GATE XE 2013: Engineering Sciences
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2013 ENGINEERING SCIENCES – XE
XE : ENGINEERING SCIENCES
Duration: Three Hours Maximum Marks:100
Please read the following instructions carefully:
General Instructions:
1. Total duration of examination is 180 minutes (3 hours).
2. The clock will be set at the server. The countdown timer in the top right corner of screen will display
the remaining time available for you to complete the examination. When the timer reaches zero, the
examination will end by itself. You will not be required to end or submit your examination.
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Navigating to a Question
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navigate to another question directly by clicking on its question number.
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Answering a Question
6. Procedure for answering a multiple choice type question:
a. To select your answer, click on the button of one of the options
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Clear Response button
c. To change your chosen answer, click on the button of another option
d. To save your answer, you MUST click on the Save and Next button
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e. To mark the question for review, click on the Mark for Review and Next button. If an
answer is selected for a question that is Marked for Review, that answer will be considered
in the evaluation.
7. Procedure for answering a numerical answer type question:
a. To enter a number as your answer, use the virtual numerical keypad
b. A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal
point
c. To clear your answer, click on the Clear Response button
d. To save your answer, you MUST click on the Save and Next button
e. To mark the question for review, click on the Mark for Review and Next button. If an
answer is entered for a question that is Marked for Review, that answer will be considered
in the evaluation.
8. To change your answer to a question that has already been answered, first select that question for
answering and then follow the procedure for answering that type of question.
9. Note that ONLY Questions for which answers are saved or marked for review after answering will be
considered for evaluation.
Choosing an Optional Section
10. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can
be viewed by clicking on the name of that Section. The Section you are currently viewing is
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questions in the Section, but you will not be able to answer questions in the Section.
13. After clicking the Save and Next button for the last question in a Section, you will automatically be
taken to the first question of the next Section in sequence.
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Changing the Optional Section
15. After answering the chosen optional Sections, partially or completely, you can change an optional
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Section will DELETE all the answers for questions in that Section. Hence, if you think that you
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previously chosen optional Sections, then click on the BACK button.
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Do you want to deselect this Section?" If you want to deselect, click on the RESET button. If you do
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17. You can shuffle between different Sections any number of times. You can change the optional
Sections any number of times.
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Paper specific instructions:
1. There are a total of 65 questions carrying 100 marks. The question paper consists of questions of
multiple choice type and numerical answer type. Multiple choice type questions will have four
choices for the answer with only one correct choice. For numerical answer type questions, the answer
is a number and no choices will be given. A number as the answer should be entered using the
virtual keyboard on the monitor.
2. There are Eight sections: GA (General Aptitude), A (Engineering Mathematics), B (Fluid
Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer Science
& Engineering) and G (Food Technology).
3. Section GA (General Aptitude) and Section A (Engineering Mathematics) are compulsory. Attempt
any two optional Sections B through G.
4. There are 10 questions carrying 15 marks in General Aptitude (GA) section, which is compulsory.
Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each.
5. There are 11 questions carrying 15 marks in Section A (Engineering Mathematics), which is
compulsory. Questions Q.1 - Q.7 carry 1 mark each and questions Q.8- Q.11 carry 2 marks each.
6. Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks. Questions
Q.1 - Q.9 carry 1 mark each and questions Q.10 - Q.22 carry 2 marks each. The 2 marks questions
include two pairs of common data questions and one pair of linked answer questions. The answer to
the second question of the linked answer questions depends on the answer to the first question of the
pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to
the second question in the pair will not be evaluated
7. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions
will result in NEGATIVE marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong
answer. For all 2 marks questions, ⅔ mark will be deducted for each wrong answer. However, in the
case of the linked answer question pair, there will be negative marks only for wrong answer to the
first question and no negative marks for wrong answer to the second question. There is no negative
marking for questions of numerical answer type.
8. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall.
9. Do the rough work in the Scribble Pad provided.
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General Aptitude (GA) Questions
Q. 1 – Q. 5 carry one mark each.
Q.1 If 3 ≤ ≤ 5 and 8 ≤ ≤ 11 then which of the following options is TRUE?
(A) ≤ ≤
(B) ≤ ≤
(C) ≤ ≤
(D) ≤ ≤
Q.2 The Headmaster ___________ to speak to you.
Which of the following options is incorrect to complete the above sentence?
(A) is wanting
(B) wants
(C) want
(D) was wanting
Q.3 Mahatama Gandhi was known for his humility as
(A) he played an important role in humiliating exit of British from India.
(B) he worked for humanitarian causes.
(C) he displayed modesty in his interactions.
(D) he was a fine human being.
Q.4 All engineering students should learn mechanics, mathematics and how to do computation.
I II III IV
Which of the above underlined parts of the sentence is not appropriate?
(A) I (B) II (C) III (D) IV
Q.5 Select the pair that best expresses a relationship similar to that expressed in the pair:
water: pipe::
(A) cart: road (B) electricity: wire
(C) sea: beach (D) music: instrument
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Q. 6 to Q. 10 carry two marks each.
Q.6 Velocity of an object fired directly in upward direction is given by = 80 − 32 , where (time)
is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?
(A) (1, 3/2) (B) (1/2, 1)
(C) (1/2, 3/2) (D) (1, 3)
Q.7 In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents
respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a
randomly drawn autocomponent from the combined lot is found defective, what is the probability
that it was manufactured by M2?
(A) 0.35 (B) 0.45 (C) 0.5 (D) 0.4
Q.8 Following table gives data on tourists from different countries visiting India in the year 2011.
Country Number of
Tourists
USA 2000
England 3500
Germany 1200
Italy 1100
Japan 2400
Australia 2300
France 1000
Which two countries contributed to the one third of the total number of tourists who visited India in
2011?
(A) USA and Japan
(B) USA and Australia
(C) England and France
(D) Japan and Australia
Q.9 If |−2 + 9| = 3 then the possible value of |− | − would be:
(A) 30 (B) -30 (C) -42 (D) 42
Q.10 All professors are researchers
Some scientists are professors
Which of the given conclusions is logically valid and is inferred from the above arguments:
(A) All scientists are researchers
(B) All professors are scientists
(C) Some researchers are scientists
(D) No conclusion follows
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A: ENGINEERING MATHEMATICS
Q. 1 – Q. 7 carry one mark each.
Q.1
The value of the integral ∫ is
( )
√ (B) √ (C) − √ √
(A) (D) −
Q.2 Which one of the following partial differential equations CAN NOT be reduced to two
ordinary differential equations by the method of separation of variables?
(A) − =0 (B) − =0
(C) + + =0 (D) + + =0
Q.3 The Fourier series of the periodic function
( ) = | |, −1 < < 1, ( + 2) = ( ), Єℝ
is given by
1 4 cos(2 −1)
− ∑∞=1 2 .
2 (2 −1) 2
Using the above, the sum of the infinite series 1 + + + . . . is
2
(A) 4 (B) (C) (D)
Q.4 Consider the function ( ) = , Є ℂ. At = 0, the function
(A) does not satisfy the Cauchy-Riemann equations
(B) satisfies the Cauchy-Riemann equations but is not differentiable
(C) is differentiable but not analytic
(D) is analytic
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Q.5 ( )
The integral ∮ along the contour : | − (1 + )| = 2, oriented anti-
( )( )
clockwise, is equal to
(A) 0
(B) (C) − (D)
Q.6 /
The integral ∫ ∫ equals
(A) (B) (C) (D)
Q.7 If the mean and variance of a binomial distribution are 6 and 2 respectively, then the
probability of two failures is
2 7
(A) 4 (B) 4 (C) 17 (D) 17
3
Q. 8 - Q. 11 carry two marks each.
Q.8 1 0 −1
For the matrix = 0 1 −1 , consider the following statements:
1 1 −2
(P) The characteristic equation of is − = 0.
(Q) does not exist.
(R) The matrix is diagonalizable.
Which of the above statements are true?
(A) P, Q and R (B) P and R but not Q
(C) P and Q but not R (D) Q and R but not P
Q.9 The work done by the force ⃗ = ( + ) ̂+( + ) ̂ in moving a particle once
along the triangle with vertices (0,0), (1,0) and (0,1) in the anti-clockwise direction is
(A) 0 (B) 1/6 (C) 1/3 (D) 5/3
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Q.10 The general solution of the differential equation
+ + − = 0, >0
is
/ √ √
(A) + cos + sin
/ √ √
(B) + cos + sin
/ √ √
(C) + cos + sin
/ √ √
(D) + cos + sin
Q.11 Using Euler’s method to solve the differential equation
= 2 cos − , (0) = 1
with step-size ℎ = 0.25, the value of (0.5) is
(A) 1.3125 (B) 1.1875 (C) 1.125 (D) 1.0625
END OF SECTION - A
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B:FLUID MECHANICS
Q. 1 – Q. 9 carry one mark each.
Q.1 The gauge pressure inside a soap bubble of radius , with denoting the surface tension
between the soap solution and air, is.
(A) (B) (C) (D)
Q.2 Let , and represent respectively the metacentre, centre of buoyancy and the centre of
mass of a floating buoy. Which of the following statements is correct?
(A) is above ; Buoy unstable (B) is above ; Buoy stable
(C) is above ; Buoy stable (D) is above ; Buoy unstable
Q.3 A reservoir connected to a pipe line is being filled with water, as shown in the Figure. At
any time t, the free surface level in the reservoir is h. Find the time in seconds for the
reservoir to get filled up to a height of 1 m, if the initial level is 0.2 m. _________
Q.4 Bernoulli’s equation is valid for the following type of flow:
(A)Compressible, steady, inviscid (B)Incompressible, steady, viscous
(C)Compressible, unsteady, viscous (D)Incompressible, steady, inviscid
Q.5 If is the area of a circle of radius enclosing a plane forced vortex flow, with origin at
the centre of the vortex and if ω is the angular velocity, ζ is the vorticity, ⃗ is the velocity
vector, then the circulation around the contour of the circle is given by
(A) 2 (B) 2ζ (C) 2 ⃗ (D) 0
Q.6 Flow past a circular cylinder can be produced by superposition of the following elementary
potential flows:
(A)Uniform flow, doublet (B)Uniform flow, vortex
(C)Source, vortex (D)Sink, vortex
Q.7 Let δ, δ1 and δ2 denote respectively the boundary-layer thickness, displacement thickness
and the momentum thickness for laminar boundary layer flow of an incompressible fluid
over a flat plate. The correct relation among these quantities is
(A) δ < δ1< δ2 (B) δ > δ1> δ2 (C) δ > δ1< δ2 (D) δ < δ1> δ2
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Q.8 In the hydrodynamic entry region of a circular duct, the pressure forces balance the sum of
(A)viscous and buoyancy forces (B)inertia and buoyancy forces
(C)inertia and surface tension forces (D)inertia and viscous forces
Q.9 Bodies with various cross-sectional shapes subjected to cross-flow of air are shown in the
following figures. The characteristic dimension of all the shapes is the same. The cross-
sectional shape with the largest coefficient of drag (i.e. sum of the pressure and skin-
friction drags), at any moderately large Reynolds number, is
(A) (B)
(C) (D)
Q. 10 - Q. 22 carry two marks each.
Q.10 A U-tube of a very small bore, with its limbs in a vertical plane and filled with a liquid of
density ρ, up to a height of h, is rotated about a vertical axis, with an angular velocity of
ω, as shown in the Figure. The radius of each limb from the axis of rotation is R. Let pa be
the atmospheric pressure and g, the gravitational acceleration. The angular velocity at
which the pressure at the point O becomes half of the atmospheric pressure is given by
( )
(A) (B)
(C) (D)
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Q.11 An incompressible fluid at a pressure of 150 kPa (absolute) flows steadily through a two-
dimensional channel with a velocity of 5 m/s as shown in the Figure. The channel has a 90o
bend. The fluid leaves the channel with a pressure of 100 kPa (absolute) and linearly-
varying velocity profile. vmax is four times vmin. The density of the fluid is 914.3 kg/m3. The
velocity vmin, in m/s, is
(A) 25 (B) 2.5 (C) 2.0 (D) 0.2
Q.12 The velocity vector corresponding to a flow field is given, with usual notation, by ⃗ =
3 ̂+4 ̂. The magnitude of rotation at the point (2,2) in rad/s is
(A) 0.75 (B) 1.33 (C) 2 (D) 4
Q.13 The stream function for a potential flow field is given by ψ = − . The corresponding
potential function, assuming zero potential at the origin, is
(A) + (B) 2 (C) − (D) −
Q.14 Fully developed flow of an oil takes place in a pipe of inner diameter 50 mm. The pressure
drop per metre length of the pipe is 2 kPa. Determine the shear stress, in Pa, at the pipe
wall. __________
Q.15 The Darcy friction factor for a smooth pipe is given by = 64/Re for laminar flow and
by = 0.3/Re . for turbulent flow, where Re is the Reynolds number based on the
diameter. For fully developed flow of a fluid of density 1000 kg/m3 and dynamic viscosity
0.001 Pa.s through a smooth pipe of diameter 10 mm with a velocity of 1 m/s, determine
the Darcy friction factor. _________
Q.16 Air flows steadily through a channel. The stagnation and static pressures at a point in the
flow are measured by a Pitot tube and a wall pressure tap, respectively. The pressure
difference is found to be 20 mm Hg. The densities of air, water and mercury, in kg/m3, are
1.18, 1000 and 13600, respectively. The gravitational acceleration is 9.81 m/s2. Determine
the air speed in m/s. _____________
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Common Data Questions
Common Data for Questions 17 and 18:
The velocity field within a laminar boundary layer is given by the expression:
⃗= ̂+ ̂
/ 4 /
where = 100 m1/2 and the free stream velocity = 0.1 m/s.
Q.17 Calculate the x-direction component of the acceleration in m/s2 at the point = 0.5 m and
= 50 mm. _________
Q.18 Find the slope of the streamline passing through the point = 0.5 m and = 50mm. ____
Common Data for Questions 19 and 20:
The wave and eddy resistance of a sea-going vessel, 96 m in length, driven at a velocity of 12 m/s,
is to be determined. For this purpose, a 1/16 th scale model is employed in fresh water and the
-4
coefficient of resistance we of the model is found to be 1.47×10 . The quantity we is defined as
we /( /2), where we is the wave and eddy resistance, is the density, is the velocity and
is the characteristic length. The density of sea water is 1026 kg/m3.
Q.19 The velocity in m/s, at which the model is towed, is
(A)0.75 (B)1.33 (C)3 (D)192
Q.20 The resistance of the prototype, in kN, is
(A) 6 (B) 25 (C) 26.9 (D) 100.1
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Linked Answer Questions
Statement for Linked Answer Questions 21 and 22:
Water enters a symmetric forked pipe and discharges into atmosphere through the two branches as
shown in the Figure. The cross-sectional area of section-1 is 0.2 m2 and the velocity across
section-1 is 3 m/s. The density of water may be taken as 1000 kg/m3. The viscous effects and
elevation changes may be neglected.
Q.21 The gauge pressure at section-1, in kPa, is
(A)0.6 (B)13.5 (C)135 (D)600
Q.22 The magnitude of the force, in kN, required to hold the pipe in place, is
(A) 2.7 (B) 5.4 (C) 19 (D) 27
END OF SECTION - B
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C:MATERIALS SCIENCE
Useful Data:
Avogadro’s Number : 6.023 x 1023 mol-1
Boltzmann’s constant, k : 1.38 x 10-23 J.K-1
Electron Charge, e : 1.6 x 10-19 C
Electron rest mass, mo : 9.1 x 10-31 kg
Gas Constant, R : 8.314 J.mol-1K-1
Free Space Permittivity, o : 8.854 x 10-12 F.m-1
Free Space magnetic permeability, o : 4 x 10-7 H.m-1
Speed of light, c : 3 x 108 m.s-1
Planck’s constant, h : 6.63 x 10-34 J.s-1
Bohr Magneton, b : 9.27 x 10-24 A m2
1 eV = 1.6 x 10-19 J
1 calorie = 4.2 J
Q. 1 – Q. 9 carry one mark each.
Q.1 As temperature increases, diffusivity of an atom in a solid material,
(A) increases (B) decreases
(C) remains constant (D) depends on the specific material
Q.2 Which of the following is NOT correct?
(A)Dislocations are thermodynamically unstable defects.
(B)Dislocations can move inside a crystal under the action of an applied stress.
(C)Screw dislocations can change the slip plane without climb
(D)Burger’s vector of an edge dislocation is parallel to the dislocation line.
Q.3 At a constant atmospheric pressure, the number of phases, P which coexist in a chosen system at
equilibrium, is related to the number of components, C in the system and the degree of freedom, F
by
(A) P+F=C-2 (B) P+F=C+2
(C) P+F=C+1 (D) P+F=C-1
Q.4 Which one of the following metals is commonly alloyed with iron to improve its corrosion
resistance?
(A) Co (B) Cr (C) Ti (D) Nb
Q.5 The number of slip systems in a metal with FCC crystal structureis
(A) 4 (B) 6 (C) 8 (D) 12
Q.6 Upon recrystallization of a cold worked metal,
(A) strength increases and ductility decreases
(B)strength decreases but ductility increases
(C)both strength and ductility increase
(D)both strength and ductility decrease
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Q.7 In carbon fiber reinforced resin composites, for a given fiber volume content, Young’s modulus
depends on the orientation of the fiber with respect to the applied load. Which orientation of the
fibers will give the maximum value of Young’s modulus?
(A)transverse (B)longitudinal
(C)random (D)both transverse and longitudinal
Q.8 Vulcanization is related to
(A)strengthening of rubber (B)extrusion
(C)injection moulding (D)addition polymerisation
Q.9 Which one of the following oxides crystallizes into fluorite structure?
(A) UO2 (B) MgO (C) BaTiO3 (D) MgAl2O4
Q. 10 - Q. 22 carry two marks each.
Q.10 Match the conventional ceramic materials listed in Column I with their respective common
applications in Column II
Column I Column II
P. Lead Zirconate Titanate (PZT) 1. cutting tool
Q. Zinc Oxide (ZnO) 2. thermal barrier coating
R. Silicon Carbide (SiC) 3. actuator
S. Zirconia (ZrO2) 4. varistor
5. super conductor
(A) P-1, Q-2, R-3, S-5 (B) P-3, Q-2, R-1, S-5
(C) P-2, Q-1, R-5, S-3 (D)P-3, Q-4, R-1, S-2
Q.11 Match the terminologies given in Column Iwith theirrelations listed in Column II
Column I Column II
P. domain wall 1. superconductors
Q. Fick’s law 2. mechanical properties
R. Matthiessen’s rule 3. ferromagnetic materials
S. Hall-Petch relation 4. resistivity of impure metals
T. Meissner effect 5. diffusion
(A) P-1, Q-3, R-5, S-2, T-4 (B) P-3, Q-5, R-2, S-4, T-1
(C) P-3, Q- 5, R-4, S-2, T-1 (D) P-3, Q-4, R-3, S-2, T-4
Q.12 Match the microscopes listed in Column I with their principle of operation listed in Column II
Column I Column II
P. Scanning Electron Microscope (SEM) 1. van der Waals forces between atoms
Q. Transmission Electron Microscope 2. electrons to jump across a potential
(TEM) barrier
R. Scanning Tunnelling Microscope (STM) 3. diffraction of electrons
S. Atomic Force Microscope (AFM) 4. detection of secondary electrons
5. photo emission of electrons
(A) P-2, Q-5, R-3, S-1 (B)P-3, Q-4, R-5, S-2
(C) P-4, Q-3, R-2, S-1 (D)P-4, Q-3, R-5, S-2
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Q.13 X-rays of unknown wavelength are diffracted by an FCC metal with a lattice parameter of 0.352
nm. The measured ‘2’ angle for the {200} peak is 61.08. Calculate the wavelength of the X-
ray used, in nm. ___________
Q.14 A metal with HCP crystal structure has lattice constants a = 0.30 nm and c = 0.56 nm. Determine
the volume of the unit cell of this metal, in nm3. _________
Q.15 The band gap of a semiconducting material used to make an LED is 1.43 eV. What will be the
minimum wavelength ofthe radiation emitted by this LED, in µm? __________
Q.16 For automatic control of household electric water heater a relay switch is activated by thermal
expansion of a brass rod of length 50 cm as shown in the schematic below. The distance
between the rod and the lever, x, is adjusted by moving the base of the rod. As the water gets
heated the rod expands and as soon as the rod touches the lever, the circuit is broken
disconnecting the heater from the power supply. Find the distance, x, in mm, to be set at water
temperature of 20oC such that the circuit is broken at 70oC. The coefficient of linear thermal
expansion of brass is 20 x 10-6 oC-1 ______________
230 V,
AC
x
Brass Rod
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Common Data Questions
Common Data for Questions 17 and 18:
From tensile test of a particular alloy the following values were obtained. The material exhibits linear work
hardening as shown in the figure given below.
At Yield At Fracture
Stress, GPa 0.7 0.8
Strain, % 1 4
1
0.8
Stress, GPa
0.6
0.4
0.2
0
0 1 2 3 4 5
Strain, %
Q.17 If the cylindrical specimen had a dimension of diameter 10 mm and length 50 mm, find the length
of the specimen at the yield point, in mm. ___________
Q.18 Find the toughness of the material, in M J m-3. ____________
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Common Data for Questions 19 and 20:
An isomorphous alloy system contains 47 wt% of A and 53 wt % of B and is at 1300 C. Referring to the
figure given below, answer the following:
1500
1400 Liquid
Temperature, oC
1300
1200
Solid
1100
1000
0 10 20 30 40 50 60 70 80 90 100
100% A Weight Percentage of B, % 100% B
Q.19 What is the weight percentage of A in solid phase at this temperature? ___________
Q.20 What weight percentage of this alloy is liquid? __________
Linked Answer Questions
Statement for Linked Answer Questions 21 and 22:
A stress of 10 MPa is applied to an elastomer to generate a strain of 50%. The strain is held constant at this
value. After 40 days at 20OC, the stress decreases to 5 MPa.
Q.21 What is the relaxation time constant for this material? ___________
Q.22 What will be the stress after 60 days at 20OC? ______________
END OF SECTION - C
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D :SOLID MECHANICS
Q. 1 – Q. 9 carry one mark each.
Q.1 At a point in a body subjected to plane stress, the state of stress is as shown in the Figure. One of
the principal stresses is 180 MPa. Find the unknown shear stress τ (in MPa). __________
τ
160 MPa
160 MPa
τ
Q.2 A point in a body is subjected to a hydrostatic pressure of 100 MPa. Find the maximum shear
stress at this point in MPa. ___________
Q.3 A circular shaft of diameter 10 mm and length 3m is subjected to a torque of T = π N-m at a
location 2m away from the fixed end as shown in the Figure. Find out the angle of twist (in radians)
at the free end. Shear modulus of the material of the shaft is 10 GPa. ___________
T
2m 1m
Q.4 A rigid massless rod ABC is hinged at A and carries a point mass M (in kg) at C. Point B is
connected to a linear spring with spring constant k (in N/m) as shown in the figure. The length AB
and AC area and L, respectively. Neglecting the effect of gravity, the natural frequency of this
spring-mass system in rad/s is
C
M
B L
k
a
A
(A) (B) (C) (D)
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Q.5 A two bar truss is shown in the Figure. The cross-sectional area and Young’s modulus of bar 1 are
0.02 m2 and 200GPa, respectively. The cross-sectional area and Young’s modulus of bar 2 are 0.01
m2and 80GPa, respectively. The force F applied on the truss is 2 N. Find out the stress developed in
bar 2 in Pa. ___________
2
1
0 0
30 60
F
Q.6 A spring balance reads 10 kg in a lift when the lift is stationary. When the lift starts moving with a
constant acceleration, the new reading is 12.3 kg. If the upward acceleration is considered positive,
what is the acceleration of the lift? Acceleration due to gravity may be taken as 10
m/s2downwards.______________
Q.7 A force F = 2 N is applied on a block of mass M = 0.5 kg as shown in the figure. The block is
constrained to move along the horizontal direction in a guideway. Find out the distance (in meters)
travelled by the block in 2 s starting from rest. Neglect any friction between the block and the
guideway. ____________
F
0
60
M
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Q.8 A man of mass 50 kg is walking on a long wooden board of mass 200 kg (as shown in the Figure).
The wooden board is initially at rest on a frictionless ice surface. If the man walks with a velocityof
V =1 m/s in the positive x direction relative to the wooden board, find the velocity of the board in
m/s. Velocity is positive in the positive x direction. _____________
V
Wooden board
y
x Ice surface
Q.9 A rigid bar AB is hinged at B through a torsional spring with spring constant kt.. For small
rotations of the bar AB about B, the critical load Pcr is given by
P
A
L
kt
B
(A) (B) (C) (D)
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Q. 10 - Q. 22 carry two marks each.
Q.10 A disk of mass M= 14kg and radius 1 m is attached to a spring which has a stiffness k = 75 N/m and
an unstretched length of 1m. If the disk is released from rest in the position shown in the Figure and
the disk rolls without slipping, find its angular velocity (in rad/s) at the instant the center of mass is
displaced by 3 m. ______________
K
4m
M
3m
Q.11 A strain gauge is mounted on the outer surface of a thin cylindrical pressure vessel in the
circumferential direction. The mean diameter and thickness of the cylinder are 4.0 m and 20 mm,
respectively. Young’s modulus and Poisson’s ratio of the material of the cylinder are 200 GPa and
0.25, respectively. Find the pressure in MPa inside the cylindrical vessel when the strain gauge
indicates a strain of 7.0x 10-4. ____________
Q.12 A solid shaft of diameter 100 mm is rotating at a constant angular speed of (10/ π) rad/s. The shaft
carries three rigid pulleys A, B and C as shown in the Figure. Pulley B is connected to a motor
supplying 10kW power. Pulley B and C are connected to two pumps consuming 5kW each. Find
the maximum shear stress (in MPa) in the shaft due to torsion alone. __________
A B C
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Q.13 A beam is fixed at the left end and supported by a spring at the other end. The length of the beam is
L and its flexural rigidity is EI. The spring constant of the spring is = . A vertical
downward load P is applied at the right end. The deflection of the point under the load P is
P
EI
L
k
(A) (B) (C) (D)
Q.14 Find the maximum bending moment (magnitude wise) in kN-m for the beam shown in the Figure.
______
40 kN
20 kN
B
A D
C
2.5 m 3m 2m
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Q.15 A projectile is fired with a velocity V= 3√2 m/s from a point at height H = 0.8 m at an angle of 450
with respect to the horizontal direction as shown in the Figure. Find the horizontal distance S in
meters travelled by the projectile when it hits the ground. Take acceleration due to gravity as10 m/
s2. __________
v
o
45
H
S
Q.16 A particle P is moving on a circular path of radius r = 1m. The angular location of the particle is
measured as shown in the Figure. The motion of the particle is described by = 2 sin( ). Find the
magnitude of the total acceleration (in m/s2) of the particle at time t = π/3 seconds. _________
Arc of a circle
P
Y r
q
x
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Common Data Questions
Common Data for Questions 17 and 18
A frame ABC is shown in the Figure. Members AB and BC both have a length of L, and Young’s modulus
E. Members AB and BC both have a square cross-section of side a. A load P is applied at point C as
shown in the figure.
P
B C
900
A
Q.17 Neglecting the axial compression of member AB, the deflection of point C in the direction of the
load is
(A) (B) (C) (D)
Q.18 The maximum bending stress in the frame is
(A) (B) (C) (D)
Common Data for Questions 19 and 20
At a point in an object subjected to plane stress conditions, the state of stress is as shown in the Figure.
40 MPa
B 40 MPa
o
100 MPa 45 100 MPa
40 MPa A
40 MPa
Q.19 One of the principal stresses(in MPa) is
(A)40 (B) 80 (C) 120 (D) 140
Q.20 The normal stress on the plane AB (in MPa) is
(A) 30 (B) 70 (C) 100 (D) 110
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Linked Answer Questions
Statement for linked answer questions 21 and 22
Two rods are joined together and the entire assembly is supported between two rigid walls, as shown in the
Figure. The cross-sectional area and Young’s modulus for both the rods are 0.01 m2 and 10 GPa, respectively.
The coefficients of thermal expansion for the two rods are α1= 4 × 10-6 /0C and α2 = 10-6 /0C, respectively. The
entire assembly is heated by 1000 C. Neglect the effect of Poisson’s ratio.
1 2
2m 1m
Q.21 The stress in rod 1 (in MPa) is
(A) -4.0 (B) -3.0 (C) -2.5 (D) -1.0
Q.22 Considering the displacement to the right as positive, the displacement (in mm) of the interface
between the two rods is
(A)-0.2 (B) -0.1 (C) 0.1 (D) 0.2
END OF SECTION - D
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E:THERMODYNAMICS
Notation used:
p-pressure, V- volume, T-temperature, S- entropy, H- enthalpy, U- internal energy G- Gibbs free energy.
Specific properties are designated by lower case symbols.
Useful data:
Universal gas constant (R)= 8.314 J/mol K
Acceleration due to gravity = 9.81 m/s2
Molecular masses in kg/kmol: Mair = 29, Mnitrogen=28, Mwater=18, Mhelium=4
Ratio of ideal gas specific heats :ai=1.4
cpfor water = 4.186 kJ/kg K
Vapour pressure equation for water in the temperature range of5 to100 oC , with p in kPa and T in K
5190
ln( ) = 18.558 −
Q. 1 – Q. 9carry one mark each.
Q.1 The measured temperature of a system is 30oC.Its exact absolute temperature in K is
(A) 303.00 (B)303.10 (C) 303.15 (D) 303.16
Q.2 The fuel air mixture in a pertrol engine is ignited with a spark plug at the end of compression
stroke. This process
(A)increases the entropy of the fuel air mixture but decreases the entropy of the spark plug
(B)decreases the entropy of the fuel air mixture but increases the entropy of the spark plug
(C)decreases the entropy of the fuel air mixture and of the spark plug
(D)increases the entropy of the fuel air mixture and of the spark plug
Q.3 In the van der Waals equation of state given below:
( + )( − ) =
The constant a represents the effect of
(A)attractive forces between molecules
(B) repulsive forces between molecules
(C)deviation from molecules being spherical
(D)finite size of the molecule
Q.4 For a reversible isothermal expansion of an ideal gas from a state 1 to a state 2,
(A)s1=s2 (B) s1>s2 (C) s1<s2 (D)h1>h2
Q.5 For a pure substance the critical isotherm on the p-v plane exhibits
(A) a maximum (B) a minimum
(C) a point of inflection (D) a discontinuity
Q.6 For an ideal gas as a working fluid for a given heat input Q, the process that gives the maximum
work among the following four processes is
(A) isothermal (B) constant volume (C) constant pressure (D) isentropic
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Q.7 An air standard Otto cycle has the following shape on a thermodynamic property plane.
y
x
The x and y coordinates, respectively, are
(A) v and p (B) s and v (C) v and T (D) s and p
Q.8 The specific volume of steam after expansion in a turbine is 12 m3/kg. At this pressure the saturated
liquid and saturated vapour specific volumes are 0.001 and 15.25 m3/kg respectively. What is the
dryness fraction to second decimal place accuracy? _________
Q.9 Which of the following processes, shown in the figure below, represents the throttling of an ideal
gas?
1 2
T 3
5 4
S
((A) 1to2 (B) 1to 3 (C) 1to 4 (D) 1to 5
Q. 10 - Q. 22 carry two marks each.
Q.10 On a ln pvsh coordinate system, where ln p is the y-coordinate and h is the x coordinate, the slope of
a constant entropy line is
(A) 1/v (B) v (C) p/v (D) 1/(pv)
Q.11 Starting from the definition of Gibbs free energy function g=h-Ts, the Maxwell relation that can be
derived is
(A) = (B) = (C) =− (D) =−
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Q.12 A thermodynamic cycle operates between one source at a temperature of 600 K, another source at
a temperature of 300 K and a sink at a temperature T as shown in the figure below
600 K
1 kJ
T
1 kJ
300 K
If the First and Second laws of thermodynamics are not violated, what should be the value of T in
K? _____________
Q.13 A closed system containing an ideal gas undergoes a cycle as shown in the figure shown below. For the
process1-2, which one of the following statements is true?
2 3
2p
p 1
v/2 v
(A) Heat added = (B) Heat rejected =
(C) Heat added = (D) Heat rejected =
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Q.14 A well-insulated rigid hot water tank receives steady flow of water from two sources as shown in
the figure below
1 kg/ s 5 kg/ s
at 80 oC at 50 oC
Back-up
heater
at 60 oC
There is no accumulation of water in the tank. A back-up heater is provided to ensure a constant
outflow temperature of water at 60 oC from the tank under steady state. What is the required
capacity of the back-up heater to the nearest kW? __________
Q.15 1 kg of air in an insulated rigid tank of volume 1 m3is churned with a friction-less fan (see figure
below) of 600 W capacity for 10 minutes. The fan efficiency is 100 %. Treating air as an ideal gas
and neglecting kinetic and potential energy changes, what is the increase of pressure, to the nearest
kPa? _________
600 W
Q.16 The isothermal compressibility of a liquid is 5 × 10-6 /kPa. If it is compressed at constant
temperature from 5000 to 10000kPa, what is the ratio of final volume to initial volume, to second
decimal place accuracy? ____________
Common Data Questions
Common Data for Questions 17 and 18:
At a location where the atmospheric pressure is 98 kPa and the ambient temperature is 30oC, the humidity
ratio is 0.01 kg/kg of dry air. A high pressure front moves over the location which changes only the
atmospheric pressure to 102kPa,while the humidity ratio remains same.
Q.17 What is the partial pressure of water vapour in kPa to the first decimal place accuracy before the
high pressure front moves in? ____________
Q.18 What is the relative humidity of air under the influence of high pressure front to integer precision in %? _____
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Common Data for Questions 19 and 20:
A rigid insulated cylinder is divided into two chambers A and B by a thin rigid insulating barrier as
shown in the figure below
Rigid insulating
barrier
Specific Heat Data:
For He
A B cp= 5181 J/kg.K
(0.5 kg N2+0.5 kg He) (1 kg pure N2)
cv= 3102 J/kg.K
For N2
300 K 400 K
cp= 1039 J/kg.K
p 2p
cv= 742 J/kg.K
Initially, chamber A contains a mixture of 0.5 kg nitrogen and 0.5 kg helium at 300 K while chamber B
contains 1 kg of pure nitrogen at 400 K. The pressure in chamber B is twice that in chamber A. The gases and
gas mixtures are assumed to be ideal.
Q.19 What is the ratio of the volumes of chambers A and B, i.e. VA/VB, to first decimal place accuracy?
________
Q.20 If the barrier is removed and the gases are allowed to mix and reach thermodynamic equilibrium,
what is the final temperature of the mixture, to the nearest K? ________
Linked Answer Questions
Statement for Linked Answer Questions 21 and 22:
A combined vapour compression-cum-Brayton cycle is shown below
3 2 5
ln
p
1
4
6
241.7 404. 417.2 518. 538.
h (kJ/kg)
1-2: Isentropic compression, 5-6: isentropic expansion.
The refrigeration system has a cooling capacity of 30 kW and the turbine generates a power of 30 kW.
Q.21 What is the mass flow rate of the working fluid through the turbine, in kg/s, to first decimal place
accuracy? __________
Q.22 What is the power required to drive the compressor, to the nearest kW? ________
END OF SECTION - E
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F: POLYMER SCIENCE AND ENGINEERING
Q. 1 – Q. 9 carry one mark each.
Q.1 In free radical polymerization, one of the following techniques permits simultaneous increase in
rate of polymerization and polymer molecular weight.
(A) Solution polymerization.
(B) Suspension polymerization.
(C) Bulk polymerization.
(D) Emulsion polymerization.
Q.2 The shear modulus, G, of plastic is related to the elastic modulus, E, and the Poisson ratio, , as
(A) = 2(1 − ) (B) = 2(1 + )
(C) = 2(1 + ) (D) = (1 + )
Q.3 LLDPE is obtained by
(A) Ziegler-Natta polymerization of ethylene.
(B) free-Radical polymerization of ethylene.
(C) free-Radical polymerization of ethylene and alpha-olefins.
(D) Ziegler-Natta copolymerization of ethylene and alpha-olefins.
Q.4 A hindered phenol is added to a polyolefin
(A) to increase ozone resistance (B) to increase foamability
(C) to increase oxidation resistance (D) to increase crosslinkability
Q.5 Stretching of rubber leads to
(A) decrease in alignment of polymer chains
(B) increase in alignment of polymer chains
(C) no change in alignment of polymer chains
(D) decrease in strength of rubber
Q.6 In a cone and plate viscometer, the rate of strain is related to the speed of rotation of the cone,
(radian/second), and the angle between the cone and the plate, (radian), by the following relation
(A) (B) cos (C) (D)
Q.7 The tensile breaking strength of polycarbonate (I), low density polyethylene (II), polystyrene (III)
and polypropylene (IV) can be arranged as
(A) IV > II > I > III (B) I > II > IV > III (C) I > III > IV > II (D) III > I > II > IV
Q.8 High molecular weight polymers could be obtained even at low monomer conversion in case of
(A) Step growth polymerization (B) Living polymerization
(C) Chain growth polymerization (D) Solid state polymerization
Q.9 A reinforced polymer composite is made by the incorporation of
(A) elastomers into the polymer.
(B) fibers into the polymer.
(C) plasticizers into the polymer.
(D) gaseous additives into the polymer.
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Q. 10 - Q. 22 carry two marks each.
Q.10 Match the following for free-radical copolymerization of two monomers with reactivity ratios, r1
and r2.
Reactivity Ratios Copolymer Nature
P. r1 = r2 = 0 1. Random copolymer
Q. r1 = r2 = 1 2. Alternate copolymer
R. r1 >1, r2 > 1 3. Block copolymer
S. 0 < r1r2 < 1 4. Random-Block copolymer
(A) P-2; Q-1; R-3; S-4 (B) P-3; Q-1; R-2; S-4
(C) P-2; Q-4; R-3; S-1 (D) P-2; Q-3; R-1; S-4
Q.11 The relative viscosity of a 1% solution (weight/volume) of a given polymer was found to be 1.1.
The inherent viscosity of this polymer will be
(A) 0.065 dl/g (B) 0.075 dl/g (C) 0.085 dl/g (D) 0.095 dl/g
Q.12 Match the following in case of step-growth polymerization, where A reacts only with B, and B
B
reacts only with A (Note: A A is expressed as A2, and A is expressed as AB2).
B
Monomers Polymer
P. A2 + AB3 1. Hyperbranched Polymer
Q. AB2 2. Crosslinked Polymer
R. AB + B3 3. Star Polymer
S. A2 + B2 4. Linear Polymer
(A) P-2; Q-3; R-1; S-4 (B) P-2; Q-1; R-3; S-4
(C) P-1; Q-2; R-3; S-4 (D) P-2; Q-4; R-1; S-3
Q.13 Match each of the following additives for plastics with its function
Additive Function
P. α-Cellulose 1. Flame retarder
Q. Zinc chromate 2. Plasticizer extender
R. Alumina trihydrate 3. Organic fibrous filler
S. Chlorinated paraffin wax 4. Colorant
(A) P-1; Q-2; R-3; S-4 (B) P-2; Q-3; R-4; S-1
(C) P-3; Q-4; R-1; S-2 (D) P-4; Q-1; R-2; S-3
Q.14 The length of a glass fiber reinforced polymer increased by 0.03mm, from its initial length of
100mm, when the temperature was changed from –30oC to +30oC. The coefficient of linear thermal
expansion is
(A) 1.03 x 10-5 oC-1 (B) 9.82 x 10-6 oC-1 (C) 5.00 x 10-6 oC-1 (D) 14.4 x 10-5 oC-1
Q.15 A 40mm x 40mm square polymer composite sample with 5mm thickness (heat transfer distance)
exhibited a heat flow rate of 60W, when the temperatures of the warm and cold surfaces were 90oC
and 25oC respectively. The thermal conductivity of the sample in W.m-1.K-1is
(A) 5.67 (B) 15.3 (C) 2.88 (D) 0.667
Q.16 An extruder is supplied with 40 kW of power. The mass flow rate of a polymer through the
extruder is 240 kg h-1 and the specific heat capacity of the polymer is 4 kJ kg-1 K-1. The maximum
possible temperature rise in the polymer is
(A) 150 K (B) 100 K (C) 600 K (D) Zero
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Common Data Questions
Common Data for Questions 17 and 18:
For a given free-radical polymerization, the only mode of termination is the bimolecular termination and
there is no chain transfer. The final polymer produced was analyzed to contain an average of 1.60 initiator
fragments per polymer chain.
Q.17 Percentage of final polymer chains containing one initiator fragment per chain is
(A) 40 % (B) 50 % (C) 60 % (D) 70 %
Q.18 Percentage of polymer radicals terminated by coupling is
(A) 65 % (B) 75 % (C) 85 % (D) 95 %
Common Data for Questions 19 and 20:
For the synthesis of polyester, 1.5 mole of pentaerythritol (tetra-ol) was reacted with 1.0 mole of a
tricarboxylic acid.
Q.19 The extent of reaction when the number average degree of polymerization of the reaction mixture
approaches infinity is
(A) 80.33% (B) 83.33% (C) 84.33% (D) 86.33%
Q.20 The number average degree of polymerization of the reaction mixture when the polymerization was
stopped at 80% conversion, is
(A) 1000 (B) 100 (C) 50 (D) 25
Linked Answer Questions
Statement for Linked Answer Questions 21 and 22:
A viscoelastic fluid is modeled as a spring and two dashpots, all connected in series. The spring has elastic
modulus G and the fluids in two dashpots have viscosities and .
Q.21 The constitutive equation (relation between stress and strain in which overdot represents the
time derivative) for the fluid is:
(A) = +( ) ̇ (B) = +( − ) ̇
̇ ̇
(C) ̇ = + + (D) ̇ = +
Q.22 For a periodic stress = , the strain is given by
(A) = + + (B) = − +
(C) =[ +( ) ] (D) =[ −( ) ]
END OF SECTION - F
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G:FOOD TECHNOLOGY
Q. 1 – Q. 9 carry one mark each.
Q.1 Kawashiorkor disease is caused due to the deficiency of
(A) lysine (B) unsaturated fatty acids
(C) vitamin K (D) protein
Q.2 Which of the following statements is TRUE in case of oxidative rancidity of vegetable oils and
fats?
(A) It is caused by the reaction of saturated fatty acids and oxygen
(B) It involves polymerization of fatty acids
(C) It is caused by the reaction of unsaturated fatty acids with oxygen
(D) It is caused by oxidative enzymes
Q.3 The food borne disease, Q fever is caused by the organism,
(A) Clostridium perfringens (B) Coxiella burnetti
(C) Bacillus cereus (D) Staphylococcus aureus
Q.4 The primary bacterial spoilage of poultry meat at low temperature, with characteristic sliminess at
outer surface, is caused by
(A) Pseudomonas spp. (B) Aspergillus spp.
(C) Bacillus spp. (D) Candida spp.
Q.5 The weight gain (in gram) per gram protein consumed is called
(A) Net Protein Ratio (NPR) (B) Biological Value (BV)
(C) Protein Efficiency Ratio (PER) (D) Chemical Score (CS)
Q.6 Which of the following carbohydrates is NOT classified as dietary fibre?
(A) Agar (B) Pectin
(C) Sodium alginate (D) Tapioca starch
Q.7 In the extruder barrel, the compression is achieved by back pressure created by the die and by
(A) increasing pitch and decreasing diameter of the screw
(B) using the tapered barrel with constant pitch
(C) increase in the clearance between barrel surface and screw
(D) opening of the die
Q.8 The brown colour of bread crust during baking is due to Maillard reaction between
(A) aldehyde groups of sugars and amino groups of proteins
(B) aldehyde groups of sugars and vitamins
(C) aldehyde groups of sugars and salt
(D) starch and yeast
Q.9 Blanching influences vegetable tissues in terms of
(A) enzymes production
(B) alteration of cytoplasmic membrane
(C) stabilization of cytoplasmic proteins
(D) stabilization of nuclear proteins
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Q. 10 - Q. 22 carry two marks each.
Q.10 Match the toxicants of plant foods in Group I with their main plant source given in Group II.
Group I Group II
P) Gossypol 1) Khesari Dahl (Lathyrus sativus)
Q) Vicine 2) Cotton seeds
R) Glucosinolates 3) Fava beans
S) BOAA (beta-N- Oxalyl Amino L-Alanine) 4) Rapeseeds
(A) P-2, Q-3, R-4, S-1 (B) P-2, Q-4, R-3, S-1
(C) P-3, Q-1, R-2, S-4 (D) P-4, Q-3, R-1, S-2
Q.11 Match the products in Group I with the enzymes used for their preparation given in Group II.
Group I Group II
P) Aspartame 1) Lipase
Q) Cocoa butter substitute 2) Glucose isomerase
R) High fructose corn syrup 3) Thermolysin
S) Lactose free milk 4) Invertase
5) Beta galactosidase
(A) P-2, Q-1, R-4, S-3 (B) P-3, Q-1, R-2, S-5
(C) P-1, Q-3, R-2, S-4 (D) P-1, Q-2, R-4, S-5
Q.12 Match the food items in Group I with the type of colloidal dispersion given in Group II.
Group I Group II
P) Mayonnaise 1) Sol
Q) Tomato ketchup 2) Emulsion
R) Cake 3) Gel
S) Curd 4) Solid foam
(A) P-4, Q-1, R-2, S-3 (B) P-3, Q-1, R-2, S-4
(C) P-2, Q-3, R-4, S-1 (D) P-2, Q-1, R-4, S-3
Q.13 [a] Assertion: In the presence of sucrose, the temperature and time for gelatinization of starch
increases .
[r] Reason: Sucrose, due to its hygroscopic nature, competes with starch for water needed for
gelatinization.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Q.14 Thermal death of viable spores of Bacillus subtilis in a food sample follows a first order kinetics
with a specific death rate constant of 0.23 min-1 at 100 °C. The time (in minutes) required to kill
99% of spores in the food sample at 100 °C will be
(A) 10 (B) 20 (C) 23 (D) 60
Q.15 How much skim milk (in kg) containing 0.1% fat should be added to 500 kg of cream containing
50% fat to produce standardized cream containing 36% fat?.
(A) 140 (B) 165 (C) 195 (D) 210
Q.16 Which of the following statements is NOT CORRECT in relation to muscle proteins ?
(A) Actin and myosin interact to form actomyosin which is responsible for muscle contraction
(B) Collagen contributes to the toughness of muscles due to its abundant presence
(C) Elastin, a constituent of ligaments, is tougher than collagen
(D) Actomyosin is not the main state of actin and myosin in post-mortem muscles
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Common Data Questions
Common Data for Questions 17 and 18: A cold storage plant is used for storing 50 tonnes of apples in
perforated plastic crates. During the storage, apples are cooled down from 28°C to storage temperature of
2°C. (Specific heat of the apple = 0.874 kCal kg-1 °C-1)
Q.17 If the required cooling is attained in 16 hours, the refrigeration plant capacity (in Tons) is
(A) 19 (B) 24 (C) 29 (D) 32
Q.18 If the cooling is to be achieved in 8 hours, the power required (in Horse Power) to operate the plant
having a Coefficient of Performance (COP) of 2.5 will be
(A) 47 (B) 65 (C) 89 (D) 96
Common Data for Questions 19 and 20: An actively growing culture of Acetobacter aceti is added to the
vigorously aerated fermented fruit juice medium containing 10 g l-1 ethanol to produce vinegar. After some
time, the ethanol concentration in the medium is 0.8 g l-1 and acetic acid produced is 8.4 g l-1.
Q.19 What is the conversion efficiency of the process with respect to theoretical yield?
(A) 30 (B) 50 (C) 70 (D) 90
Q.20 The concentration of fermentable sugars (g l-1) required in the fruit juice to produce 10 g l-1 ethanol,
based on 90% fermentation efficiency is
(A) 20.0 (B) 21.7 (C) 22.8 (D) 25.1
Linked Answer Questions
Statement for Linked Answer Questions 21 and 22: An enzyme catalyzed reaction (following Michaelis-
Menten kinetics) exhibits maximum reaction velocity (Vm) of 75 nmol l-1 min-1. The enzyme at a substrate
concentration of 1.0x10-4 M shows the initial reaction velocity of 60 nmol l-1min-1.
Q.21 The Km value of the enzyme in molar concentration (M) is
(A) 2.5 x 10-5 (B) 5.0 x 10-5
(C) 2.5 x 10-4 (D) 5.0 x 10-4
Q.22 If the enzyme concentration for the reaction is doubled at a substrate concentration of 5.0 x 10-5 M,
the initial reaction velocity in nmol l-1 min-1 will be
(A) 37.5 (B) 50 (C) 60 (D) 100
END OF THE QUESTION PAPER
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Source: GATE. Question paper published by GATE.