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This mock test of XE Engineering Science- 2013 GATE Paper (Practice Test) for GATE helps you for every GATE entrance exam.
This contains 154 Multiple Choice Questions for GATE XE Engineering Science- 2013 GATE Paper (Practice Test) (mcq) to study with solutions a complete question bank.
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QUESTION: 1

if v then which of the following options is TRUE?

Solution:

QUESTION: 2

The Headmaster ___________ to speak to you.

Which of the following options is incorrect to complete the above sentence?

Solution:

QUESTION: 3

Mahatama Gandhi was known for his humility as

Solution:

QUESTION: 4

Which of the above underlined parts of the sentence is not appropriate?

Solution:

QUESTION: 5

Select the pair that best expresses a relationship similar to that expressed in the pair:

**water: pipe::**

Solution:

QUESTION: 6

**Q. 6 to Q. 10 carry two marks each**

**Q.**

Velocity of an object fired directly in upward direction is given by V = 80 − 32 t, where t (time)

is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?

Solution:

QUESTION: 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?

Solution:

QUESTION: 8

Following table gives data on tourists from different countries visiting India in the year 2011.

Which two countries contributed to the one third of the total number of tourists who visited India in

2011?

Solution:

QUESTION: 9

If |−2x + 9| = 3 then the possible value of |−x| − x^{2} would be:

Solution:

QUESTION: 10

All professors are researchers

Some scientists are professors

Which of the given conclusions is logically valid and is inferred from the above arguments:

Solution:

QUESTION: 11

**Q. 11 – Q. 17 carry one mark each.**

**Q.**

The value of the integral

Solution:

QUESTION: 12

Which one of the following partial differential equations CAN NOT be reduced to two

ordinary differential equations by the method of separation of variables?

Solution:

QUESTION: 13

The Fourier series of the periodic function

is given by

Using the above, the sum of the infinite series

Solution:

QUESTION: 14

Consider the function the function f

Solution:

QUESTION: 15

The integral along the contour C: |z − (1 + i)| = 2, oriented anticlockwise,

is equal to

Solution:

QUESTION: 16

The integral equals

Solution:

QUESTION: 17

If the mean and variance of a binomial distribution are 6 and 2 respectively, then the

probability of two failures is

Solution:

QUESTION: 18

**Q. 18 - Q. 21 carry two marks each.**

**Q**

For the matrix consider the following statements

(P) The characteristic equation of λ is λ^{3} − λ = 0.

(Q) M^{-1} does not exist.

(R) The matrix M is diagonalizable.

Which of the above statements are true?

Solution:

QUESTION: 19

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

Solution:

QUESTION: 20

The general solution of the differential equation

is

Solution:

QUESTION: 21

Using Euler’s method to solve the differential equation

with step-size h = 0.25, the value of y(0.5) is

Solution:

QUESTION: 22

**Q. 22 – Q. 30 carry one mark each.**

**Q.**

The gauge pressure inside a soap bubble of radius R, with σ denoting the surface tension between the soap solution and air, is.

Solution:

QUESTION: 23

Let M, B and G represent respectively the metacentre, centre of buoyancy and the centre of

mass of a floating buoy. Which of the following statements is correct?

Solution:

*Answer can only contain numeric values

QUESTION: 24

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. _________

**(Important : you should answer only the numeric value)**

Solution:

QUESTION: 25

Bernoulli’s equation is valid for the following type of flow:

Solution:

QUESTION: 26

If A is the area of a circle of radius r 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

Solution:

QUESTION: 27

Flow past a circular cylinder can be produced by superposition of the following elementary

potential flows:

Solution:

QUESTION: 28

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

Solution:

QUESTION: 29

In the hydrodynamic entry region of a circular duct, the pressure forces balance the sum of

Solution:

QUESTION: 30

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 crosssectional

shape with the largest coefficient of drag (i.e. sum of the pressure and skinfriction

drags), at any moderately large Reynolds number, is

Solution:

QUESTION: 31

**Q. 31 - Q. 44 carry two marks each.**

**Q.**

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 p_{a} 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

Solution:

QUESTION: 32

An incompressible fluid at a pressure of 150 kPa (absolute) flows steadily through a twodimensional

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 linearlyvarying

velocity profile. v_{max} is four times vmin. The density of the fluid is 914.3 kg/m^{3}. The

velocity v_{min}, in m/s, is.

Solution:

QUESTION: 33

The velocity vector corresponding to a flow field is given, with usual notation, by

= The magnitude of rotation at the point (2,2) in rad/s is

Solution:

QUESTION: 34

The stream function for a potential flow field is given by ψ = x^{2}-y^{2}. The corresponding

potential function, assuming zero potential at the origin, is

Solution:

*Answer can only contain numeric values

QUESTION: 35

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. __________

**(Important : you should answer only the numeric value)**

Solution:

*Answer can only contain numeric values

QUESTION: 36

The Darcy friction factor f for a smooth pipe is given by f = 64/Re for laminar flow and

by f = 0.3/Re^{0.25} for turbulent flow, where Re is the Reynolds number based on the

diameter. For fully developed flow of a fluid of density 1000 kg/m^{3} 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. _________

**(Important : you should answer only the numeric value)**

Solution:

*Answer can only contain numeric values

QUESTION: 37

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/m^{3}, are

1.18, 1000 and 13600, respectively. The gravitational acceleration is 9.81 m/s^{2}. Determine

the air speed in m/s. _____________

Solution:

*Answer can only contain numeric values

QUESTION: 38

**Common Data for Questions 38 and 39:**

**The velocity field within a laminar boundary layer is given by the expression**

where B = 100 m^{1/2} and the free stream velocity u_{∞} = 0.1 m/s.

**Q.**

Solution:

*Answer can only contain numeric values

QUESTION: 39

Calculate the x-direction component of the acceleration in m/s^{2} at the point x = 0.5 m and

y = 50 mm. _________

**(Important : you should answer only the numeric value)**

Solution:

*Answer can only contain numeric values

QUESTION: 40

**The velocity field within a laminar boundary layer is given by the expression**

**where B = 100 m ^{1/2} and the free stream velocity u_{∞} = 0.1 m/s.**

**Q.**

**Find the slope of the streamline passing through the point x = 0.5 m and y = 50mm. ____**

Solution:

QUESTION: 41

**Common Data for Questions 41 and 42:**

**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
coefficient of resistance C**

Q.

The velocity in m/s, at which the model is towed, is

Solution:

QUESTION: 42

**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
coefficient of resistance C**

**Q.**

The resistance of the prototype, in kN, is

Solution:

QUESTION: 43

**Statement for Linked Answer Questions 43 and 44:**

**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 m ^{2} and the velocity across
section-1 is 3 m/s. The density of water may be taken as 1000 kg/m^{3}. The viscous effects and
elevation changes may be neglected.**

Q.

The gauge pressure at section-1, in kPa, is

Solution:

QUESTION: 44

**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 m ^{2} and the velocity across
section-1 is 3 m/s. The density of water may be taken as 1000 kg/m^{3}. The viscous effects and
elevation changes may be neglected.**

Q.

The magnitude of the force, in kN, required to hold the pipe in place, is

Solution:

QUESTION: 45

**Q. 45 – Q. 53 carry one mark each**

**Q.**

As temperature increases, diffusivity of an atom in a solid material

Solution:

QUESTION: 46

Which of the following is NOT correct?

Solution:

QUESTION: 47

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

Solution:

QUESTION: 48

Which one of the following metals is commonly alloyed with iron to improve its corrosion

resistance?

Solution:

QUESTION: 49

The number of slip systems in a metal with FCC crystal structureis

Solution:

QUESTION: 50

Upon recrystallization of a cold worked metal

Solution:

QUESTION: 51

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?

Solution:

QUESTION: 52

Vulcanization is related to

Solution:

QUESTION: 53

Which one of the following oxides crystallizes into fluorite structure?

Solution:

QUESTION: 54

**Q. 54 - Q. 66 carry two marks each.**

**Q.**

Match the conventional ceramic materials listed in Column I with their respective common

applications in Column II

Solution:

QUESTION: 55

Match the terminologies given in Column Iwith theirrelations listed in Column II

Solution:

QUESTION: 56

Match the microscopes listed in Column I with their principle of operation listed in Column II

Solution:

*Answer can only contain numeric values

QUESTION: 57

X-rays of unknown wavelength are diffracted by an FCC metal with a lattice parameter of 0.352

nm. The measured ‘2θ’ angle for the {200} peak is 61.08^{o}. Calculate the wavelength of the Xray

used, in nm. ___________

Solution:

*Answer can only contain numeric values

QUESTION: 58

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. _________

Solution:

*Answer can only contain numeric values

QUESTION: 59

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? __________

Solution:

*Answer can only contain numeric values

QUESTION: 60

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 20^{o}C such that the circuit is broken at 70^{o}C. The coefficient of linear thermal

expansion of brass is 20 x 10^{-6} ^{o}C^{-1} ______________

Solution:

*Answer can only contain numeric values

QUESTION: 61

**Common Data for Questions 61 and 62:**

**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.**

**Q.**

**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. ___________**

Solution:

*Answer can only contain numeric values

QUESTION: 62

**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.**

**Q.**

**Find the toughness of the material, in M J m-3. ____________**

Solution:

*Answer can only contain numeric values

QUESTION: 63

**Common Data for Questions 63 and 64:**

**An isomorphous alloy system contains 47 wt% of A and 53 wt % of B and is at 1300 ^{o} C. Referring to the figure given below, answer the following:**

**Q.**

**What is the weight percentage of A in solid phase at this temperature? ___________**

Solution:

*Answer can only contain numeric values

QUESTION: 64

**An isomorphous alloy system contains 47 wt% of A and 53 wt % of B and is at 1300 ^{o} C. Referring to the figure given below, answer the following:**

**Q.**

**What weight percentage of this alloy is liquid? __________**

Solution:

*Answer can only contain numeric values

QUESTION: 65

**Question not available**

Solution:

*Answer can only contain numeric values

QUESTION: 66

Question not available

Solution:

*Answer can only contain numeric values

QUESTION: 67

**Q. 67 – Q. 65 carry one mark each.**

**Q.**

Question not available

Solution:

*Answer can only contain numeric values

QUESTION: 68

A point in a body is subjected to a hydrostatic pressure of 100 MPa. Find the maximum shear

stress at this point in MPa. ___________

Solution:

*Answer can only contain numeric values

QUESTION: 69

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. ___________

Solution:

QUESTION: 70

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

Solution:

*Answer can only contain numeric values

QUESTION: 71

A two bar truss is shown in the Figure. The cross-sectional area and Young’s modulus of bar 1 are

0.02 m^{2} and 200GPa, respectively. The cross-sectional area and Young’s modulus of bar 2 are 0.01

m^{2 }and 80GPa, respectively. The force F applied on the truss is 2 N. Find out the stress developed in

bar 2 in Pa. ___________

Solution:

*Answer can only contain numeric values

QUESTION: 72

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/s^{2} downwards.______________

Solution:

*Answer can only contain numeric values

QUESTION: 73

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. ____________

Solution:

*Answer can only contain numeric values

QUESTION: 74

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. _____________

Solution:

QUESTION: 75

A rigid bar AB is hinged at B through a torsional spring with spring constant k_{t}.. For small

rotations of the bar AB about B, the critical load P_{cr} is given by

Solution:

*Answer can only contain numeric values

QUESTION: 76

Q. 76 - Q. 88 carry two marks each.

Q.

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. ______________

Solution:

*Answer can only contain numeric values

QUESTION: 77

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}. ____________

Solution:

*Answer can only contain numeric values

QUESTION: 78

Question not available

Solution:

QUESTION: 79

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 k=3El/ L^{3}. A vertical downward load P is applied at the right end. The deflection of the point under the load P is

Solution:

*Answer can only contain numeric values

QUESTION: 80

Find the maximum bending moment (magnitude wise) in kN-m for the beam shown in the Figure.

______

Solution:

*Answer can only contain numeric values

QUESTION: 81

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 45^{0}

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/

s^{2}. __________

Solution:

*Answer can only contain numeric values

QUESTION: 82

A particle P is moving on a circular path of radius r = 1m. The angular location θ of the particle is

measured as shown in the Figure. The motion of the particle is described by θ = 2 sin(t). Find the

magnitude of the total acceleration (in m/s^{2}) of the particle at time t = π/3 seconds. _________

Solution:

QUESTION: 83

**Common Data for Questions 83 and 84.**

**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.**

**Q.**

**Neglecting the axial compression of member AB, the deflection of point C in the direction of the
load is**

Solution:

QUESTION: 84

**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.**

Q.

The maximum bending stress in the frame is

Solution:

QUESTION: 85

**Common Data for Questions 85 and 86.**

**At a point in an object subjected to plane stress conditions, the state of stress is as shown in the Figure**

**Q.**

**One of the principal stresses(in MPa) is**

Solution:

QUESTION: 86

At a point in an object subjected to plane stress conditions, the state of stress is as shown in the Figure.

**Q.**

**The normal stress on the plane AB (in MPa) is**

Solution:

QUESTION: 87

**Statement for linked answer questions 87 and 88**

**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 α _{1}= 4 × 10^{-6} /0C and α_{2} = 10^{-6} /0C, respectively. The entire assembly is heated by 1000 C. Neglect the effect of Poisson’s ratio.**

**Q.**

The stress in rod 1 (in MPa) is

Solution:

QUESTION: 88

**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 α _{1}= 4 × 10^{-6} /0C and α_{2} = 10^{-6} /0C, respectively. The entire assembly is heated by 1000 C. Neglect the effect of Poisson’s ratio.**

**Q.**

Considering the displacement to the right as positive, the displacement (in mm) of the interface

between the two rods is

Solution:

QUESTION: 89

**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/s**

**Q. 89 – Q. 97carry one mark each.**

**Q.**

The measured temperature of a system is 30^{o}C.Its exact absolute temperature in K is

Solution:

QUESTION: 90

The fuel air mixture in a pertrol engine is ignited with a spark plug at the end of compression

stroke. This process

Solution:

QUESTION: 91

In the van der Waals equation of state given below:

The constant a represents the effect of

Solution:

QUESTION: 92

For a reversible isothermal expansion of an ideal gas from a state 1 to a state 2,

Solution:

QUESTION: 93

For a pure substance the critical isotherm on the p-v plane exhibits

Solution:

QUESTION: 94

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

Solution:

QUESTION: 95

An air standard Otto cycle has the following shape on a thermodynamic property plane.

The x and y coordinates, respectively, are

Solution:

*Answer can only contain numeric values

QUESTION: 96

The specific volume of steam after expansion in a turbine is 12 m^{3}/kg. At this pressure the saturated

liquid and saturated vapour specific volumes are 0.001 and 15.25 m^{3}/kg respectively. What is the

dryness fraction to second decimal place accuracy? _________

Solution:

QUESTION: 97

Which of the following processes, shown in the figure below, represents the throttling of an ideal

gas?

Solution:

QUESTION: 98

**Q. 98 - Q. 110 carry two marks each.**

**Q.**

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

Solution:

QUESTION: 99

Starting from the definition of Gibbs free energy function g=h-Ts, the Maxwell relation that can be

derived is

Solution:

*Answer can only contain numeric values

QUESTION: 100

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

If the First and Second laws of thermodynamics are not violated, what should be the value of T in

K? _____________

Solution:

QUESTION: 101

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?

Solution:

*Answer can only contain numeric values

QUESTION: 102

A well-insulated rigid hot water tank receives steady flow of water from two sources as shown in

the figure below

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 ^{o}C from the tank under steady state. What is the required

capacity of the back-up heater to the nearest kW? __________

Solution:

*Answer can only contain numeric values

QUESTION: 103

1 kg of air in an insulated rigid tank of volume 1 m^{3 }is 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? _________

Solution:

*Answer can only contain numeric values

QUESTION: 104

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? ____________

Solution:

*Answer can only contain numeric values

QUESTION: 105

**Common Data for Questions 105 and 106:**

At a location where the atmospheric pressure is 98 kPa and the ambient temperature is 30^{o}C, 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.

What is the partial pressure of water vapour in kPa to the first decimal place accuracy before the

high pressure front moves in? ____________

Solution:

*Answer can only contain numeric values

QUESTION: 106

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.

What is the relative humidity of air under the influence of high pressure front to integer precision in %? _____

Solution:

*Answer can only contain numeric values

QUESTION: 107

**Common Data for Questions 107 and 108:
A rigid insulated cylinder is divided into two chambers A and B by a thin rigid insulating barrier as
shown in the figure below**

**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.**

**What is the ratio of the volumes of chambers A and B, i.e. VA/VB, to first decimal place accuracy?
________**

Solution:

*Answer can only contain numeric values

QUESTION: 108

**Common Data for Questions 107 and 108:
A rigid insulated cylinder is divided into two chambers A and B by a thin rigid insulating barrier as
shown in the figure below**

**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.**

**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? ________**

Solution:

*Answer can only contain numeric values

QUESTION: 109

**Statement for Linked Answer Questions 109 and 110:
A combined vapour compression-cum-Brayton cycle is shown below**

**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.**

**What is the mass flow rate of the working fluid through the turbine, in kg/s, to first decimal place
accuracy? __________**

Solution:

*Answer can only contain numeric values

QUESTION: 110

**Statement for Linked Answer Questions 109 and 110:
A combined vapour compression-cum-Brayton cycle is shown below**

**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.**

**What is the power required to drive the compressor, to the nearest kW? ________**

Solution:

QUESTION: 111

**Q. 111 – Q. 119 carry one mark each.**

**Q.**

**In free radical polymerization, one of the following techniques permits simultaneous increase in
rate of polymerization and polymer molecular weight.**

Solution:

QUESTION: 112

The shear modulus, G, of plastic is related to the elastic modulus, E, and the Poisson ratio, *v*, as

Solution:

QUESTION: 113

LLDPE is obtained by

Solution:

QUESTION: 114

A hindered phenol is added to a polyolefin

Solution:

QUESTION: 115

Stretching of rubber leads to

Solution:

QUESTION: 116

In a cone and plate viscometer, the rate of strain is related to the speed of rotation of the cone, ω

(radian/second), and the angle between the cone and the plate, α (radian), by the following relation

Solution:

QUESTION: 117

The tensile breaking strength of polycarbonate (I), low density polyethylene (II), polystyrene (III)

and polypropylene (IV) can be arranged as

Solution:

QUESTION: 118

High molecular weight polymers could be obtained even at low monomer conversion in case of

Solution:

QUESTION: 119

A reinforced polymer composite is made by the incorporation of

Solution:

QUESTION: 120

**Q. 120 - Q. 132 carry two marks each.**

**Q.**

Match the following for free-radical copolymerization of two monomers with reactivity ratios, r1

and r2.

Solution:

QUESTION: 121

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

Solution:

QUESTION: 122

Match the following in case of step-growth polymerization, where A reacts only with B, and B

reacts only with A (Note: A A is expressed as A_{2}, and is expressed as AB_{2}).

**(Note: correct answer will be updated soon, Temporary marked A)**

Solution:

QUESTION: 123

Match each of the following additives for plastics with its function

Solution:

QUESTION: 124

The length of a glass fiber reinforced polymer increased by 0.03mm, from its initial length of

100mm, when the temperature was changed from –30^{o}C to +30^{o}C. The coefficient of linear thermal

expansion is

Solution:

QUESTION: 125

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 25^{o}C respectively. The thermal conductivity of the sample in W.m^{-1}.K^{-1}is

Solution:

QUESTION: 126

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

Solution:

QUESTION: 127

**Common Data for Questions 127 and 128:**

**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.**

Percentage of final polymer chains containing one initiator fragment per chain is

Solution:

QUESTION: 128

**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.**

**Percentage of polymer radicals terminated by coupling is**

Solution:

QUESTION: 129

**Common Data for Questions 129 and 130:**

**For the synthesis of polyester, 1.5 mole of pentaerythritol (tetra-ol) was reacted with 1.0 mole of a
tricarboxylic acid.**

**Q.**

**The extent of reaction when the number average degree of polymerization of the reaction mixture
approaches infinity is**

Solution:

QUESTION: 130

**For the synthesis of polyester, 1.5 mole of pentaerythritol (tetra-ol) was reacted with 1.0 mole of a
tricarboxylic acid.**

**Q.**

**The number average degree of polymerization of the reaction mixture when the polymerization was
stopped at 80% conversion, is**

Solution:

QUESTION: 131

**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 η _{1} and η_{2}.**

**Q.**

**The constitutive equation (relation between stress σ and strain γ in which overdot represents the
time derivative) for the fluid is:**

Solution:

QUESTION: 132

**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 η _{1} and η_{2}.**

**Q.**

For a periodic stress , the strain is given by

Solution:

QUESTION: 133

**Q. 133 – Q. 141 carry one mark each.**

**Q.**

**Kawashiorkor disease is caused due to the deficiency of**

Solution:

QUESTION: 134

Which of the following statements is TRUE in case of oxidative rancidity of vegetable oils and

fats?

**(Note: correct answer will be updated soon, Temporary marked A)**

Solution:

QUESTION: 135

The food borne disease, Q fever is caused by the organism,

Solution:

QUESTION: 136

The primary bacterial spoilage of poultry meat at low temperature, with characteristic sliminess at

outer surface, is caused by

Solution:

QUESTION: 137

The weight gain (in gram) per gram protein consumed is called

Solution:

QUESTION: 138

Which of the following carbohydrates is NOT classified as dietary fibre?

Solution:

QUESTION: 139

In the extruder barrel, the compression is achieved by back pressure created by the die and by

Solution:

QUESTION: 140

The brown colour of bread crust during baking is due to Maillard reaction between

Solution:

QUESTION: 141

Blanching influences vegetable tissues in terms of

Solution:

QUESTION: 142

**Q. 142 - Q. 154 carry two marks each.**

**Q.**

Match the toxicants of plant foods in Group I with their main plant source given in Group II.

Solution:

QUESTION: 143

Match the products in Group I with the enzymes used for their preparation given in Group II.

Solution:

QUESTION: 144

Match the food items in Group I with the type of colloidal dispersion given in Group II.

Solution:

QUESTION: 145

[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.

Solution:

QUESTION: 146

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

Solution:

QUESTION: 147

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?.

Solution:

QUESTION: 148

Which of the following statements is NOT CORRECT in relation to muscle proteins ?

Solution:

QUESTION: 149

**Common Data for Questions 149 and 150: **

**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.**

**If the required cooling is attained in 16 hours, the refrigeration plant capacity (in Tons) is**

Solution:

QUESTION: 150

** 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.**

**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**

Solution:

QUESTION: 151

**Common Data for Questions 151 and 152: **

**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.**

**What is the conversion efficiency of the process with respect to theoretical yield?**

Solution:

QUESTION: 152

**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.**

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

Solution:

QUESTION: 153

**Statement for Linked Answer Questions 153 and 154:**

**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^{-1}min^{-1}.**

**Q.**

**The K _{m }value of the enzyme in molar concentration (M) is**

Solution:

QUESTION: 154

**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^{-1}min^{-1}.**

**Q.**

**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**

Solution:

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