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# Chemical Engineering (CH) 2015 GATE Paper without solution (unsolved) GATE Notes | EduRev

## GATE : Chemical Engineering (CH) 2015 GATE Paper without solution (unsolved) GATE Notes | EduRev

``` Page 1

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 1/15
Q. 1 â€“ Q. 25 carry one mark each.
Q.1  The following set of three vectors
?
1
2
1
?,   ?
???? 6
???? ?   and   ?
3
4
2
?,

is linearly dependent when x is equal to

(A)    0 (B)    1 (C)    2 (D)    3

Q.2
For the matrix ?
4 3
3 4
? ,  if  ?
1
1
? is an eigenvector, the corresponding eigenvalue is ______.

Q.3
Consider a linear ordinary differential equation: ( ) ( ) x r y x p
dx
dy
= + . Functions ( ) x p and ( ) x r 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
(C) Second order differential equation (D) Exact differential equation

Q.4  A complex-valued function, f(z), given below is analytic in domain D:

( ) ( ) ( ) iy x z y x iv y x u z f + = + = , ,

Which of the following is NOT correct?

(A)

y
u
i
y
v
dz
df
?
?
+
?
?
= (B)

x
v
i
x
u
dz
df
?
?
+
?
?
=
(C)

y
u
i
y
v
dz
df
?
?
-
?
?
= (D)

x
v
i
y
v
dz
df
?
?
+
?
?
=

Q.5
A scalar function in the xy-plane is given by ???? ( ???? , ???? ) = ???? 2
+ ???? 2
. If  i
Ë†
and j
Ë†
are unit vectors in the
x and y directions, the direction of maximum increase in the value of ???? at (1,1) is along:
(A) -2i
Ë†
+  2 j
Ë†
(B) 2 i
Ë†
+  2 j
Ë†

(C) -2i
Ë†
-  2 j
Ë†
(D) 2 i
Ë†
-  2 j
Ë†

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
temperature (in K) at which it will boil at 1 bar (up to one decimal place) is ______________.

Q.7  Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T
1
,
P
1
) to a final state (T
2
, P
2
), 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.)
(A) ?U, ?S, Q are same (B) W, ?U, ?G are same
(C) ?S, W, Q are same (D) ?G, ?U, ?S are same
Page 2

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 1/15
Q. 1 â€“ Q. 25 carry one mark each.
Q.1  The following set of three vectors
?
1
2
1
?,   ?
???? 6
???? ?   and   ?
3
4
2
?,

is linearly dependent when x is equal to

(A)    0 (B)    1 (C)    2 (D)    3

Q.2
For the matrix ?
4 3
3 4
? ,  if  ?
1
1
? is an eigenvector, the corresponding eigenvalue is ______.

Q.3
Consider a linear ordinary differential equation: ( ) ( ) x r y x p
dx
dy
= + . Functions ( ) x p and ( ) x r 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
(C) Second order differential equation (D) Exact differential equation

Q.4  A complex-valued function, f(z), given below is analytic in domain D:

( ) ( ) ( ) iy x z y x iv y x u z f + = + = , ,

Which of the following is NOT correct?

(A)

y
u
i
y
v
dz
df
?
?
+
?
?
= (B)

x
v
i
x
u
dz
df
?
?
+
?
?
=
(C)

y
u
i
y
v
dz
df
?
?
-
?
?
= (D)

x
v
i
y
v
dz
df
?
?
+
?
?
=

Q.5
A scalar function in the xy-plane is given by ???? ( ???? , ???? ) = ???? 2
+ ???? 2
. If  i
Ë†
and j
Ë†
are unit vectors in the
x and y directions, the direction of maximum increase in the value of ???? at (1,1) is along:
(A) -2i
Ë†
+  2 j
Ë†
(B) 2 i
Ë†
+  2 j
Ë†

(C) -2i
Ë†
-  2 j
Ë†
(D) 2 i
Ë†
-  2 j
Ë†

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
temperature (in K) at which it will boil at 1 bar (up to one decimal place) is ______________.

Q.7  Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T
1
,
P
1
) to a final state (T
2
, P
2
), 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.)
(A) ?U, ?S, Q are same (B) W, ?U, ?G are same
(C) ?S, W, Q are same (D) ?G, ?U, ?S are same
GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 2/15

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
to be ideal. The universal gas constant R = 8.314 J/mol.K.  The fractional molar conversion of A at
equilibrium 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
the correct option.
P.   - ( ?u/ ?v)
s
I.      Temperature
Q.    ( ?g/ ?P)
T
II.     Pressure
R.    - ( ?g/ ?T)
P
III.    v
S.     ( ?u/ ?s)
v
IV.    s

(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, ???? max ,1
, whereas in the second pipe, the flow is
turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, ???? max ,2
.
For equal volumetric flow rates in both the pipes, the ratio ???? max ,1
/ ???? max ,2
(up to two decimal
places) is ________.

Q.11  For uniform laminar flow over a flat plate, the thickness of the boundary layer, ???? , at a distance x
from the leading edge of the plate follows the relation:

(A)   ???? ( ???? ) ? ???? -1
(B)   ???? ( ???? ) ? ????
(C)   ???? ( ???? ) ? ???? 1/2
(D)   ???? ( ???? ) ? ???? -1/2

Q.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/m
3
. The void fraction of the bed is 0.45. The bed is
fluidized using air (density 1 kg/m
3
).  If the acceleration due to gravity is 9.8 m/s
2
, the pressure
drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is _____________.

Page 3

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 1/15
Q. 1 â€“ Q. 25 carry one mark each.
Q.1  The following set of three vectors
?
1
2
1
?,   ?
???? 6
???? ?   and   ?
3
4
2
?,

is linearly dependent when x is equal to

(A)    0 (B)    1 (C)    2 (D)    3

Q.2
For the matrix ?
4 3
3 4
? ,  if  ?
1
1
? is an eigenvector, the corresponding eigenvalue is ______.

Q.3
Consider a linear ordinary differential equation: ( ) ( ) x r y x p
dx
dy
= + . Functions ( ) x p and ( ) x r 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
(C) Second order differential equation (D) Exact differential equation

Q.4  A complex-valued function, f(z), given below is analytic in domain D:

( ) ( ) ( ) iy x z y x iv y x u z f + = + = , ,

Which of the following is NOT correct?

(A)

y
u
i
y
v
dz
df
?
?
+
?
?
= (B)

x
v
i
x
u
dz
df
?
?
+
?
?
=
(C)

y
u
i
y
v
dz
df
?
?
-
?
?
= (D)

x
v
i
y
v
dz
df
?
?
+
?
?
=

Q.5
A scalar function in the xy-plane is given by ???? ( ???? , ???? ) = ???? 2
+ ???? 2
. If  i
Ë†
and j
Ë†
are unit vectors in the
x and y directions, the direction of maximum increase in the value of ???? at (1,1) is along:
(A) -2i
Ë†
+  2 j
Ë†
(B) 2 i
Ë†
+  2 j
Ë†

(C) -2i
Ë†
-  2 j
Ë†
(D) 2 i
Ë†
-  2 j
Ë†

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
temperature (in K) at which it will boil at 1 bar (up to one decimal place) is ______________.

Q.7  Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T
1
,
P
1
) to a final state (T
2
, P
2
), 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.)
(A) ?U, ?S, Q are same (B) W, ?U, ?G are same
(C) ?S, W, Q are same (D) ?G, ?U, ?S are same
GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 2/15

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
to be ideal. The universal gas constant R = 8.314 J/mol.K.  The fractional molar conversion of A at
equilibrium 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
the correct option.
P.   - ( ?u/ ?v)
s
I.      Temperature
Q.    ( ?g/ ?P)
T
II.     Pressure
R.    - ( ?g/ ?T)
P
III.    v
S.     ( ?u/ ?s)
v
IV.    s

(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, ???? max ,1
, whereas in the second pipe, the flow is
turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, ???? max ,2
.
For equal volumetric flow rates in both the pipes, the ratio ???? max ,1
/ ???? max ,2
(up to two decimal
places) is ________.

Q.11  For uniform laminar flow over a flat plate, the thickness of the boundary layer, ???? , at a distance x
from the leading edge of the plate follows the relation:

(A)   ???? ( ???? ) ? ???? -1
(B)   ???? ( ???? ) ? ????
(C)   ???? ( ???? ) ? ???? 1/2
(D)   ???? ( ???? ) ? ???? -1/2

Q.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/m
3
. The void fraction of the bed is 0.45. The bed is
fluidized using air (density 1 kg/m
3
).  If the acceleration due to gravity is 9.8 m/s
2
, the pressure
drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is _____________.

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 3/15
Q.13  Two infinitely large parallel plates (I and II ) are held at temperatures T
I
and T
II
(T
I
>  T
II
)
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:

(A) 0.5 (B) 0.75 (C)  0.25 (D)  0

Q.14  For a binary mixture of components A and B, N
A
and N
B
denote the total molar fluxes of
components A and B, respectively. J
A
and J
B
are the corresponding molar diffusive fluxes.
Which of the following is true for equimolar counter-diffusion in the binary mixture?
(A)   N
A
+ N
B
=  0  and  J
A
+ J
B
?  0
(B)   N
A
+ N
B
?  0  and  J
A
+ J
B
=  0
(C)   N
A
+ N
B
?  0  and  J
A
+ J
B
?  0
(D)   N
A
+ N
B
=  0  and  J
A
+ J
B
=  0

Q.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
state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates of
liquid and gas phases inside the column.

For this process, the value of the absorption factor (up to two decimal places) is ___________.

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 ×10
-6
m
2
/s.

The value of mass transfer coefficient is B × 10
-3
m/s, where B (up to one decimal place)  is
___________.

Q.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.

Page 4

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 1/15
Q. 1 â€“ Q. 25 carry one mark each.
Q.1  The following set of three vectors
?
1
2
1
?,   ?
???? 6
???? ?   and   ?
3
4
2
?,

is linearly dependent when x is equal to

(A)    0 (B)    1 (C)    2 (D)    3

Q.2
For the matrix ?
4 3
3 4
? ,  if  ?
1
1
? is an eigenvector, the corresponding eigenvalue is ______.

Q.3
Consider a linear ordinary differential equation: ( ) ( ) x r y x p
dx
dy
= + . Functions ( ) x p and ( ) x r 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
(C) Second order differential equation (D) Exact differential equation

Q.4  A complex-valued function, f(z), given below is analytic in domain D:

( ) ( ) ( ) iy x z y x iv y x u z f + = + = , ,

Which of the following is NOT correct?

(A)

y
u
i
y
v
dz
df
?
?
+
?
?
= (B)

x
v
i
x
u
dz
df
?
?
+
?
?
=
(C)

y
u
i
y
v
dz
df
?
?
-
?
?
= (D)

x
v
i
y
v
dz
df
?
?
+
?
?
=

Q.5
A scalar function in the xy-plane is given by ???? ( ???? , ???? ) = ???? 2
+ ???? 2
. If  i
Ë†
and j
Ë†
are unit vectors in the
x and y directions, the direction of maximum increase in the value of ???? at (1,1) is along:
(A) -2i
Ë†
+  2 j
Ë†
(B) 2 i
Ë†
+  2 j
Ë†

(C) -2i
Ë†
-  2 j
Ë†
(D) 2 i
Ë†
-  2 j
Ë†

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
temperature (in K) at which it will boil at 1 bar (up to one decimal place) is ______________.

Q.7  Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T
1
,
P
1
) to a final state (T
2
, P
2
), 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.)
(A) ?U, ?S, Q are same (B) W, ?U, ?G are same
(C) ?S, W, Q are same (D) ?G, ?U, ?S are same
GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 2/15

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
to be ideal. The universal gas constant R = 8.314 J/mol.K.  The fractional molar conversion of A at
equilibrium 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
the correct option.
P.   - ( ?u/ ?v)
s
I.      Temperature
Q.    ( ?g/ ?P)
T
II.     Pressure
R.    - ( ?g/ ?T)
P
III.    v
S.     ( ?u/ ?s)
v
IV.    s

(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, ???? max ,1
, whereas in the second pipe, the flow is
turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, ???? max ,2
.
For equal volumetric flow rates in both the pipes, the ratio ???? max ,1
/ ???? max ,2
(up to two decimal
places) is ________.

Q.11  For uniform laminar flow over a flat plate, the thickness of the boundary layer, ???? , at a distance x
from the leading edge of the plate follows the relation:

(A)   ???? ( ???? ) ? ???? -1
(B)   ???? ( ???? ) ? ????
(C)   ???? ( ???? ) ? ???? 1/2
(D)   ???? ( ???? ) ? ???? -1/2

Q.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/m
3
. The void fraction of the bed is 0.45. The bed is
fluidized using air (density 1 kg/m
3
).  If the acceleration due to gravity is 9.8 m/s
2
, the pressure
drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is _____________.

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 3/15
Q.13  Two infinitely large parallel plates (I and II ) are held at temperatures T
I
and T
II
(T
I
>  T
II
)
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:

(A) 0.5 (B) 0.75 (C)  0.25 (D)  0

Q.14  For a binary mixture of components A and B, N
A
and N
B
denote the total molar fluxes of
components A and B, respectively. J
A
and J
B
are the corresponding molar diffusive fluxes.
Which of the following is true for equimolar counter-diffusion in the binary mixture?
(A)   N
A
+ N
B
=  0  and  J
A
+ J
B
?  0
(B)   N
A
+ N
B
?  0  and  J
A
+ J
B
=  0
(C)   N
A
+ N
B
?  0  and  J
A
+ J
B
?  0
(D)   N
A
+ N
B
=  0  and  J
A
+ J
B
=  0

Q.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
state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates of
liquid and gas phases inside the column.

For this process, the value of the absorption factor (up to two decimal places) is ___________.

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 ×10
-6
m
2
/s.

The value of mass transfer coefficient is B × 10
-3
m/s, where B (up to one decimal place)  is
___________.

Q.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.

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 4/15
Q.18  For which reaction order, the half-life of the reactant is half of the full lifetime (time for 100 %
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:

A
A A
C
C C
Rate
50 1
1 . 0 2
2
+
+
= , where C
A
is the concentration of A.

C
A
varies in the range 0.5 - 50 mol/m
3
.

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
change in the input signal.

P: Gas chromatograph, with a long capillary
tube

Q: Venturi tube

R: Thermocouple with first order dynamics

S: Pressure transducer with second order
dynamics

(A)   P-IV, Q-III, R-II, S-I (B)   P-III, Q-I, R-II, S-IV
(C)   P-IV, Q-I, R-II, S-III (D)   P-II, Q-IV, R-III, S-I

Q.21
The transfer function for the disturbance response in an open-loop process is given by ( ) s G
d
open
.
The corresponding transfer function for the disturbance response in a closed-loop feedback
control system with proportional controller is given by ( ) s G
d
closed
. Select the option that is
ALWAYS correct { ( ) [ ] s G O represents order of transfer function ( ) s G }:

(A)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
=
(B)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
?
(C)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
=
(D)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
=

I
II
III

time
Output
Signal
IV
III
II
I
Page 5

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 1/15
Q. 1 â€“ Q. 25 carry one mark each.
Q.1  The following set of three vectors
?
1
2
1
?,   ?
???? 6
???? ?   and   ?
3
4
2
?,

is linearly dependent when x is equal to

(A)    0 (B)    1 (C)    2 (D)    3

Q.2
For the matrix ?
4 3
3 4
? ,  if  ?
1
1
? is an eigenvector, the corresponding eigenvalue is ______.

Q.3
Consider a linear ordinary differential equation: ( ) ( ) x r y x p
dx
dy
= + . Functions ( ) x p and ( ) x r 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
(C) Second order differential equation (D) Exact differential equation

Q.4  A complex-valued function, f(z), given below is analytic in domain D:

( ) ( ) ( ) iy x z y x iv y x u z f + = + = , ,

Which of the following is NOT correct?

(A)

y
u
i
y
v
dz
df
?
?
+
?
?
= (B)

x
v
i
x
u
dz
df
?
?
+
?
?
=
(C)

y
u
i
y
v
dz
df
?
?
-
?
?
= (D)

x
v
i
y
v
dz
df
?
?
+
?
?
=

Q.5
A scalar function in the xy-plane is given by ???? ( ???? , ???? ) = ???? 2
+ ???? 2
. If  i
Ë†
and j
Ë†
are unit vectors in the
x and y directions, the direction of maximum increase in the value of ???? at (1,1) is along:
(A) -2i
Ë†
+  2 j
Ë†
(B) 2 i
Ë†
+  2 j
Ë†

(C) -2i
Ë†
-  2 j
Ë†
(D) 2 i
Ë†
-  2 j
Ë†

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
temperature (in K) at which it will boil at 1 bar (up to one decimal place) is ______________.

Q.7  Three identical closed systems of a pure gas are taken from an initial temperature and pressure (T
1
,
P
1
) to a final state (T
2
, P
2
), 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.)
(A) ?U, ?S, Q are same (B) W, ?U, ?G are same
(C) ?S, W, Q are same (D) ?G, ?U, ?S are same
GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 2/15

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
to be ideal. The universal gas constant R = 8.314 J/mol.K.  The fractional molar conversion of A at
equilibrium 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
the correct option.
P.   - ( ?u/ ?v)
s
I.      Temperature
Q.    ( ?g/ ?P)
T
II.     Pressure
R.    - ( ?g/ ?T)
P
III.    v
S.     ( ?u/ ?s)
v
IV.    s

(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, ???? max ,1
, whereas in the second pipe, the flow is
turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, ???? max ,2
.
For equal volumetric flow rates in both the pipes, the ratio ???? max ,1
/ ???? max ,2
(up to two decimal
places) is ________.

Q.11  For uniform laminar flow over a flat plate, the thickness of the boundary layer, ???? , at a distance x
from the leading edge of the plate follows the relation:

(A)   ???? ( ???? ) ? ???? -1
(B)   ???? ( ???? ) ? ????
(C)   ???? ( ???? ) ? ???? 1/2
(D)   ???? ( ???? ) ? ???? -1/2

Q.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/m
3
. The void fraction of the bed is 0.45. The bed is
fluidized using air (density 1 kg/m
3
).  If the acceleration due to gravity is 9.8 m/s
2
, the pressure
drop (in Pa) across the bed at incipient fluidization (up to one decimal place) is _____________.

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 3/15
Q.13  Two infinitely large parallel plates (I and II ) are held at temperatures T
I
and T
II
(T
I
>  T
II
)
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:

(A) 0.5 (B) 0.75 (C)  0.25 (D)  0

Q.14  For a binary mixture of components A and B, N
A
and N
B
denote the total molar fluxes of
components A and B, respectively. J
A
and J
B
are the corresponding molar diffusive fluxes.
Which of the following is true for equimolar counter-diffusion in the binary mixture?
(A)   N
A
+ N
B
=  0  and  J
A
+ J
B
?  0
(B)   N
A
+ N
B
?  0  and  J
A
+ J
B
=  0
(C)   N
A
+ N
B
?  0  and  J
A
+ J
B
?  0
(D)   N
A
+ N
B
=  0  and  J
A
+ J
B
=  0

Q.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
state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates of
liquid and gas phases inside the column.

For this process, the value of the absorption factor (up to two decimal places) is ___________.

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 ×10
-6
m
2
/s.

The value of mass transfer coefficient is B × 10
-3
m/s, where B (up to one decimal place)  is
___________.

Q.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.

GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 4/15
Q.18  For which reaction order, the half-life of the reactant is half of the full lifetime (time for 100 %
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:

A
A A
C
C C
Rate
50 1
1 . 0 2
2
+
+
= , where C
A
is the concentration of A.

C
A
varies in the range 0.5 - 50 mol/m
3
.

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
change in the input signal.

P: Gas chromatograph, with a long capillary
tube

Q: Venturi tube

R: Thermocouple with first order dynamics

S: Pressure transducer with second order
dynamics

(A)   P-IV, Q-III, R-II, S-I (B)   P-III, Q-I, R-II, S-IV
(C)   P-IV, Q-I, R-II, S-III (D)   P-II, Q-IV, R-III, S-I

Q.21
The transfer function for the disturbance response in an open-loop process is given by ( ) s G
d
open
.
The corresponding transfer function for the disturbance response in a closed-loop feedback
control system with proportional controller is given by ( ) s G
d
closed
. Select the option that is
ALWAYS correct { ( ) [ ] s G O represents order of transfer function ( ) s G }:

(A)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
=
(B)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
?
(C)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
=
(D)

( ) [ ] ( ) [ ] s G O s G O
d d
closed open
=

I
II
III

time
Output
Signal
IV
III
II
I
GATE 2015                                                                                                                                                                                           CHEMICAL â€“  CH
CH 5/15
Q.22  Identify the WRONG statement amongst the following:
(A)   Steam distillation is used for mixtures that are immiscible with water.
(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
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

(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
Q. Coal gasification II.  Ultra-low sulphur diesel
R. Controlled release of chemicals III. Shale oil
S. Deep hydrodesulphurization IV. Prilling tower
V.  Gas hydrates
VI. Gas-solid non-catalytic reaction

(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
(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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