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XE Engineering Science- 2014 GATE Paper (Practice Test)


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XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 1

Q. 1 – Q. 5 carry one mark each.

Q.

A student is required to demonstrate a high level of comprehension of the subject, especially in the
social sciences.
The word closest in meaning to comprehension is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 2

Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 3

Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above sentences?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 4

If y = 5x2 + 3, then the tangent at x = 0, y = 3

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 5

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q,
where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily
production of 100 tonnes?

 

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 6

Q. 6 – Q. 10 carry two marks each.

Q.

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 7

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building
(the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered
floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors
below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor
immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the
following floor-person combinations is correct?

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 8

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The
ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its
smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the
largest angle of the quadrilateral?

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 9

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y
are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both
countries together, what is the percentage of people taller than 6 ft?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 10

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure.
Which of the following are true? (k percentile is the value such that k percent of the data fall below
that value)

(i) On average, it rains more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 11

Q. 11 – Q. 17 carry one mark each.

Q.

If 1, 0, and -1 are the eigenvalues of a 3x3 matrix A, then the trace of A2 + 5Ais equal to ________

 

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 12

Which of the following is a solution of the differential equation
x2 y''+ xy'+ y = 4sin(ln x), x > 0?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 13

At z = 0 , the complex function 

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 14

Ten chocolates are distributed randomly among three children standing in a row. The probability
that the first child receives exactly three chocolates is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 15

Let the function f :[0, 5]→R be defined by

The number of points where f is not differentiable in (0, 5) , is ___________.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 16

An integrating factor of the differential equation   is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 17

If a cubic polynomial passes through the points (0, 1), (1, 0), (2, 1) and (3, 10), then it also passes
through the point

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 18

Q. 18 – Q. 21 carry two marks each.

Q.

Let the function f :[0,∞)→ R be such that  for x > 0 and f (0) = 1.Then f (1) lies in the interval

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 19

The perimeter of a rectangle having the largest area that can be inscribed in the ellipse

 is _____________

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 20

If the work done in moving a particle once around a circle x2 + y2 = 4 under the force field  then |a| is equal to _________.

 

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 21

Let r and s be real numbers. If  then the system of linear equations AX = b has

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 22

Q. 22 – Q. 30 carry one mark each.

Q.

A dam with a curved shape is shown in the figure. The cross sectional area of the dam (shaded
portion) is 100 m2 and its centroid is at The vertical component of the hydrostatic force,
Fz , is acting at a distance xp . The value of xp is ____ m.

 

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 23

For an unsteady incompressible fluid flow, the velocity field is   where
x , y are in meters and t is in seconds. Acceleration in m/s2 at the point x =10 m and y = 0 , as
measured by a stationary observer is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 24

For an incompressible flow, the existence of components of acceleration for different types of flow
is described in the table below.

Which one of the following options connecting the left column with the right column is correct?

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 25

Velocity in a two-dimensional flow field is specified as: u = x2 y ; v = −y2 x . The magnitude of
the rate of angular deformation at a location ( x = 2 m and y = 1 m) is ____ s-1.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 26

For a plane irrotational flow, equi-potential lines and streamlines are

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 27

Flow around a Rankine half-body is represented by the superposition of

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 28

It is required to carry out model studies on a boat having a characteristic length of 3.6 m and
travelling at a speed of 3 m/s. Assume the acceleration due to gravity as 10 m/s2 and neglect the
effects due to viscous and surface tension forces. The value of appropriate non-dimensional number
is ____


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 29

Which one of the following velocity profiles typically represents a fully developed incompressible,
turbulent flow in a pipe?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 30

Consider an incompressible, laminar flow past a circular cylinder of diameter d . The flow is
uniform at the far upstream. Which one of the following figures typically represents the wake
velocity profile just downstream of the cylinder?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 31

Q. 31 – Q. 43 carry two marks each

Q.

A container of square cross-section is partially filled with a liquid of density ρ1 . The cylinder is
intended to float in another liquid of density ρ2 as shown in the figure. The distance between metacentre and centre of buoyancy is  are area moment of inertia of the
cross-section and submerged volume, respectively. Neglect the weight of the container

Which one of the following is the correct condition for stability?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 32

In a steady state two-dimensional potential flow field due to a point source, the acceleration of a
particle at a distance r from the point source is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 33

Velocity in a two-dimensional flow at time t and location (x, y) is described as:  

The equation for the path line of a particle passing through the point (1,0) at t = 0 is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 34

The gravity driven flow over a hump of height h in a canal is shown in the figure. The height of
the free surface from the canal bed at upstream of the hump is H . The free surface height reduces
to  H1 above the hump.

Assuming the canal bed to be horizontal, the discharge per unit width is given by

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 35

Steady state incompressible flow through a pipe network is shown in the figure. Inlets marked as
(1), (2) and (3) and exit marked as (4), are shown with their respective diameters. The exit flow rate
at (4) is 0.1 m3/s. A 20% increase in flow rate through (3) results in a 10% increase in flow rate
through (4). The original velocity through inlet (3) is _____ m/s.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 36

A reducing elbow is used to deflect water upward by 30o as shown in the figure. The mass flow rate
at the inlet is 14 kg/s. Water is entering at a gauge pressure of 200 kPa and exits to the atmosphere.
The cross-sectional area is 113 cm2 at the inlet and 7 cm2 at the exit. Density of water and
acceleration due to gravity are 1000 kg/m3 and 10 m/s2, respectively. Magnitude of x - component
of the water force on the elbow is ____ N.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 37

A source with a strength of  k1 and a vortex with a strength of  k2 are located at the origin. The
resultant velocity at a radial distance r from the origin due to the superposition of the source and
vortex is expressed as

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 38

Velocity potential for an incompressible fluid flow is given as: φ = 2(x2 + 2y − y2 ). Assume the
value of stream function at the origin to be zero. The value of stream function at [ ( x, y) ≡ (2, 2) ]
is ____.

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 39

The model of a conduit is scaled to 1/100 of the actual size. Seawater is used in the prototype and
fresh water is used in the model. Velocity in the prototype is 0.5 m/s. Density and dynamic
viscosity of the seawater are 1025 kg/m3 and 1.07 × 10-3 kg/m-s, respectively. Density and
dynamic viscosity of fresh water are 1000 kg/m3 and 1 × 10-3 kg/m-s, respectively. Assume the
viscous forces to be dominant. The velocity to be maintained in the model to ensure dynamic
similarity is____ m/s.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 40

A fluid is flowing through a pipe of circular cross-section. Reynolds number of the flow is 1600.
The head loss over a 45 m length of the pipe is 0.6 m. The average flow velocity of the fluid is
1 m/s and the acceleration due to gravity is 10 m/s2. The diameter of the pipe is ____ m.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 41

Consider a laminar flow over a flat plate of widthw. At Section 1-1, the velocity profile is uniform
as shown in the figure. The x -direction velocity profile at Section 2-2 is given by  where δ is the boundary layer thickness.

The volume flow rate through Section 2-2 is given by

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 42

A cube of weight W and side a falls at a constant speed in a medium as shown in the figure. If the
medium is air (mass density =ρair ) let Uair be the velocity of the cube. If the medium is water
(mass density =ρwater ) let Uwater be the velocity of the cube.

Neglecting the buoyancy force and assuming drag coefficient to be same for both cases, the ratio of
velocities, (Uair/ Uwater)  is given by

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 43

Water is flowing through a venturimeter having a diameter of 0.25 m at the entrance (Station 1) and
0.125 m at the throat (Station 2) as shown in the figure. A mercury manometer measures the
piezometric head difference between Stations 1 and 2 as 1.3505 m. The loss of head between these
two stations, is 1/7 times the velocity head at the Station 2. Assume the acceleration due to gravity
to be 10 m/s2. The velocity of water at the throat is ____ m/s.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 44

 

Q. 44 – Q. 52 carry one mark each.

Q.

Neoprene is rendered non-inflammable because

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 45

Nylon-6 is manufactured from

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 46

At room temperature, the typical barrier potential for silicon p-n junction in Volt (V) is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 47

Quantitative measurement of the roughness of a polysilicon wafer can be performed with

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 48

The temperature of the antiferromagnetic-to-paramagnetic transition is called

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 49

At low injection level, a forward biased p-n junction would have

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 50

Which of the following mechanical properties of a material depend on the mobile dislocation
density in it.

(P) Young’s modulus (Q) yield strength (R) ductility (S) fracture toughness

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 51

The equilibrium concentration of vacancies in a pure metal

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 52

The materials belonging to which one of the following crystal classes would be both piezoelectric
and ferroelectric

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 53

Q. 53 – Q. 65 carry two marks each.

Q.

Polymerized isotactic polybutadiene has a molecular weight of 3 x 105 g/mol. The degree of
polymerization is _______________.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 54

A bar of Ti with Young’s modulus of 110 GPa and yield strength of 880 MPa is tested in tension. It
is noticed that the alloy does not exhibit any strain hardening and fails at a total strain of 0.108. The
mechanical energy that is necessary to break the material in MJ/m3 is ____________.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 55

A copper cup weighing 140 g contains 80 g of water at 4°C. Specific heats of water and copper are
4.18 and 0.385 J/g °C, respectively. If 100 g of water that is at 90 °C is added to the cup, the final
temperature of water in °C is ______________.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 56

Match the reaction in Column I with its name in Column II.

L – liquid, α, β, γ – different solid solution phases

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 57

The Young’s modulus of a unidirectional SiC fiber reinforced Ti matrix composite is 185 GPa. If
the Young’s moduli of Ti and SiC are 110 and 360 GPa respectively, the volume fraction of fibers
in the composite is _________.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 58

Match the composite in Column I with the most suitable application in Column II.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 59

Which among the following rules need to be satisfied for obtaining an isomorphous phase diagram
in a binary alloy system?

(P) The atomic size difference should be less than 15%.
(Q) Both the end components should have the same crystal structure
(R) The valency of the end components should be the same.
(S) The end components should have dissimilar electronegativities

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 60

The energy in eV and the wavelength in μm, respectively, of the photon emitted when an electron
in a hydrogen atom falls from n = 4 to n = 2 state is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 61

The weight in kg of gallium (Ga) to be mixed with arsenic (As) for obtaining 1.0 kg of gallium
arsenide (GaAs) is ______________. (MGa = 69.72 g/mol; MAs = 74.92 g/mol


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 62

Match the material in Column I with the property in Column II

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 63

Relevant portion of a binary phase diagram of elements A and B is shown below. The mass fraction
of liquid phase at 1000 °C for an alloy with 15 wt.% B is ___________.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 64

The expected diffraction angle (in degrees) for the first order reflection from the (113) set of planes
for face centered cubic Pt (lattice parameter = 0.392 nm) using monochromatic radiation of
wavelength 0.1542 nm is ___________.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 65

The diffusion coefficients of Mg in Al at 500 and 550 °C are 1.9x10-13 and 5.8x10-13 m2/s
respectively. The activation energy for diffusion of Mg in Al in kJ/mol is ___________.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 66

Q. 66 – Q. 74 carry one mark each.

Q.

A steel wire of diameter 5 mm is bent around a cylindrical drum of radius 0.5 m. The steel wire has
modulus of elasticity of 200 GPa. Find the bending moment in the wire in N-m.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 67

A compressed air tank having an inner diameter of 480 mm and a wall thickness of 8 mm is formed
by welding two steel hemispheres. If the allowable shear stress in the steel is 40 MPa, find the
maximum permissible pressure (in MPa) inside the tank.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 68

The Euler’s buckling load of a column fixed at both the ends is P. If one of the ends is made free,
the buckling load shall change to

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 69

A point in a body is subjected to a bi-axial state of stress, equal in magnitude but opposite in nature.
On a plane inclined at an angle 45° with respect to x-axis (passing through the point), the

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 70

A weightless beam subjected to two point loads is shown in the figure below

The shear force diagram of the beam is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 71

For the pin jointed truss, find the axial force (in kN) in the member 2-5.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 72

The supporting structure of a water tank is made of reinforced concrete (RC) with a tubular cross
section of inner diameter di, outer diameter do, height l, and Young’s modulus E. The mass of the
tank is m. If mass of the supporting structure is neglected, then the natural frequency of the water
tank in transverse direction is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 73

A mass is attached to a spring and placed horizontally in a frictionless surface. A simple pendulum
has been pivoted to the mass. The degree of freedom of this system is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 74

Consider the following two statements
Statement 1: A body of weight W falls from a height h and strikes the ground. If the body starts
from rest, the velocity with which it strikes the ground is  , where g is the acceleration due to
gravity.

Statement 2: If the same body (initially at rest) slides without friction along an inclined plane PQ
(angle of inclination α) starting from an elevation h above point Q, then its velocity at point Q is  

The correct option is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 75

Q. 75 – Q. 87 carry two marks each.

Q.

A composite bar of length ‘L’ is made of a centrally placed steel plate (50 mm wide x 10 mm thick)
with two copper plates (each 30 mm wide x 5 mm thick) connected rigidly on each side. If the
temperature of the composite bar is raised by 50°C, find the stress developed in each copper plate in
MPa.
(For Steel: Es = 2x105 MPa and αs= 12x10-6 /°C; For Copper: Ec = 1x105 MPa and αc= 17x10-6 /°C)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 76

The vertical deflection at the free end of the cantilever beam as shown in figure is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 77

A hollow shaft and a solid shaft have the same length and the same outer radius R. The inner radius
of the hollow shaft is 0.6 R. Assuming that both the shafts are made of same material and are
subjected to the same torque, find the ratio of shear stress in hollow shaft to that in solid shaft.


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 78

A beam with overhangs carries one point load acting downwards and the other upward. The
clockwise moment Pb is applied at each support. The bending moment at the midpoint of the beam
is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 79

A cantilever beam of length L supports a concentrated load P at the free end. The cross section of
the beam is rectangular with constant width b and varying depth h. The depth h of this idealized
cantilever beam varies in such a way that the maximum normal stress at every cross section remains
equal to the allowable bending stress. Considering only the bending stresses, the depth hx of the
fully stressed beam at any distance x from the free end shall vary

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 80

A cantilever beam is subjected to following three different loading conditions:
(a) a concentrated load P at its free end,
(b) a couple Mo at its free end and
(c) both loads acting simultaneously

The flexural rigidity of the beam may be assumed as EI. The strain energy due to bending when
both loads act simultaneously

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 81

A tapered rod has diameter d1 at one end which reduces uniformly to a diameter d2 over the length
(L). If the modulus of elasticity of the material is E, the change in the length of the rod due to the
application of axial force (P) is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 82

For a point in a body subjected to a plane stress condition (σx= 100 MPa, σy= 50 MPa and
τxy = τyx = 25 MPa), the maximum principal stress in MPa is_____________


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 83

An isotropic body is subjected to a state of stress given by: σx= 10 MPa and τxy = τyx = −20 MPa.
Assuming G = 0.4E, the volumetric strain is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 84

A block of weight Q rests on an inclined plane and it is attached to a string which runs over a
frictionless pulley to carry a block of weight P at its other end. The coefficient of friction between
the block of weight Q and the inclined plane is μ. Consider the following cases:
Case I: weight Q starts moving down the inclined plane
Case II: weight P starts falling down

The limiting values of ratio P/Q for Case I and Case II respectively are

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 85

To unload an item from a truck a crane boom is raised with a constant angular velocity of 1 rad/s
relative to the cab and then the cab is rotated about a vertical axis with constant angular velocity of
0.5 rad/s.

If the length of the boom (OP) is 10 m, the velocity of the tip (P) of the boom in m/s is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 86

A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the
direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets
embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact
is

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 87

A balloon with ballast (weight) inside it has a gross weight of 500 N. It is falling vertically with a
constant acceleration of 2 m/s2. If air resistance is negligible, find the weight of ballast (in N) that
must be thrown out in order to give the balloon an upward acceleration of 2 m/s2. (Acceleration due
to gravity, g = 9.81 m/s2)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 88

Notations used:
P-pressure, V-volume, T-temperature, S-entropy, H-enthalpy, U-internal energy, cp-specific heat at constant pressure, cv-specific heat at constant volume; specific properties are designated by lower case symbols.

Subscripts: R-reduced, C-critical, f-saturated liquid, g-saturated vapor,
Properties of air: cp = 1.005 kJ/(kg.K), specific heat ratio γ = 1.4, Gas constant = 0.287 kJ/(kg.K), Molecular weight = 29 gm/mol.
Universal gas constant = 8.314 kJ/(kmol.K).

Q. 88 – Q. 96 carry one mark each.

Q.

Entropy is a

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 89

A small container has gas at high pressure. It is placed in an evacuated space. If the container is
punctured, work done by the gas is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 90

The molecular weight of a mixture is 38.4 gm/mol. The mixture is composed of methane and
carbon-dioxide gases. The atomic weights of the elements C, H, and O are 12, 1, and 16 gm/mol,
respectively. The mole fraction of methane (Xmethane) is ____________ and that of carbon-dioxide
(Xcarbon-dioxide) is _______.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 91

A system undergoes a change from state 1 to state 2. During this process, the change in the internal
energy is ΔU. The change in internal energy of the system when executing the cycle 1-2-1 is equal
to

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 92

Which among the following plots represents a line joining two states with the same dew point
temperature on a standard psychrometric chart, with the dry bulb temperature on the X-axis and the
humidity ratio on the Y-axis?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 93

The efficiency of a reversible engine operating between two temperatures is 40 % . The COP of a
reversible refrigerator operating between the same temperatures is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 94

For a superheated vapor that cannot be approximated as an ideal gas, the expression determining a
small change in the specific internal energy is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 95

The minimum and maximum volumes in an air standard Otto cycle are 100 and 800 cm3. Its
thermal efficiency (%) is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 96

At a saturation temperature Tsat, the difference between the entropy of saturated vapor and entropy
of saturated liquid can be expressed as

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 97

Q. 97 – Q. 109 carry two marks each

Q.

A gas in a closed system is compressed reversibly from an initial volume of 0.2 m3 to 0.1 m3 at a
constant pressure of 3 bar. During this process, there was a heat transfer of 50 kJ from the gas. The
change in internal energy of the gas during this process in kJ is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 98

In a closed rigid vessel, air is initially at a pressure of 0.3 MPa and volume of 0.1 m3 at 300 K. A
stirrer supplies 100 kJ of work to the air, while 20 kJ of heat is lost to the atmosphere across the
container walls. After these processes, the temperature of air changes to _________K.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 99

A reversible heat engine (E) operates using three thermal reservoirs with temperatures as shown in
the following figure. If Q1=Q2, the efficiency of the engine is ___________.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 100

A metal block of mass 25 kg at 300 K is immersed in an infinitely large liquid nitrogen bath
maintained at 77 K. The system comprising of the block and liquid nitrogen attains thermal
equilibrium. The average specific heat of the metal is 0.45 kJ/(kg.K). The entropy generated during
the process is ___________kJ/K.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 101

For a gas obeying the equation of state given by   the values of the critical
volume and the critical temperature are 0.004 m3/kg and 100 °C, respectively. If the value of the
gas constant is 250 J/(kg.K), then the value of the constant ‘a’ is _____________ (N.m4/kg2). Note
that the critical point is the point of inflection on the critical isotherm.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 102

A rigid closed vessel is initially filled with 2 kg of water which is a mixture of saturated liquid and
saturated vapor states at 2 bar. The vessel is placed in an oven which heats the mixture to the
critical state. Using the saturated and critical property values from the table given below, the heat
transferred from the oven to the vessel is __________kJ.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 103

The equation of state for a certain gas is given by  where C1 is 50,000
(K2.m3)/kg and C2 is 0.8 m3/kg. The relation is known for the gas. The inversion temperature, given by the condition is ____________K.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 104

The maximum pressure and temperature in an air standard diesel cycle are 44 bar and 1600 K,
respectively. If the minimum pressure and temperature are 1 bar and 300 K, respectively, then the
cut-off ratio (the ratio of the volume at the end of the heat addition process to that at the beginning
of the heat addition process) is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 105

The thermal efficiency of an air standard Brayton cycle 0.35. The pressure ratio across the turbine
is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 106

Steam is isentropically expanded in a turbine from 80 bar to 7 bar. At the inlet of the turbine (state
1) h1 is 3246 kJ/kg and s1 is 6.52 kJ/(kg.K).

The enthalpy of the steam exiting the turbine (state 2) in kJ/kg is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 107

A thin insulating membrane separates two tanks initially filled with nitrogen [mean cv = 21.6
J/(mol.K)] and carbon-dioxide [mean cv = 11.6 J/(mol.K)] as shown below.

 

The membrane is ruptured and the gases are allowed to mix to form a homogeneous mixture at
equilibrium. During this process there are no heat or work interactions between the tank contents
and the surroundings. The final temperature at the equilibrium state in Kelvin is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 108

Two moist air streams MAS1 and MAS2 are mixed adiabatically. The details of MAS1 and MAS2
are given below in the table.

With pressure remaining same and with no work interactions during the mixing process, the
enthalpy of the mixed stream is ________________ kJ/kg of dry air.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 109

Consider the steady flow of air through an insulated nozzle. The pressure and temperature at the
inlet are 120 kPa and 320 K, respectively. The outlet pressure is 1 bar. The inlet velocity is very
small and the air undergoes a reversible adiabatic process. The outlet velocity, in m/s, is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 110

Q. 110– Q. 119 carry one mark each

Q.

The estimation of the molecular weight of a polymer by gel permeation chromatography (GPC) is
based on its

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 111

Elastomers are characterized by

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 112

Thermodynamically, two polymers with enthalpy of mixing (ΔH) and entropy of mixing (ΔS) form
a miscible blend at temperature T when

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 113

The tensile strain of a uniformly extending plastic specimen of initial length L0 and extended length
L is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 114

In natural rubber compounding, a peptizer is added

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 115

A continuous annular product is produced by

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 116

Relate the three varieties of polyethylene in the left column with their chain structures given in the
right column.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 117

Match the following changes observed in the calorimetric analysis of a polymer sample when heat
flow (y-axis) is plotted against temperature (x-axis):

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 118

A Bingham plastic fluid is flowing under gravity, down a vertical plate, as a film. Find the
appropriate match for the fully developed velocity profile of the fluid in the film, from among those
shown below.

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 119

Q. 119 – Q. 131 carry two marks each.

Q.

Calculate the mass percent of the crystalline phase in a polymer sample of density 975 kg/m3. The
density of amorphous phase is 866 kg/m3 and that of the crystalline phase is 996 kg/m3.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 120

Find the rate of initiation (molL-1s-1) of a polymerization reaction using a peroxide initiator with a
half life of 0.1 s and efficiency of 70%, if the concentration of the initiator is 0.05 molL-1.


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 121

The constitutive equation of a shear thinning polymeric fluid is given by

where ?? represents shear stress (Pa), and ???, the corresponding shear rate (s-1). The quantities ??0 =
20 Pas and γ0 = 10 s−1 are constants. Find the apparent viscosity of the sample (Pas) when the
applied shear rate is 40 s-1.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 122

Identify the monomer for the polymer shown below prepared by ring opening metathesis
polymerization.

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 123

The most appropriate order of toughness of nylon based materials is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 124

The shear rates involved in calendering (γcal), compression molding (γcomp), extrusion (γext), and
injection molding (γinj) processes follow the order

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 125

The dynamic mechanical response of a thermoplastic automotive component has shown a loss
angle of 45° and storage modulus of 3500 MPa. Calculate the loss modulus (MPa) of the
component.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 126

Match the terms in Column A with the appropriate terms in Column B:

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 127

Match the following additives for plastics with their respective functions:

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 128

Match the following catalyst/initiator with the type of polymerization reaction:

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 129

For AIBN (mol. wt. = 164 gmol-1) initiated free radical polymerization of methyl methacrylate
(mol. wt. = 100 gmol-1), where the termination is only by radical coupling, the  of PMMA is
found to be 4636 gmol-1. Calculate the degree of polymerization.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 130

A polymer solution is made by dissolving 5 g of polymer in 1000 ml of solvent. The flow time of
the solvent and that of the polymer solution between two appropriate marks in a viscometer are 40 s
and 60 s, respectively. The reduced viscosity (in dLg-1) of the polymer solution is:

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 131

The volume resistivity of a polymeric material is 107 Ωm. Find the resistance (in MΩ) of a cube of
the material of side 1 cm. The direction of current flow is as shown in the figure below.

(Important : you should answer only the numeric value)


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 132

Q. 132 – Q. 141 carry one mark each.

Q.

The systematic name of sucrose is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 133

A non-hydrolyzable lipid is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 134

The respiratory quotient (RQ) for the reaction 

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 135

Liver necrosis may be caused by the deficiency of

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 136

Which of the following non-nutritive sweeteners contains similar calories per gram as that of
sucrose?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 137

The objective of heating milk to about 65°C before homogenization is to inactivate

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 138

Make the correct match of the processes in Column I with the suitable materials/products in
Column II

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 139

A fruit juice of viscosity μ and density ρ is agitated using an impeller of diameter D at a speed of N
revolutions per minute. The terms   represent three process related
numbers, where P is power imparted by impeller and g is acceleration due to gravity. Which of the
following is correct representation of these numbers?

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 140

The energy required to reduce the size of a food material from a mean diameter of 12 mm to 4 mm
is 10 kJ kg-1. From Rittingers’ law, the energy needed to reduce the same material from a diameter
of 1.2 mm to 0.4 mm in kJ kg-1 is __________

(Important : you should answer only the numeric value)


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 141

Q. 141 – Q. 153 carry two marks each

Q.

Saccharomyces cerevisiae (mean doubling time 3.2 h) is grown in a batch fermenter with an
operating volume of 12 m3. A 2% (v/v) inoculum, which contains 5 kg cells per 100 m3 is
mixed with the substrate. The residence time in the fermenter is 24 h and the density of broth is
1010 kg m-3. The mass of S. cerevisiae obtained from the fermenter, in kg, is ________


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 142

Make the correct combination of operations in Column I with the machines in Column II

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 143

The correct order for D121 values of the spores of food spoilage bacteria in aqueous medium is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 144

Make the correct combination of pigments/microorganisms in Column I with the process/ products
in Column II

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 145

Make the correct combination of underlying principles in Column I with the processes in
Column II

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 146

Which one of the following statements is FASLE?

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 147

Which one of the following statements is TRUE?

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 148

Fish fillet having 84% moisture (wet basis) is frozen from top using an air blast freezer maintained
at −32°C. The initial temperature of the fillet (density 1050 kg m-3) is −2°C (freezing point).
Convective heat transfer coefficient of air is 25 Wm-2 K-1, thermal conductivity of frozen fish is 1.0
Wm-1K-1 and latent heat of crystallization is 340 kJ kg-1. The freezing time, in min, for a 20 mm
thick block of fish fillet weighing 1 kg is __________


XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 149

Make the correct combination of properties in Column I with their dimensions in Column II

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 150

The viscosity and density of a fruit juice at 21°C are 6.3 x 10-3 Pa s and 1029 kg m-3, respectively.
The juice flows at the rate of 0.12 m3 min-1 in a 2.54 cm inner diameter steel pipe. Correct
combination of the Reynolds number (NRe) and the nature of flow of juice is

XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 151

For a typical food sorption isotherm curve (Figure 1), which one of the following statements is
CORRECT ?

 

Figure 1: Food sorption isotherm curve

*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 152

10,000 kg milk (7% fat) is passed through a cream separator to obtain cream (40% fat) and skim
milk (0.1 % fat). The cream, thus obtained, is churned to make butter of 80.5% fat. If a loss of 0.5%
of initial milk fat occurs during the manufacturing process, the % overrun is _________________


*Answer can only contain numeric values
XE Engineering Science- 2014 GATE Paper (Practice Test) - Question 153

A 50 mm thick pack of farm fresh berries is cooled at one side from 24°C to 7°C. The relevant
properties of berries are: density 1025 kg m-3, specific heat 3.78 kJ kg-1K-1, convective heat transfer
coefficient 30 Wm-2K-1, and thermal conductivity 0.3 Wm-1 K-1. The Fourier number for a cooling
span of 30 min is ________________


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