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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 = 5x^{2} + 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 A^{2} + 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 x^{2} + y^{2} = 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 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)**

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/s^{2} 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 = 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)**

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/s^{2} 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 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?

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 H_{1} 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 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.

*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 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.

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

*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/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.

*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/s^{2}. 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 =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

*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/s^{2}. 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 10^{5} 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/m^{3} 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 ______________. (M_{Ga} = 69.72 g/mol; M_{As} = 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} m^{2}/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 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

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

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

*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 (σ_{x}= 100 MPa, σ_{y}= 50 MPa and

τ_{xy} = τ_{yx} = 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: σ_{x}= 10 MPa and τ_{xy} = τ_{yx} = −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/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})

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, 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

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

(X_{carbon-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