) BOTH water and air are tie components 
 (D) There are no tie components 
 
5. Dehydrogenation of ethane, C
2
H
6
 (g) ? C
2
H
4
 (g) + H
2
 (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 product, 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 T
1
 and pressure P
1
 is compressed isothermally to pressure P
2
 (> P
1
( 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) U
1
 = U
2
, G
1
 > G
2
   (B) U
1
 = U
2
, G
1
 < G
2
 
 (C) U
1
 > U
2
, G
1
 = G
2
   (D) U
1
 < U
2
, G
1
 = G
2 
 
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 
 
Wet air Dry air
Water
Dehumidifier
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Page 2 of 11 
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 viscosity 
 
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 does not shift 
 
13. For a homogenous reaction system, where 
  C
j
 is the concentration of j at time t 
  N
j
 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) 
dt
dC
j
  (B) 
?
?
?
?
?
?
?
?
?
dt
dC
j
 (C) 
dt
dN
V
1
j
  (D) 
?
?
?
?
?
?
?
?
?
dt
dN
V
1
j
 
 
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 
 (A) 
rate diffusion
rate reaction rinsic int
   (B) 
rate reaction rinsic int
rate diffusion
 
 (C) 
rate diffusion
rate reaction rinsic int
   (D) 
rate reaction rinsic int
rate diffusion
 
 
16. Which ONE of the following sensors is used for the measurement of temperature in combustion 
process (T > 1800 ?C)? 
 (A) Type J thermocouple   (B) Thermistor 
 (C) Resistance temperature detector  (D) Pyrometer 
 
17. The roots of the characteristic equation of an underdamped second order system are 
 (A) real, negative and equal   (B) real, negative and unequal 
 (C) real, positive and unequal  (D) complex conjugates 
 
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 
 
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Page 3 of 11 
19. In petroleum refining operations, the process used for converting paraffins and naphthenes to 
aromatics is 
 (A) catalytic reforming   (B) catalytic cracking 
 (C) hydrocracking    (D) alkylation 
 
20. The active component of catalysts use in steam reforming of methane to produce synthesis gas is 
 (A) Nickel  (B) Iron  (C) Platinum (D) Palladium 
 
Q. 2    1 to Q. 60 carry two marks each. 
 
21. The value of the limit 
3
) 2 / x (
x cos
? ?
 is 
 (A) ??  (B) 0  (C) 1  (D) ? 
 
22. The general solution of the differential equation 
  
dx
dy
dx
y d
2
2
? ?6y = 0, 
 with C
1
 and C
2
 as constants of integration, is 
 (A) C
1
 e
?3x
 + C
2
 e
?2x   
(B) C
1
 e
3x
 + C
2
 e
?2x 
 
(C) C
1
 e
3x
 + C
2
 e
2x    
(D) C
1
 e
?3x
 + C
2
 e
2x 
 
23. Using the residue theorem, the value of the integral (counterclockwise)  
  dz
4 z
z 7 8
?
?
?
 
 around a circle with center at z = 0 and radius = 8 (where z is a complex number and i = 1 ? , is 
 (A) ?20 ? i  (B) ?40 ?  (C) ?40 ?i  (D) 40 ?i 
 
24. Consider the integral 
  
??
? ? ? dS n ˆ ) k
ˆ
z 5 j
ˆ
y 2 i
ˆ
x 2 (
 over the surface a sphere of radius = 3 with center at the origin, and surface unit normal n ˆ pointing 
away from the origin. Using the Gauss divergence theorem, the value of this integral is 
 (A) ?180 ?  (B) 0  (C) 90 ?  (D) 180 ? 
 
25. Using the trapezoidal rule and 4 equal intervals (n = 4), the calculated value of the integral (rounded 
to the first place of decimal)  is 
?
?
?
0
d sin
 (A) 1.7  (B) 1.9  (C) 2.0  (D) 2.1 
 
26. The eigenvalues of matrix A =  and 5 and ?1. Then the eigenvalues of ?2A + 3I (I is a 2 ? 2 
identity matrix) are 
?
?
?
?
?
?
3 4
2 1
 (A) ?7 and 5 (B) 7 and ?5 (C) ?
7
1
 and 
5
1
 (D) 
7
1
 and ?
5
1
 
 
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 
 
 
 
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Page 4 of 11 
28. Pure water (stream W) is to be obtained from a feed containing 5 wt % salt using a desalination unit 
as shown below 
 
 
 
 
 
 
 
 
 
 
 
 
 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 ( ?
i
) and mole fraction (x
i
) is thermodynamically consistent? 
 (A) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 = 
2
1
x
2
1
2
1
x (B) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 =  
2
1
x
2
1
x
 (C) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 = ?
2
1
x
2
1
2
1
x (D) ln ?
1
 = ?1 + 2x
1
 ? , ln ?
2
 = ? 
2
1
x
2
1
x
 
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 (D
1
 > 
D
2
) 
  
 
 
 
 
 
 
 
 
 
 
 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 D
1
/D
2
 is 
 (A) 2  (B) 4  (C) 8  (D) 16 
 
31. For an incompressible flow, the x- and y-components of the velocity vector are 
 v
x
 = 2(x + y); v
y
 = 3 (y + z) 
 where x, y, z are in metres and velocities are in m/s. Then the z-component of the velocity vector (v
z
) 
of the flow for the boundary condition v
z
 = 0 at z = 0 is 
 (A) 5z   (B) ?5z  (C) 2x + 3z  (D) ?2x ? 3z 
 
32. The terminal settling velocity of a 6 mm diameter glass sphere (density: 2500 kg/m
3
) in a viscous 
Newtonian liquid (density: 1500 kg/m
3
) is 100 ?m/s. If the particle Reynolds number is small and the 
value of acceleration due to gravity is 9.81 m/s
2
, then the viscosity of the liquid (in Pa ?s) is 
 (A) 100  (B) 196.2  (C) 245.3  (D) 490.5 
 
 
 
Feed (F) 
5 wt % salt 
Mixed feed 
10 wt % salt
Desalination 
unit 
Pure water (W)
0% salt 
Recycle (R)
Effluent 
L 
D
1 
L
D
2
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Page 5 of 11 
33. A well-insulated hemispherical furnace (radius = 1m) 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/m
2
 ? K. Then the 
ratio of the heat transfer areas required for the co-current to counter-current modes of operation 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 
reduced 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/cm
2
?s, the 
diffusive flux (in mol/cm
2
?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 
 
surface 2
surface 1
500 ?C 
L 
P 
Q
180 ?C 20 ?C 
Case 1 Case 2
500 ?C
2L
P
Case 1
Q 
20 ?C