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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

Solution:

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.

Solution:

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?

Solution:

QUESTION: 4

If y = 5x^{2} + 3, then the tangent at x = 0, y = 3

Solution:

*Answer can only contain numeric values

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)**

Solution:

QUESTION: 6

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

**Q.**

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

Solution:

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?

Solution:

*Answer can only contain numeric values

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)**

Solution:

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?

Solution:

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

Solution:

*Answer can only contain numeric values

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 A^{2} + 5Ais equal to ________

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

Solution:

QUESTION: 12

Which of the following is a solution of the differential equation

x2 y''+ xy'+ y = 4sin(ln x), x > 0?

Solution:

QUESTION: 13

At z = 0 , the complex function

Solution:

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

Solution:

*Answer can only contain numeric values

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)**

Solution:

QUESTION: 16

An integrating factor of the differential equation is

Solution:

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

Solution:

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

Solution:

*Answer can only contain numeric values

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)**

Solution:

*Answer can only contain numeric values

QUESTION: 20

If the work done in moving a particle once around a circle x^{2} + y^{2} = 4 under the force field then |a| is equal to _________.

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

Solution:

QUESTION: 21

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

Solution:

*Answer can only contain numeric values

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 m^{2} and its centroid is at The vertical component of the hydrostatic force,

F_{z} , is acting at a distance x_{p} . The value of x_{p} is ____ m.

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

Solution:

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/s^{2} at the point x =10 m and y = 0 , as

measured by a stationary observer is

Solution:

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?

Solution:

*Answer can only contain numeric values

QUESTION: 25

Velocity in a two-dimensional flow field is specified as: u = x^{2} y ; v = −y^{2} 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)**

Solution:

QUESTION: 26

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

Solution:

QUESTION: 27

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

Solution:

*Answer can only contain numeric values

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/s^{2} and neglect the

effects due to viscous and surface tension forces. The value of appropriate non-dimensional number

is ____

Solution:

QUESTION: 29

Which one of the following velocity profiles typically represents a fully developed incompressible,

turbulent flow in a pipe?

Solution:

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?

Solution:

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 ρ_{1} . The cylinder is

intended to float in another liquid of density ρ_{2} 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?

Solution:

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

Solution:

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

Solution:

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 H_{1} above the hump.

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

Solution:

*Answer can only contain numeric values

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 m^{3}/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.

Solution:

*Answer can only contain numeric values

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 cm^{2} at the inlet and 7 cm^{2} at the exit. Density of water and

acceleration due to gravity are 1000 kg/m3 and 10 m/s^{2}, respectively. Magnitude of x - component

of the water force on the elbow is ____ N.

Solution:

QUESTION: 37

A source with a strength of k_{1} and a vortex with a strength of k_{2} 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

Solution:

*Answer can only contain numeric values

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)**

Solution:

*Answer can only contain numeric values

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/m^{3} and 1.07 × 10^{-3} kg/m-s, respectively. Density and

dynamic viscosity of fresh water are 1000 kg/m^{3} 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.

Solution:

*Answer can only contain numeric values

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/s^{2}. The diameter of the pipe is ____ m.

Solution:

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

Solution:

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 =ρ_{air} ) let U_{air} be the velocity of the cube. If the medium is water

(mass density =ρ_{water} ) let U_{water} be the velocity of the cube.

Neglecting the buoyancy force and assuming drag coefficient to be same for both cases, the ratio of

velocities, (U_{air}/ U_{water}) is given by

Solution:

*Answer can only contain numeric values

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/s^{2}. The velocity of water at the throat is ____ m/s.

Solution:

QUESTION: 44

**Q. 44 – Q. 52 carry one mark each.**

**Q.**

Neoprene is rendered non-inflammable because

Solution:

QUESTION: 45

Nylon-6 is manufactured from

Solution:

QUESTION: 46

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

Solution:

QUESTION: 47

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

Solution:

QUESTION: 48

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

Solution:

QUESTION: 49

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

Solution:

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

Solution:

QUESTION: 51

The equilibrium concentration of vacancies in a pure metal

Solution:

QUESTION: 52

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

and ferroelectric

Solution:

*Answer can only contain numeric values

QUESTION: 53

**Q. 53 – Q. 65 carry two marks each.**

**Q.**

Polymerized isotactic polybutadiene has a molecular weight of 3 x 10^{5} g/mol. The degree of

polymerization is _______________.

Solution:

*Answer can only contain numeric values

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/m^{3} is ____________.

Solution:

*Answer can only contain numeric values

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 ______________.

Solution:

QUESTION: 56

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

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

Solution:

*Answer can only contain numeric values

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 _________.

Solution:

QUESTION: 58

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

Solution:

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

Solution:

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

Solution:

*Answer can only contain numeric values

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 ______________. (M_{Ga} = 69.72 g/mol; M_{As} = 74.92 g/mol

Solution:

QUESTION: 62

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

Solution:

*Answer can only contain numeric values

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 ___________.

Solution:

*Answer can only contain numeric values

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 ___________.

Solution:

*Answer can only contain numeric values

QUESTION: 65

The diffusion coefficients of Mg in Al at 500 and 550 °C are 1.9x10^{-13} and 5.8x10^{-13} m^{2}/s

respectively. The activation energy for diffusion of Mg in Al in kJ/mol is ___________.

Solution:

*Answer can only contain numeric values

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.

Solution:

*Answer can only contain numeric values

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.

Solution:

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

Solution:

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

Solution:

QUESTION: 70

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

The shear force diagram of the beam is

Solution:

*Answer can only contain numeric values

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)

Solution:

QUESTION: 72

The supporting structure of a water tank is made of reinforced concrete (RC) with a tubular cross

section of inner diameter d_{i}, outer diameter d_{o}, 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

Solution:

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

Solution:

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

Solution:

*Answer can only contain numeric values

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: E_{s} = 2x10^{5} MPa and α_{s}= 12x10^{-6} /°C; For Copper: E_{c} = 1x10^{5} MPa and α_{c}= 17x10^{-6} /°C)

Solution:

QUESTION: 76

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

Solution:

*Answer can only contain numeric values

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.

Solution:

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

Solution:

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

Solution:

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 M_{o} 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

Solution:

QUESTION: 81

A tapered rod has diameter d_{1} at one end which reduces uniformly to a diameter d_{2} 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

Solution:

*Answer can only contain numeric values

QUESTION: 82

For a point in a body subjected to a plane stress condition (σ_{x}= 100 MPa, σ_{y}= 50 MPa and

τ_{xy} = τ_{yx} = 25 MPa), the maximum principal stress in MPa is_____________

Solution:

QUESTION: 83

An isotropic body is subjected to a state of stress given by: σ_{x}= 10 MPa and τ_{xy} = τ_{yx} = −20 MPa.

Assuming G = 0.4E, the volumetric strain is

Solution:

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

Solution:

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

Solution:

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

Solution:

*Answer can only contain numeric values

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/s^{2}. 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/s^{2}. (Acceleration due

to gravity, g = 9.81 m/s^{2})

Solution:

QUESTION: 88

**Notations used:
P-pressure, V-volume, T-temperature, S-entropy, H-enthalpy, U-internal energy, c _{p}-specific heat at constant pressure, c_{v}-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: c _{p} = 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

Solution:

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

Solution:

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 (X_{methane}) is ____________ and that of carbon-dioxide

(X_{carbon-dioxide}) is _______.

Solution:

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

Solution:

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?

Solution:

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

Solution:

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

Solution:

QUESTION: 95

The minimum and maximum volumes in an air standard Otto cycle are 100 and 800 cm3. Its

thermal efficiency (%) is

Solution:

QUESTION: 96

At a saturation temperature T_{sat}, the difference between the entropy of saturated vapor and entropy

of saturated liquid can be expressed as

Solution:

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 m ^{3} to 0.1 m^{3} 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

Solution:

QUESTION: 98

In a closed rigid vessel, air is initially at a pressure of 0.3 MPa and volume of 0.1 m^{3} 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.

Solution:

QUESTION: 99

A reversible heat engine (E) operates using three thermal reservoirs with temperatures as shown in

the following figure. If Q_{1}=Q_{2}, the efficiency of the engine is ___________.

Solution:

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.

Solution:

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.m^{4}/kg^{2}). Note

that the critical point is the point of inflection on the critical isotherm.

Solution:

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.

Solution:

QUESTION: 103

The equation of state for a certain gas is given by where C1 is 50,000

(K^{2}.m^{3})/kg and C^{2} is 0.8 m^{3}/kg. The relation is known for the gas. The inversion temperature, given by the condition is ____________K.

Solution:

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

Solution:

QUESTION: 105

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

is

Solution:

QUESTION: 106

Steam is isentropically expanded in a turbine from 80 bar to 7 bar. At the inlet of the turbine (state

1) h_{1} is 3246 kJ/kg and s_{1} is 6.52 kJ/(kg.K).

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

Solution:

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

Solution:

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.

Solution:

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

Solution:

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

Solution:

QUESTION: 111

Elastomers are characterized by

Solution:

QUESTION: 112

Thermodynamically, two polymers with enthalpy of mixing (ΔH) and entropy of mixing (ΔS) form

a miscible blend at temperature T when

Solution:

QUESTION: 113

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

L is

Solution:

QUESTION: 114

In natural rubber compounding, a peptizer is added

Solution:

QUESTION: 115

A continuous annular product is produced by

Solution:

QUESTION: 116

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

right column.

Solution:

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):

Solution:

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.

Solution:

*Answer can only contain numeric values

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/m^{3}. The

density of amorphous phase is 866 kg/m^{3} and that of the crystalline phase is 996 kg/m^{3}.

Solution:

*Answer can only contain numeric values

QUESTION: 120

Find the rate of initiation (molL^{-1}s^{-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}.

Solution:

*Answer can only contain numeric values

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 γ_{0} = 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)**

Solution:

QUESTION: 122

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

polymerization.

Solution:

QUESTION: 123

The most appropriate order of toughness of nylon based materials is

Solution:

QUESTION: 124

The shear rates involved in calendering (γ_{cal}), compression molding (γ_{comp}), extrusion (γ_{ext}), and

injection molding (γ_{inj}) processes follow the order

Solution:

*Answer can only contain numeric values

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)

Solution:

QUESTION: 126

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

Solution:

QUESTION: 127

Match the following additives for plastics with their respective functions:

Solution:

QUESTION: 128

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

Solution:

*Answer can only contain numeric values

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)**

Solution:

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:

Solution:

*Answer can only contain numeric values

QUESTION: 131

The volume resistivity of a polymeric material is 10^{7} 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)**

Solution:

QUESTION: 132

**Q. 132 – Q. 141 carry one mark each.**

**Q.**

**The systematic name of sucrose is**

Solution:

QUESTION: 133

A non-hydrolyzable lipid is

Solution:

QUESTION: 134

The respiratory quotient (RQ) for the reaction

Solution:

QUESTION: 135

Liver necrosis may be caused by the deficiency of

Solution:

QUESTION: 136

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

sucrose?

Solution:

QUESTION: 137

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

Solution:

QUESTION: 138

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

Column II

Solution:

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?

Solution:

*Answer can only contain numeric values

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)

Solution:

*Answer can only contain numeric values

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 m^{3}. A 2% (v/v) inoculum, which contains 5 kg cells per 100 m^{3} 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 ________

Solution:

QUESTION: 142

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

Solution:

QUESTION: 143

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

Solution:

QUESTION: 144

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

in Column II

Solution:

QUESTION: 145

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

Column II

Solution:

QUESTION: 146

Which one of the following statements is FASLE?

Solution:

QUESTION: 147

Which one of the following statements is TRUE?

Solution:

*Answer can only contain numeric values

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^{-1}K^{-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 __________

Solution:

QUESTION: 149

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

Solution:

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 m^{3} min-1 in a 2.54 cm inner diameter steel pipe. Correct

combination of the Reynolds number (N_{Re}) and the nature of flow of juice is

Solution:

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

Solution:

*Answer can only contain numeric values

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 _________________

Solution:

*Answer can only contain numeric values

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^{-1}K^{-1}, convective heat transfer

coefficient 30 Wm^{-2}K^{-1}, and thermal conductivity 0.3 Wm^{-1} K^{-1}. The Fourier number for a cooling

span of 30 min is ________________

Solution:

### Engineering Sciences (XE) 2014 GATE Paper with solution

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