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Identify the correct spelling of the word.
The correct spelling of the word is 'definitive' which means '(of a conclusion or agreement) done or reached decisively and with authority.' Thus option 2 is the correct answer.
The preposition 'about' is mandatory here thus option 1 and 4 are eliminated. Option 2 is correct as the tense present perfect continuous fits here. It conveys the meaning that the person usually talked about the place.
She is brave. Her brother is more brave.
Select the most suitable sentence with respect to grammar and usage.
Options 1 and 2 are incorrect as they change the meaning of what is mentioned. Option 3 is incorrect as with 'less' we use the adjective in positive form and not comparative form. The correct word here should be 'brave.' Option 4 is thus the correct answer.
When a four digit number is divided by 65, it leaves a remainder of 29. If the same number is divided by 13, the remainder would be______
Let number is N
Complete the following sentence.
I was ___ ___ for the bus and then I ___ sight of Craig passing by.
The word 'here' and 'there' both can be used here but should be followed with 'waiting' as no other word can fit here. The word 'caught' is correct here as 'catch a sight' means 'to see something.' Option 2 thus has the correct combination of words. The word 'cot' means 'a small bed with high barred sides for a baby or very young child.'
4 – digit number greater than 5000 are randomly formed from the digits 0, 2, 3, 5 and 7. The probability of forming a number divisible by 5 when the digits are repeated is ______
For a number to be greater than 5000, d_{1} should be filled with either 5 or 7
∴ Total numbers formed when the digits are repeated = 2 × 5 × 5 × 5 = 250
total cases = 250 1 = 249 ( case of 5000 is not included)
Now, For the number to be divisible by 5, unit digit d_{4} should be either 0 or 5.
∴ Total no. of ways = 2 × 5 × 5 × 2 = 100
favorable cases = 100  1=9 ( 5000 is not included))
∴Required Probability = 99/249 = 0.397
It is theoretically possible that bacteria developed on Venus early in its history and that some were carried to Earth by a meteorite. However, strains of bacteria from different planets would probably have substantial differences in protein structure that would persist over time, and no two bacterial strains on Earth are different enough to have arisen on different planets. So, even if bacteria did arrive on Earth from Venus, they must have died out.
The argument is most vulnerable to which of the following criticisms?
The question asks which of the statements given in the options can weaken the argument put by the author that all bacteria from Venus must have died out.
The passage states that since there is a single strain of bacteria which exists on the Earth, they all must be belonging to the Earth or let's say a single planet. But here the author does not take into consideration (as can be argued from his theory) the fact that may be all the bacteria came from Venus and there are none which originally belong to the Earth. So this criticism as mentioned in option 3 makes the argument of the author vulnerable.
Options 1, 2 and 4 are completely irrelevant criticisms as they do not address the main argument. The argument claims that if there were Venusian bacteria on Earth, then they must have died out by now. Whether there are bacteria originally from Earth that have also disappeared from Earth is irrelevant to the question and has no effect on the given argument.
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A man sells three articles A, B, C and gains 10% on A, 20% on B and loses 10% on C. He breaks even when combined selling prices of A and C are considered, whereas he gains 5% when combined selling prices of B and C are considered. What is his net loss or gain on the sale of all the articles?
Let a, b and c be the cost prices of the three articles A, B and C.
SP = CP + Profit (or) SP = CP – Loss
⇒ SP of A = 1.1a; SP of B = 1.2b; SP of C = 0.9c
By question,
1.1a + 0.9c = a + c ⇒ 0.1a = 0.1c ⇒ a = c
1.2b + 0.9c = 1.05(b + c) ⇒ 0.15b = 0.15c ⇒ b = c = a
Gain% = {(SP – CP)/CP} × 100
⇒ Net gain on the sale of all the articles =
∴ Net gain on the sale of all the articles = 6.66%
Which of the following inferences can be drawn from the above graph?
Option 1 is false as graph says there is decrease in students qualifying in Physics in 2015 compared to 2014.
Option 2 Let no. of students qualifying in Biology in 2013 be 100
⇒ No. of students qualifying in Biology in 2014 = 100 – 10% of 100 = 90
⇒ No. of students qualifying in Biology in 2015 = 90 + 10% of 100 = 99
∴ The number of students qualifying in Biology in 2015 is less than that in 2013
Option 3 and option 4 are incorrect since no detail is given regarding how many students qualified the subject in 2013.
DRQP is a small square of side 'a' in the corner of a big square ABCD of side 'A'. What is the ratio of the area of the quadrilateral PBRQ to that of the square ABCD, given A/a = 3?
Let f(z) = (x^{2} + y^{2}) + i2xy and g(z) = 2xy + i(y^{2} – x^{2}) for z = x + iy ϵ C. Then, in the complex plane C.
Given that f(z) = (x^{2} + y^{2}) + i 2xy
g(z) = 2xy + i (y^{2} – x^{2})
To check analyticity of a function, we need to check CR equations.
u_{x} = v_{y}, u_{y} =  v_{x}
f(z) = (x^{2} + y^{2}) + i 2xy
u = x^{2} + y^{2}, v = 2xy
u_{x }= 2_{x}
u_{y} = 2_{y}
v_{x} = 2_{y}
v_{y} = 2_{x}
u_{x} = v_{y} but u_{y} ≠ v_{x}
Hence, f(z) is not analytic
g(z) = 2xy + i (y^{2} – x^{2})
u = 2xy, v = y^{2 }– x^{2}
u_{x} = 2y
u_{y} = 2x
v_{x} = 2x
v_{y} = 2y
u_{x} = v_{y} and u_{y} = v_{x}
Hence g(z) is analytic.
If the Laplace transform of y(t) is given by then y(0) + y'(0) = _____.
Consider the following statements P and Q:
(Q): Let S be a diagonalizable matrix. If T is a matrix such that S + 5 T = I, then T is diagonalizable.
Which of the above statements hold TRUE?
A matrix is said to be singular, if determinant of that matrix is zero.
= 1 (18 – 12)  1 (9 – 4) + 1 (3 – 2)
= 6 – 5 + 1 = 2 ≠ 0
M is non singular
(Q) A matrix can be diagonalizable when it has distinct eigen values
S is a diagonalizable matrix. Hence, has distinct eigen values.
Let S be a 3 × 3 matrix and the eigen values of s are λ_{1}, λ_{2}, λ_{3}
Given that, S + 5T = I
From the properties of Eigen values,
(a) If λ_{1} is an eigen value of matrix A, then λ_{1 }will be on eigen value of matrix A.
(b) If λ_{1} is an eigen value of matrix A, then (λ_{1} + 1) will be an eigen value of matrix (A + I)
(c) If λ_{1} is an eigen value of matrix A, then λ_{1} will be an eigen value of matrix where K is a scalar.
From the above properties, eigen values of T are,
As λ_{1}, λ_{2}, λ_{3} are distinct values, will be distinct.
Hence, matrix T is diagonalizable
So, only Q is true.
Consider the differential equation
.If x = 0 at t = 0 and x = 1 at t = 1, the value of x at t = 2 is
If for two vectors and , sum is perpendicular to the difference The ratio of their magnitude is
For an activity of duration 8 days in a network,
Total float = 10 days
Free float = 4 days
Independent float = 0
Then find no. of days an activity can be delayed without effecting project completion time is
Total float is the time by which an activity can be delayed without delaying the project completion date. Thus, it is the extra time available for an activity.
In this case, total float = 10 days,
So, an activity can be delayed by 10 days.
Principal stress at a point in an elastic material are 100 MPa tensile, 50 MPa tensile and 25 MPa compressive. Determine the factor of safety against maximum principal stress theory. The elastic limit in simple tension is 220 MPa and Poisson’s Ratio is 0.3
Maximum Principal stress theory
Which of the given formula is CORRECT for calculating the angle of static friction θ_{s}?
The angle at which the resultant of force of limiting friction f and normal reaction R makes with direction of normal reaction R is called angle of friction.
Coefficient of static friction, μ = tan θ
A steel shaft of 40 mm diameter is subjected to a twisting moment of 1200 N.m. What will be the maximum shear stress (in N/mm^{2})?
An engine operating at 25% efficiency produces work at a rate of 0.1 MW. At what rate (in MW) is heat exhausted into the surroundings?
In a 5 × 5 transportation problem, degeneracy would arise if the number of filled slots are
In transportation model, if number of nonnegative independent allocations is less than (m + n  1), then solution is called degenerate solution.
Here m = no. of rows
n = no. of columns
The solution is said to be degenerate, as optimality test can’t be performed.
In this question m + n  1 = 5 + 5  1 = 9
So solution will become degenerate, if allocation is less than 9.
A horizontal water jet of area 10 cm^{2} and velocity 5 m/s strikes on a vertical plate which is moving with velocity 2 m/s towards the nozzle.
The force acting on the plane is _____ (in N)
Force on that vertical plate moving in the direction of jet:
Relative velocity of jet with respect to plane
The input link O_{2}P a fourbar linkage is rotated at ω rad/s. The angular velocity of the coupler PQ is 1 rad/s. Find the value of ω at an instant when θ is 180°.
Concept:
Angular velocity Ratio Theorem
If it is required to find the angular velocity of the link 4 when the angular velocity of the link 2 of a four – link mechanism is known, locate the I – centre 24
The angular velocity ratio if two link relative to a third link is inversely proportional to the distances of their common I – centre form their respective centres of rotation.
Calculation:
A 250 mm thick slab of a nickel alloy is subjected to cold rolling using a roll of diameter 450 mm. If the angle of bite during rolling is 10°, the maximum reduction (in mm) during rolling is ___ (answer upto two decimal places)
Initial thickness (hi) = 250 mm.
Roller diameter (D) = 450 mm
Draft or Reduction in thickness ∆h = D (1  cosα)
Where α is angle of bite.
∆h = 450 (1 – cos 10°) = 6.83 mm
An ideal gas is kept in thermal contact with a heat reservoir at 57°C while it is compressed from a volume of 20 L to a volume of 10 L. During the compression, an average force of 33.3 kN is used to move the piston a distance of 0.15 m. How much heat (in kJ) is exchanged between the gas and the reservoir?
As it is in contact with heat reservoir (infinite heat capacity), it will be an isothermal process
ΔU = 0
Q = W + ΔU
Word done on the system
W = f × d = 33.3 × 0.15 = 5 kJ
Q = 5 kJ (Heat flows out of the system)
Which of the following model does not fall in time series models?
Time Series Models: Uses a series of data points to predict future demand.
Associative Model: Uses variables and factors that affect the future demand.
A wheel has an unbalance mass of 10 kg at a radius of 40 mm. Determine the balancing mass (in kg) required in the same plane opposite at a radial distance of 50 mm.
A 20 cm diameter spherical ball at 800 K is suspended in the air. Assuming that the ball closely approximates a black body. What will be the total amount of radiation emitted by the ball in 5 min in kJ. (σ = 5.67 × 10^{8} W/m^{2}K^{4})
Q̇ = σAT^{4}
= 5.67 × 10^{8} × π (0.2)^{2} × (800)^{4}
Q̇ = 2.918 kW
Q = 2.918 × 5 × 60 = 875.54 kJ
A manometer is used to measure the pressure of a gas in a tank. The fluid used has a specific gravity of 0.85 and the manometer column height is 55 cm, as shown in figure. If the local atmospheric pressure is 96 kPa, what is the absolute pressure in the tank?
P – 0.55 × 0.85 × 1000 × 9.8 = 96 × 10^{3}
P = 100581 Pa
P = 100.6 kPa
Find the natural frequency of the system.
In a simple impulse turbine, the nozzle angle at the entrance is 30°. What will be the bladespeed ratio for maximum diagram efficiency?
Blade or diagram efficiency is defined as the ratio of work done on the blades to the energy supplied to the blades.
Blade speed ratio is the ratio of blade speed to a steam speed
Calculate the flow rate across A(16,6) and B (0,3) if stream function is given by
Flow rate across A and B is
A string of 20 cm length is attached to a point on a smooth vertical wall and another end with the sphere whose diameter is 20 cm and weight is 50 kN. The sphere rests against the wall as shown in figure. Tension in the string and wall reaction at the point of contact will be _____ respectively.
In a PV diagram for pure substance, the constant temperature lines in saturated liquidvapour region are ________.
In a PV diagram for a pure substance, the constant temperature line in the saturated liquidvapor region is parallel whereas, in the superheated region, these lines are diverging.
A metric thread with 3 mm pitch & 60° thread angle is inspected for pitch diameter using three wire method. The diameter of the best size wire is
Consider the matrix equation
The condition for existence of a nontrivial solution, and the corresponding normalised solution (up to a sign) is
For nontrivial solution, the rank of the matrix should be less than the number of variables. i.e. r < n.
For this, A = 0
⇒ (4c – 3b) – (2c – 6) + (b – 4) = 0
⇒ 4c – 3b – 2c + 6 + b – 4 = 0
⇒ 2c – 2b + 2 = 0
⇒ b = c + 1
The vectors x_{1}, x_{2} ….. x_{n }are said to be linearly dependent, if there exist numbers λ_{1}, λ_{2} ……. λ_{n}, not all zero such that
Two points are chosen randomly on a line 9 cm long. Determine the probability that the distance between them is less than 3 cm
x: The distance of first point from the start of the line
y: distance of second point from the start of the line segment
x,y ϵ[0,9]
So sample space is Area of region bounded by
x ≥ 0, y ≥ 0, x ≤ 9, y ≤ 9
This is square of side 9
Area = 81 cm^{2}
The region of our interest is
xy < 3
0 ≤ x ≤ 9
0 ≤ y ≤ 9
Area of shaded region = 2 (area of triangle) + area of rectangle
The area bounded by the curve y =x (3 – x)^{2}, the xaxis and the ordinates of the maximum and minimum points of the curve is
Given N > 0, the iterative equation for finding 3√N using NewtonRaphson method is:
If y = 3e^{2x} + e^{2x}  αx is the solution of the initial value problem
Complementary solution
(D^{2} + β) = 0 (1)
The given is, y = 3e^{2x} + e^{2x} – αx
It indicates, 2 and 2 are the roots of auxiliary equations.
⇒ (D + 2) (D – 2) = 0
⇒ D^{2} – 4 = 0
By comparing this equation with equation (1)
β = 4
The distance between (111) planes in face centered cubic crystal (FCC) is 2Å. Determine the atomic radius (in Å)
Jobs are produced in a shop at the rate of 600 per month and consumed at a rate of 300 per month. The production and consumption continue simultaneously till maximum inventory is reached. The lot size of production is 600. If backlog is not allowed, the maximum inventory level is ______
Concept: In case of production or Built up Inventory model,
Here P = production rate (units/time)
d = demand or consumption rate (units/time)
t_{p} = Production or manufacturing cycle time
Maximum Inventory
Also, Total Inventory cost = ordering cost (or) setup cost + holding cost
Now, For Finding average inventory, converting the maximum inventory triangle into average inventory rectangle,
Calculation:
P = 600 per month
d = 300 per month
Q = 600 units
Consider the following linear programming (LP) model
Maximize, Z = 600 x_{1} + 700 x_{2}
Subjected to
6x_{1} + 10x_{2} ≤ 60
7x_{1} + 12x_{2} ≤ 84
6x_{1} + 8x_{2} ≤ 48
X_{1}, x_{2}, ≥ 0
The optimal value of the solution is _______
converting all the constraints to equality and plotting on graph.
6x_{1} + 10x_{2} = 60
7x_{1} + 12x_{2} = 84
6x_{1} + 8x_{2} = 48
X_{1}, x_{2} = 0
The region ABC is feasible region,
Finding the value of objective function at all corner points.
Z_{A} = Z(0,6) = 600 × 0 + 700 × 6 = 4200
Z_{B} = Z(0,0) = 0 + 0 = 0
Z_{c} = Z(8,0) = 600 × 8 + 700 × 0 = 4800
∴ Z_{max} = 4800
What is the increase of volume per unit volume of thinwalled steel cylinder closed at both ends and subjected to a uniform internal pressure of 0.5 MPa. The wall thickness is 1.5 mm, the radius 350 mm and Poisson’s ratio are 0.33. Consider Young’s Modulus of elasticity as 200 GPa.
Concept:
Change is volume per unit volume.
A block weighing 2500 N rests on a horizontal plane for which coefficient of friction is 0.2. This block is pulled by a force of 1000 N acting at an angle of 30° to the horizontal. Find the velocity (in m/s) of the block after it moves 30 m starting from rest.
A tension member is formed by connecting with glue two wooden scantlings each 100 mm × 200 mm at their ends which are cut at an angle of 60° as shown in figure. The member is subjected to a pull P. Calculate the safe value of P (in kN) if the permissible normal and shear stress in the glue are 2 MPa and 1 MPa respectively.
A heat engine working on Cannot cycle absorbs heat from three reservoirs at 1000 K, 800 K and 600 K. The engine does 10 kW of net work and rejects 400 kJ/min of heat to a heat sink at 300 K. If heat supplied by the reservoir at 1000 K is 50% of the heat supplied by reservoir at 600 K, the quantity of heat exchanged with the reservoir at 800 K will be _____ (in kW).
W = 10 kW, Q_{4} = 400 kJ/min = 6.67 kW
Q_{1} = 0.5 Q_{3}
Energy balance:
In an orthogonal machining experiment carried out using a cutting tool with zero degree rake angle, the measured cutting force was 1700 N. If the friction angle at the rake facechip interface is 26°, then the thrust force value in N is _____
Rake angle (α) = 0°
Cutting force(F_{c}) = 1700 N
Friction angle (β) = 26°
A strut 3 m long is 4 cm in diameter. One end of the strut is fixed while its other end is hinged. Find the safe compressive load for the member allowing a factor of safety of 3. take E = 210 GPa
The thermal conductivity of pure aluminium is 214 W/mK and 228 W/mK at 200°C and 300°C, respectively. One surface of a large slab of aluminium of thickness 40 cm is exposed to 300°C while other surface is maintained at 200°C. Assuming that the thermal conductivity of aluminium varies linearly in this temperature range, determine the rate of conduction heat transfer per unit area (kW/m^{2}) through the slab.
A single stage air compressor running at 80 RPM, compress air from a pressure of 1 bar and temperature of 15°C to a pressure of 5 bar (see Figure) The clearance volume is 5% of swept volume which is 0.42 m^{3}. Assuming that the compression and expansion to follow the law pV^{1.3} = constant, determine the power required to drive the compressor (in kW)
Volumetric efficiency referred to the suction conditions.
In slider crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.
2000 cc of air takes 1.6 minutes to pass through a standard specimen of sand (5.08 cm high and 5.08 cm in diameter). The manometer indicates pressure as 5 g/cm^{2}. The permeability number is
The Dry Bulb temp and the wet bulb temp of moist air are 30°C and 20°C respectively. The atmospheric pressure is 740 mm of Hg
Determine the enthalpy of moist air (in kJ/kg)?
P = 740 mm of Hg = 740 × 13.6 × 9.8 = 98627.84 = 0.986 bar
Enthalpy (h) = 1.005t + ω (2500 + 1.88t)
Where ω is the specific humidity and t is the DBT in °C.
= 1.005 × 30 + 0.01076 (2500 + 1.88 × 30)
= 57.65 kJ/kg of Bar
A composite spring consists of two closecoiled helical springs connected in series. Each spring has 14 coils at a mean dimeter of 20 mm. The stiffness of the composite spring is 800 N/m. If the wire diameter of one spring is 2.5 mm, find the wire dimeter of the other spring in mm. G = 78 GPa
Given D =20 mm, n_{1} = n_{2} = 14, K_{eq }= 800 N/m d_{1} = 2.5 mm, d_{2 }= d
Deflection in the spring:
If the head loss due to sudden enlargement of water main from 180 mm to 460 mm diameter is 0.17 cm of mercury. The flow rate in the water main is ________ l/s. Take relative density of mercury as 13.6.
Head loss due to sudden enlargement is given by:
A spring of stiffness 0.3 N/mm is attached to a mass which has viscous damping device. When the mass was displaced and released, the period of vibration was 1.8 second and the ratio of consecutive amplitude was 4.2 : 1. The natural frequency of the system will be ______ (rad/s).
In an epicyclic gear train with a sun gear planet gear and a moving arm, the planet gear is fixed, and the arm has an angular velocity of 200 rpm. If the sun gear having 40 teeth, rotates at 250 rpm, what will be the number of teeth on planet gear ______.
In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take C_{v} = 0.718 kJ/kg K, γ = 1.4
Given:
P_{1} = 1 bar, T_{1} = 15°C = 288 K, r = 8, Q_{1} = 1000 kJ/kg
Q_{1} = C_{v} (T_{3} – T_{2})
Q_{1} = C_{v}(T_{3} – T_{2})
1000 = 0.718 (T_{3} – 521.69)
T_{3} = 2054.41 K = 1781.41°C
A shaft is subjected to a torque varying between –1000 N.mm to 4000 N.mm The yield strength and endurance strength of material in shear is 300 MPa and 250 MPa. Determine the required diameter of the steel shaft using factor of safety of 2.
In a CNC milling operation in xy plane, the tool has to machine the circular arc from point (30, 30) to (20, 20) with feed of 2 inch per minute at sequence number 10 of the CNC part program. The centre of Arc is (20, 30). If the machine has absolute mode of defining position coordinates, the correct tool path command is:
Circular interpolation with I, J & K concepts:
G90: Absolute positioning
G91: Incremental positioning
The curvature of motion is determined by the location of its centre point (I, JK or K) which must also be specified in same block (if radius is not used). The I, and J values are distance from the starting point centre point of the curvature of motion.
N010 G90 G02 X20 Y20 I10 J0 F2
In first quadrant if centre is towards the origin from start point, then I will be negative or if away take it positive (In 1^{st} quadrant and 4^{th} quadrant) and vice versa in 2^{nd} and and 3^{rd} quadrants.
If starting point is in 1^{st} and 2^{nd} quadrant then J will be taken with Negative sign towards centre and J with positive sign in 3^{rd} and 4^{th} quadrant.
At a cutting speed of 60 m/min & 90 m/min the total life is expected to be 16 min & 12 min respectively, then what would be the tool life at a speed at 30 m/min.
V_{1}T_{1}^{n} = V_{2}T_{2}^{n} (Taylor’s equation)
From Taylor’s equation it can be easily, derived that
Use the value of ‘n’ in Taylor’s equation, to find tool life.
A counter flow shell and tube exchanger is used to heat water with hot exhaust gases. The water (C = 4180 J/kg°C) flows at a rate of 2 kg/s while the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 30 m^{2} and the overall heat transfer coefficient is 200 W/m^{2}°C, what is the NTU for the heat exchanger?
Heat capacity Ratio, C:
ṁ_{c} = C_{pc} = C_{c}
ṁ_{h} = C_{ph} = C_{h}
NTU (number of transfer units): Measure of the effectiveness of the heat exchanger
If the pressure inside the droplet of water is 10% more than that of outside pressure of the droplet of water. The diameter of droplet of water is 0.06mm and surface tension of water is taken as 0.0725 N/m of water, the pressure inside the droplet is ____ N/cm^{2}
The pressure inside the droplet, in excess of outside pressure is given by
σ = surface tension between water and air
σ = 0.0725 N/m
R = Radius of Droplet
Pressure inside the droplet = ΔP + Pressure
outside the droplet
The net heat supplied in are welding process is 1400 J/mm. The melting efficiency is 40%. The welding speed is 6 mm/sec. The rate of melting is 20 J/mm^{3}. Calculate the area of the joint (in mm^{2}) that can be obtained.
Concept: Heat required for melting = volume melted × rate of welding
Volume method = Area of Joint × welding speed
Calculation:
Melting efficiency (η ) = 0.40
Welding speed = 6 mm/s
Rate of melting = 20 J/mm^{3}
Net heat supplied = 1400 J/mm
∴ Heat required to melt = 1400 × 0.40
= 560 J/mm
Now, Heat required for melting = volume melted × rate of melting
Volume method = Area of Joint × Welding speed
∴ 560 = Area × 20
Area = 28 mm^{2}
Mistake Point: Note that unit of net heat supplied is in J/mm, so in find step there will not be any need to multiply with welding speed.
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