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Question 1Mathematics and Basic Sciences

A pressure vessel contains gas at 350 kPa gauge. Atmospheric pressure is 101 kPa. What is the absolute pressure of the gas in kPa?

  1. 101
  2. 350
  3. 249
  4. 451 Correct answer.

Explanation

Absolute pressure equals gauge pressure plus atmospheric pressure, so 350 + 101 = 451 kPa. Gauge pressure is measured relative to the local atmosphere, so the atmospheric term must always be added to obtain absolute pressure used in gas-law calculations.

Question 2Mathematics and Basic Sciences

In a steady-flow process with negligible changes in kinetic and potential energy, the first law for a control volume reduces to which statement?

  1. Work output equals the change in entropy times temperature.
  2. Heat transfer equals the change in internal energy alone.
  3. Heat transfer minus work done by the system equals the mass flow rate times enthalpy change. Correct answer.
  4. Heat transfer plus work input equals zero for all fluids.

Explanation

For a steady-flow control volume with negligible kinetic and potential energy changes, energy balance gives Q - W = m(h2 - h1), where h is specific enthalpy. Enthalpy, not internal energy alone, appears because flow work is included in the enthalpy term.

Question 3Mathematics and Basic Sciences

A 2 kg block is pushed with a constant net force of 6 N. What is its acceleration?

  1. 12 m/s^2
  2. 3 m/s^2 Correct answer.
  3. 0.33 m/s^2
  4. 8 m/s^2

Explanation

Newton's second law gives a = F/m, so a = 6 N / 2 kg = 3 m/s^2. The result has units of acceleration because newtons reduce to kilogram-metres per second squared.

Question 4Mathematics and Basic Sciences

A simply supported beam of span L carries a concentrated load P at midspan. What is the maximum bending moment?

  1. PL/2
  2. PL
  3. PL/8
  4. PL/4 Correct answer.

Explanation

For a simply supported beam with a central point load, each reaction is P/2, so the moment at midspan is (P/2)(L/2) = PL/4. This is the standard maximum moment for that loading case.

Question 5Mathematics and Basic Sciences

In a stress-strain diagram for a ductile metal, what does the slope of the initial linear portion represent?

  1. Young's modulus Correct answer.
  2. Yield strength
  3. Toughness
  4. Poisson's ratio

Explanation

The initial linear region is the elastic range, and its slope is the modulus of elasticity, or Young's modulus. It measures stiffness, that is, how much stress is needed per unit of elastic strain.

Question 6Mathematics and Basic Sciences

A steel rod has an original length of 2.0 m and stretches by 1.2 mm under load. What is the axial strain?

  1. 0.6
  2. 0.0006 Correct answer.
  3. 0.00006
  4. 0.06

Explanation

Strain is change in length divided by original length: 0.0012 m / 2.0 m = 0.0006. Strain is dimensionless, so no unit is attached to the result.

Question 7Mathematics and Basic Sciences

Which statement correctly distinguishes mass from weight in engineering mechanics?

  1. Weight is a force equal to mass times gravitational acceleration. Correct answer.
  2. Mass and weight are both measured in newtons in SI.
  3. Weight is a scalar quantity with no direction.
  4. Mass varies with gravitational field while weight is constant.

Explanation

Weight is the gravitational force on a body and equals mg, measured in newtons. Mass is an intrinsic property measured in kilograms and does not change with location.

Question 8Mathematics and Basic Sciences

A fluid with density 850 kg/m^3 flows through a pipe of cross-sectional area 0.02 m^2 at 3 m/s. What is the mass flow rate?

  1. 51 kg/s Correct answer.
  2. 170 kg/s
  3. 25.5 kg/s
  4. 0.06 kg/s

Explanation

Mass flow rate is density times area times velocity: 850 x 0.02 x 3 = 51 kg/s. The volumetric flow rate is 0.06 m^3/s, which must then be multiplied by density.

Question 9Mathematics and Basic Sciences

Water flows through a horizontal pipe that narrows from a large section to a smaller section. Assuming ideal incompressible flow, what happens to the pressure in the narrower section?

  1. It increases because velocity decreases.
  2. It becomes zero at the throat.
  3. It decreases because velocity increases. Correct answer.
  4. It stays the same because the pipe is horizontal.

Explanation

By continuity, a smaller area gives a higher velocity. Bernoulli's equation along a horizontal streamline then requires that the pressure fall as velocity rises, so the throat pressure is lower.

Question 10Mathematics and Basic Sciences

Which dimensionless group compares inertial forces to viscous forces in fluid flow?

  1. Prandtl number
  2. Mach number
  3. Reynolds number Correct answer.
  4. Nusselt number

Explanation

The Reynolds number, Re = rho V D / mu, expresses the ratio of inertial to viscous forces and determines whether flow is laminar or turbulent. Each other group compares different transport phenomena.

Question 11Mathematics and Basic Sciences

A heat engine receives 500 kJ from a hot reservoir and rejects 350 kJ to a cold reservoir per cycle. What is its thermal efficiency?

  1. 0.35
  2. 0.30 Correct answer.
  3. 0.70
  4. 1.43

Explanation

Net work is 500 - 350 = 150 kJ, and efficiency is work divided by heat input: 150/500 = 0.30, or 30 percent. Efficiency must always be less than one for a real cycle operating between two reservoirs.

Question 12Mathematics and Basic Sciences

According to the second law of thermodynamics, which statement about a cyclic heat engine is true?

  1. Efficiency depends only on the amount of fuel supplied.
  2. No engine can convert all absorbed heat into work in a continuous cycle. Correct answer.
  3. Any engine can reach 100 percent efficiency if friction is eliminated.
  4. Heat can flow spontaneously from cold to hot without work input.

Explanation

The Kelvin-Planck statement of the second law forbids a cyclic device that converts all heat from a single reservoir into work. Some heat must be rejected to a lower-temperature sink, so efficiency is always below unity.

Question 13Mathematics and Basic Sciences

A Carnot engine operates between 600 K and 300 K. What is its maximum theoretical efficiency?

  1. 0.25
  2. 0.50 Correct answer.
  3. 1.00
  4. 0.75

Explanation

Carnot efficiency is 1 - Tc/Th = 1 - 300/600 = 0.50. Temperatures must be absolute, and no real engine between these reservoirs can exceed this value.

Question 14Mathematics and Basic Sciences

In a closed system at constant pressure, the heat transferred equals which quantity change?

  1. Enthalpy Correct answer.
  2. Gibbs free energy
  3. Entropy
  4. Internal energy

Explanation

At constant pressure with only expansion work, Q = delta H, because enthalpy is defined as H = U + PV. At constant volume, the corresponding heat transfer equals the change in internal energy.

Question 15Mathematics and Basic Sciences

A 0.5 kg sample of water is heated from 20 C to 60 C. Taking the specific heat of water as 4.18 kJ/(kg K), how much heat is absorbed?

  1. 167.2 kJ
  2. 41.8 kJ
  3. 20.9 kJ
  4. 83.6 kJ Correct answer.

Explanation

Q = mc(delta T) = 0.5 x 4.18 x 40 = 83.6 kJ. The temperature difference is 40 K, which equals 40 C degrees in magnitude.

Question 16Mathematics and Basic Sciences

Which mode of heat transfer requires a material medium and involves no bulk motion of the medium?

  1. Radiation
  2. Conduction Correct answer.
  3. Convection
  4. Advection

Explanation

Conduction transfers energy through molecular collisions and lattice vibrations within a material, without bulk fluid motion, and requires a medium. Radiation, by contrast, needs no medium.

Question 17Mathematics and Basic Sciences

A wall of thickness 0.2 m and thermal conductivity 0.5 W/(m K) has a temperature difference of 40 K across it. What is the steady heat flux?

  1. 100 W/m^2 Correct answer.
  2. 10 W/m^2
  3. 400 W/m^2
  4. 4 W/m^2

Explanation

Fourier's law gives q'' = k(delta T)/L = 0.5 x 40 / 0.2 = 100 W/m^2. The flux is proportional to conductivity and temperature gradient and inversely proportional to thickness.

Question 18Mathematics and Basic Sciences

A particle moves in a straight line with constant acceleration of 2 m/s^2 starting from rest. How far does it travel in 5 s?

  1. 10 m
  2. 25 m Correct answer.
  3. 20 m
  4. 50 m

Explanation

Using s = ut + 0.5at^2 with u = 0 gives s = 0.5 x 2 x 25 = 25 m. The velocity at 5 s is 10 m/s, but distance depends on the average velocity over the interval.

Question 19Mathematics and Basic Sciences

A projectile is launched at 30 m/s at 30 degrees above the horizontal on level ground, neglecting air resistance. What is its horizontal velocity component?

  1. 15 m/s
  2. 26 m/s Correct answer.
  3. 30 m/s
  4. 0 m/s

Explanation

The horizontal component is v cos(theta) = 30 x cos 30 degrees, which is about 26 m/s. In the absence of air resistance this component stays constant throughout the flight.

Question 20Mathematics and Basic Sciences

Two gears mesh with 20 teeth and 60 teeth. If the smaller gear rotates at 300 rpm, what is the rotational speed of the larger gear?

  1. 150 rpm
  2. 300 rpm
  3. 900 rpm
  4. 100 rpm Correct answer.

Explanation

For meshing gears the speed ratio is inverse to the tooth ratio: n2 = n1(N1/N2) = 300 x (20/60) = 100 rpm. The larger gear turns more slowly and with greater torque.

Question 21Engineering Sciences and Mechanics

A simply supported beam of span 6 m carries a central point load of 12 kN. What is the maximum bending moment in the beam?

  1. 18 kN·m Correct answer.
  2. 72 kN·m
  3. 36 kN·m
  4. 9 kN·m

Explanation

For a simply supported beam with a central point load P over span L, the maximum moment occurs at midspan and equals PL/4. Substituting gives 12 × 6 / 4 = 18 kN·m.

Question 22Engineering Sciences and Mechanics

In a stress–strain diagram for a mild steel specimen, the point at which the material begins to yield with a measurable permanent strain after the proportional limit is best described as which of the following?

  1. The elastic limit
  2. The ultimate tensile strength
  3. The proportional limit
  4. The upper yield point Correct answer.

Explanation

After the proportional limit, mild steel shows a distinct yield plateau; the first peak stress is the upper yield point, followed by a lower yield point. The proportional limit marks the end of linearity, and ultimate strength occurs much later at maximum load.

Question 23Engineering Sciences and Mechanics

A force of 50 N acts at a perpendicular distance of 0.4 m from a pivot. What is the moment about the pivot?

  1. 125 N·m
  2. 0.008 N·m
  3. 20 N·m Correct answer.
  4. 45 N·m

Explanation

The moment of a force about a point equals force times perpendicular distance, M = F × d. Multiplying 50 N by 0.4 m yields 20 N·m.

Question 24Engineering Sciences and Mechanics

For a body to remain in static equilibrium under a coplanar force system, which set of conditions must be satisfied?

  1. Sum of forces and sum of moments about any point both equal zero Correct answer.
  2. Sum of moments about any point equals zero only
  3. Sum of forces equals the sum of moments
  4. Sum of forces in one direction equals zero only

Explanation

Coplanar static equilibrium requires both translational and rotational balance: the vector sum of all forces is zero and the sum of moments about any point is zero. Either condition alone permits acceleration or rotation.

Question 25Engineering Sciences and Mechanics

A steel bar of original length 2 m is subjected to a uniform axial tensile strain of 0.0005. What is its elongation?

  1. 2.0 mm
  2. 0.25 mm
  3. 0.5 mm
  4. 1.0 mm Correct answer.

Explanation

Axial strain is elongation divided by original length, so elongation equals strain times length. Multiplying 0.0005 by 2000 mm gives 1.0 mm.

Question 26Engineering Sciences and Mechanics

In a hydrostatic system, the pressure at a point in a static fluid depends on which quantity?

  1. The depth below the free surface and the fluid density Correct answer.
  2. The horizontal cross-sectional area of the container
  3. The total volume of fluid present
  4. The shape of the containing vessel

Explanation

Hydrostatic pressure equals density times gravitational acceleration times depth, p = ρgh. In a static fluid, pressure is independent of vessel shape, total volume, and horizontal area.

Question 27Engineering Sciences and Mechanics

A body moves in a straight line with constant acceleration from rest. After 4 s its velocity is 12 m/s. What is the acceleration?

  1. 0.33 m/s²
  2. 3 m/s² Correct answer.
  3. 48 m/s²
  4. 16 m/s²

Explanation

For constant acceleration starting from rest, v = at, so a = v/t. Dividing 12 m/s by 4 s gives 3 m/s².

Question 28Engineering Sciences and Mechanics

In the International System of Units, the derived unit for pressure is expressed in base units as which of the following?

  1. kg·m²/s²
  2. kg/(m·s²) Correct answer.
  3. kg·m/s²
  4. kg/(m²·s)

Explanation

The pascal is one newton per square metre, and a newton is kg·m/s². Dividing by m² gives kg/(m·s²), the base-unit expression for pressure.

Question 29Engineering Sciences and Mechanics

A simply supported beam of span L carries a uniformly distributed load w over its entire length. The maximum shear force occurs at which location and equals what magnitude?

  1. At the supports, equal to wL
  2. At the supports, equal to wL/2 Correct answer.
  3. At midspan, equal to wL/8
  4. At midspan, equal to wL/4

Explanation

For a uniformly distributed load w over span L, each support reaction is wL/2. The shear force diagram is linear, with maximum magnitude wL/2 at the supports and zero at midspan.

Question 30Engineering Sciences and Mechanics

A circular shaft of diameter d transmits torque T. Which expression gives the maximum shear stress in the shaft?

  1. 32T/(πd⁴)
  2. T/(πd³/16)
  3. 8T/(πd²)
  4. 16T/(πd³) Correct answer.

Explanation

Torsion shear stress is τ = Tr/J, with polar moment J = πd⁴/32 and radius r = d/2. Substituting gives τ_max = 16T/(πd³).

Question 31Engineering Sciences and Mechanics

A cantilever of length 3 m carries a point load of 8 kN at its free end. What are the maximum bending moment and maximum shear force at the fixed support?

  1. M = 8 kN·m, V = 24 kN
  2. M = 12 kN·m, V = 8 kN
  3. M = 24 kN·m, V = 24 kN
  4. M = 24 kN·m, V = 8 kN Correct answer.

Explanation

For a cantilever with an end point load P over length L, the fixed-end moment is PL and the shear force equals P. Here PL = 8 × 3 = 24 kN·m and V = 8 kN.

Question 32Engineering Sciences and Mechanics

A thin-walled cylindrical pressure vessel of radius r and wall thickness t is subjected to internal pressure p. Which statement correctly compares the hoop and longitudinal stresses?

  1. Hoop stress is pr/(2t) and longitudinal stress is pr/t
  2. Hoop stress equals longitudinal stress, both being pr/t
  3. Longitudinal stress is pr/t and is twice the hoop stress
  4. Hoop stress is pr/t and is twice the longitudinal stress pr/(2t) Correct answer.

Explanation

For a closed thin cylinder, the hoop stress from force balance around a longitudinal section is pr/t, while the longitudinal stress from the end-cap load is pr/(2t). Thus hoop stress is twice the longitudinal stress.

Question 33Engineering Sciences and Mechanics

A block of mass 10 kg rests on a horizontal surface. The coefficient of static friction is 0.4 and gravitational acceleration is 9.81 m/s². What is the minimum horizontal force needed to initiate sliding?

  1. 98.1 N
  2. 9.81 N
  3. 39.2 N Correct answer.
  4. 24.5 N

Explanation

The normal force equals the weight, mg = 10 × 9.81 = 98.1 N. The limiting static friction is μN = 0.4 × 98.1 ≈ 39.2 N, which is the minimum force to start sliding.

Question 34Engineering Sciences and Mechanics

Water flows steadily through a horizontal pipe that narrows from a cross-section of 0.02 m² to 0.01 m². If the velocity in the wider section is 2 m/s, what is the velocity in the narrower section?

  1. 4 m/s Correct answer.
  2. 1 m/s
  3. 8 m/s
  4. 2 m/s

Explanation

Continuity for incompressible steady flow gives A₁v₁ = A₂v₂. Since the area halves from 0.02 to 0.01 m², the velocity doubles from 2 m/s to 4 m/s.

Question 35Engineering Sciences and Mechanics

A steel rod is constrained between two rigid walls at both ends and is heated uniformly. Which stress state develops in the rod?

  1. Compressive stress because expansion is prevented Correct answer.
  2. Zero stress because no external load is applied
  3. Shear stress because the ends are fixed
  4. Tensile stress because the rod tries to expand

Explanation

Prevented thermal expansion induces a compressive stress equal to EαΔT when both ends are fully restrained. The rod attempts to lengthen, but the rigid walls push back, producing compression.

Question 36Engineering Sciences and Mechanics

A beam has a rectangular cross-section of width b and depth h, bent about its horizontal centroidal axis. Which expression gives the second moment of area (moment of inertia) about that axis?

  1. bh³/3
  2. bh²/6
  3. bh³/12 Correct answer.
  4. b³h/12

Explanation

For a rectangle bent about its centroidal axis parallel to side b, the second moment of area is bh³/12. The depth enters cubed because area elements are distributed over the depth.

Question 37Engineering Sciences and Mechanics

In a two-dimensional stress state, the principal stresses are 80 MPa and 20 MPa. What is the maximum in-plane shear stress?

  1. 100 MPa
  2. 60 MPa
  3. 30 MPa Correct answer.
  4. 50 MPa

Explanation

Maximum in-plane shear stress equals half the difference of the principal stresses: (80 − 20)/2 = 30 MPa. The associated normal stress on those planes is the average, 50 MPa.

Question 38Engineering Sciences and Mechanics

A solid circular column of diameter 200 mm carries an axial compressive load of 300 kN. What is the average axial stress?

  1. 9.55 MPa Correct answer.
  2. 15 MPa
  3. 1.5 MPa
  4. 4.77 MPa

Explanation

The cross-sectional area is π(0.1)² = 0.0314 m². Dividing 300 kN by this area gives about 9.55 MPa compressive stress.

Question 39Engineering Sciences and Mechanics

A projectile is launched at 20 m/s at 30° above the horizontal on level ground, with air resistance neglected. What is the horizontal range? (Use g = 9.81 m/s².)

  1. 17.7 m
  2. 40.8 m
  3. 20.4 m
  4. 35.3 m Correct answer.

Explanation

The range of a projectile on level ground is R = v² sin(2θ)/g. With v = 20 m/s and θ = 30°, sin 60° ≈ 0.866, giving R ≈ 400 × 0.866 / 9.81 ≈ 35.3 m.

Question 40Engineering Sciences and Mechanics

A simply supported beam of span 4 m carries a point load of 10 kN at 1 m from the left support. What is the reaction at the right support?

  1. 10 kN
  2. 5.0 kN
  3. 7.5 kN
  4. 2.5 kN Correct answer.

Explanation

Taking moments about the left support gives R_right × 4 = 10 × 1, so R_right = 2.5 kN. The left support then carries the remaining 7.5 kN.

Question 41Engineering Sciences and Mechanics

A hollow circular shaft has outer diameter 100 mm and inner diameter 60 mm. Which value is closest to its polar second moment of area J?

  1. 1.57 × 10⁶ mm⁴
  2. 3.68 × 10⁶ mm⁴
  3. 8.55 × 10⁶ mm⁴ Correct answer.
  4. 9.82 × 10⁶ mm⁴

Explanation

For a hollow circle, J = π(D⁴ − d⁴)/32. Here D⁴ − d⁴ = 10⁸ − 1.296 × 10⁷ = 8.704 × 10⁷ mm⁴; multiplying by π/32 gives about 8.55 × 10⁶ mm⁴.

Question 42Engineering Sciences and Mechanics

A thin-walled cylindrical pressure vessel with closed ends has radius r, thickness t, and internal pressure p. If the material's allowable shear stress is τ_allow, which expression governs the maximum in-plane shear stress at a point on the wall?

  1. pr/t
  2. pr/(4t) Correct answer.
  3. pr/(2t)
  4. 3pr/(4t)

Explanation

The wall stresses are hoop pr/t and longitudinal pr/(2t), with the radial stress negligible. The in-plane maximum shear stress is half the difference of these principal stresses, giving pr/(4t).

Question 43Engineering Sciences and Mechanics

A beam of rectangular section is loaded in pure bending. If the depth is doubled while the width and bending moment stay constant, how does the maximum bending stress change?

  1. It remains unchanged
  2. It is doubled
  3. It is reduced to one half of the original value
  4. It is reduced to one quarter of the original value Correct answer.

Explanation

Bending stress is σ = My/I, and for a rectangle I = bh³/12 with y = h/2, so σ ∝ 1/h². Doubling the depth increases the second moment by a factor of eight and halves y, reducing stress to one quarter.

Question 44Engineering Sciences and Mechanics

An ideal fluid flows steadily along a horizontal streamline. At point A the pressure is 120 kPa and the velocity is 2 m/s; at point B the velocity is 6 m/s. Taking density as 1000 kg/m³, what is the pressure at B?

  1. 136 kPa
  2. 104 kPa Correct answer.
  3. 100 kPa
  4. 88 kPa

Explanation

Bernoulli's equation along a horizontal streamline gives p_A + ½ρv_A² = p_B + ½ρv_B². The kinetic term increases by ½ × 1000 × (36 − 4) = 16 kPa, so pressure falls from 120 kPa to 104 kPa.

Question 45Engineering Sciences and Mechanics

A rigid body rotates about a fixed axis with a constant angular acceleration of 2 rad/s², starting from rest. Through what angle does it turn in 5 s?

  1. 10 rad
  2. 50 rad
  3. 5 rad
  4. 25 rad Correct answer.

Explanation

For constant angular acceleration from rest, θ = ½αt². Substituting α = 2 rad/s² and t = 5 s gives θ = ½ × 2 × 25 = 25 rad.

Question 46Engineering Sciences and Mechanics

A pump delivers a steady volumetric flow rate of 0.004 m³/s through a pipe of internal diameter 50 mm. What is the average flow velocity in the pipe?

  1. 8.15 m/s
  2. 2.04 m/s Correct answer.
  3. 1.02 m/s
  4. 0.51 m/s

Explanation

Continuity gives Q = A·v, so v = Q/A. The pipe area is A = π(0.05)²/4 = 1.963×10⁻³ m², giving v = 0.004/1.963×10⁻³ ≈ 2.04 m/s. Velocity scales with the inverse square of diameter, so small errors in diameter cause large errors in velocity.

Question 47Engineering Sciences and Mechanics

In a steady-flow energy analysis of a horizontal nozzle with negligible heat transfer, which quantity is conserved between inlet and outlet along with the sum of pressure energy and kinetic energy per unit volume?

  1. The mass flow rate multiplied by the pressure drop
  2. Enthalpy plus kinetic energy per unit mass for an adiabatic device Correct answer.
  3. The product of pressure and velocity
  4. Total mechanical energy per unit mass, excluding internal energy changes

Explanation

For an adiabatic steady-flow device with no shaft work, the steady-flow energy equation reduces to conservation of stagnation enthalpy h + V²/2. Bernoulli's equation is the incompressible, frictionless special case of this statement.

Question 48Engineering Sciences and Mechanics

A flat plate of area 0.5 m² slides over a stationary surface with a 2 mm oil film between them. If the oil has dynamic viscosity 0.1 Pa·s and the plate moves at 0.5 m/s, what is the viscous drag force on the plate, assuming a linear velocity profile?

  1. 0.25 N
  2. 0.05 N
  3. 12.5 N Correct answer.
  4. 0.0125 N

Explanation

Newton's law of viscosity gives shear stress τ = μ·(du/dy). With du/dy = 0.5/0.002 = 250 s⁻¹, τ = 0.1×250 = 25 Pa, and F = τ·A = 25×0.5 = 12.5 N.

Question 49Engineering Sciences and Mechanics

A simply supported beam carries a concentrated moment M applied at its midspan. Which statement describes the bending moment diagram?

  1. It is constant over each half-span, with a jump of magnitude M at midspan Correct answer.
  2. It varies linearly from zero at each support to a peak at midspan
  3. It is a single constant value across the whole span
  4. It is a parabola with maximum at midspan

Explanation

A concentrated moment produces a step change in the internal bending moment equal to the applied moment, while the shear force remains unaffected. Between the supports and the load point the moment is therefore constant on each side, with a discontinuity at midspan.

Question 50Engineering Sciences and Mechanics

In a kinematic analysis of a rigid link rotating about a fixed pin, which term describes the acceleration component directed toward the center of rotation?

  1. Coriolis acceleration
  2. Tangential acceleration
  3. Centripetal acceleration Correct answer.
  4. Angular jerk

Explanation

For a point on a rotating rigid body, the acceleration has a tangential part r·α and a normal part r·ω² directed toward the center. The inward normal component is the centripetal acceleration.