WorksheetsDay 5 page 36-38
Total questions: 52
Worksheet time: 26mins
The integral of sin^m θ cos^n θ dθ can easily be determined by using Wallis formula provided the limits are form
0 to π
0 to π/2
0 to π/4
0 to 2 π
The integral of any quotient whose numerator is the difference of the denominator is the of the denominator
Reciprocal
Product
Logarithm
Derivative
Many integrals may be evaluated by introducing a new variable of integration in place of the original variable, the two variables being connected by some suitable formulas. This process is called
Integration by parts
Integration by substitution
Partial derivatives
The chain rule
The variable inside the integral is called variable of integration or integration variable. It is sometimes referred to as
Calculus variable
Dummy variable
Limits variable
Limits range
The value of x in trigonometric substitution with an integrand involving (a^2 – x^2) is
a sec θ
a tan θ
a cos θ
a sin θ
The area of the surface generated by rotating any plane curve about a certain axis in its plane id equal to the product of the length of the arc and the distance traveled by its centroid.
Varignon’s theorem
First proposition of Pappus
Method of section
Second proposition of Pappus
The volume of any solid revolution is equal to the generating are times the circumference of the circle described by the centroid of the area. This is known as
First proposition of Pappus
Cavalieri’s theorem
Second proposition of Pappus
Simpson’s Rule
Newton was inspired by an apple. Pappus propositions were inspired by what fruits?
Apple and pear
Lemon and orange
Apple and Lemon
Apple and banana
When the ellipse is rotated about is shorter axis, the ellipsoid is
Paraboloid
Prolate
Spheroid
Oblate
When the ellipse is rotated about its longer axis, the ellipsoid is
Paraboloid
Prolate
Spheroid
Oblate
When a catenary (y = cosh x) is rotated about its axis of symmetry, it generates a solid called
Paraboloid
Conoid
Catenoid
Hyperboloid
A solid of revolution of a parabola is known as
Paraboloid
Hyperboloid
Catenoid
Conoid
A section of a surface of revolution is the section containing the axis of revolution
Right
Central
Median
Meridian
An infinite series in which successive terms are of the form of constant times successive integral power of the variable. It takes the form of a_0 + a_1 x + a_2 x^2 + a_3 x^3 + ....
Fourier series
Taylor’s series
McClaurin series
Power series
Who invented the symbol “∞” for infinity?
John Stockton
John Venn
John Wallis
John Napier
Calculus was invented by
Newton
Leibniz
Gauss
Newton and Leibniz
Varignon’s theorem is used to determine
Location of centroid
Moment of inertia
Mass moment of inertia
Moment of area
In Physics, if Lf and Lv are the latent heat of fusion and vaporization, respectively, which of the following equations apply in determining the amount of energy needed to freeze a liquid?
Q = -mLf
Q = -mlV
Q = mLv
Q = mLf
is the quality of being physically elongated
Flexibility
Ductility
Malleability
Plasticity
When the total kinetic energy of a system is the same as before and after collision of two bodies, it is called
Plastic collision
Inelastic collision
Elastic collision
Static collision
Momentum is a property related to the object’s
Motion and mass
Mass and acceleration
Motion and weight
Weight and velocity
The amount of heat needed to change solid to liquid is
Condensation
Cold fusion
Latent heat of fusion
Solid fusion
The energy stored in a stretched elastic material such as a spring is
Mechanical energy
Elastic potential energy
Internal energy
Kinetic energy
According to this law, “The force between two charges varies directly as the magnitude of each charge and inversely as the square of the distance between them”.
Law of universal gravitation
Coulomb’s Law
Newton’s Law
Inverse square law
A free falling body is a body in rectilinear motion and with constant
Acceleration
Speed
Deceleration
Velocity
Centrifugal force
Directly proportional to the radius of the curvature
Directly proportional to the square of the tangential velocity
Inversely proportional to the square of the tangential velocity
Directly proportional to the square of the weight of the object
The fluid pressure is the same in all directions. This is known as
Pascal’s Principle
Bernoulli’s Theorem
Ideal Fluid Principle
Archimedes principle
The reciprocal of bulk modulus of any fluid is called
Volume stress
Compressibility
Shape elasticity
Volume strain
Momentum is the product of mass and
Acceleration
Velocity
Force
Time
One horsepower is equivalent to
746 watts
7460 watts
74.6 watts
7.46 watts
What is the latent heat fusion required to turn ice to liquid?
2, 256 kJ/kg
970 BTU/lbm
334 kJ.kg
168 BTU/lbm
What is the value of the work done for a closed reversible, isometric system?
Positive or negative
Negative
Positive
Zero
The sum of the pressure head, elevation head and the velocity head remains constant. This is known as
Boyle’s Law
Torrecelli’s theorem
Archimedes principle
Bernoulli’s theorem
A leak from a faucet comes out in separate drops. Which of the following is the main cause of this phenomenon?
Surface tension
Air resistance
Gravity
Viscosity of the fluid
Absolute viscosity is essentially independent of pressure and is primarily dependent on
Temperature
Density
Specific gravity
Velocity
In describes the luminous flux incidence per unit area and is expressed in lumens per square meter
Illuminance
Luminance
Luminous intensity
Radiance
When two waves of the same frequency, speed and amplitude traveling in opposite directions are superimposed,
Standing waves are produced
Constructive interference always results
The phase difference is always zero
Destructive interference always results
Linear momentum is the product of mass and velocity and this can be expressed also as a function of
Force, acceleration, time
Force, velocity, time
Force, time
Force, displacement
The transmission of heat from one place to another by fluid circulation between the spots of different temperature is called
Convection
Radiation
Conduction
Conservation
It is the measure of randomness of the molecules of a substance
Entropy
Enthalpy
Internal energy
Kinetic energy
The amount of heat needed to raise the temperature of one pound of that substance one degree Fahrenheit is
Specific heat
BTU
Latent heat
Calorie
What is the gage used to measure 0.001 to 1 atm pressure?
Bourdon
Water manometer
Mercury manometer
Metallic diaphragm
One of the types of non-material nuclear radiation is
Transmission radiation
Walton radiation
Gamma radiation
Betatron radiation
The flower pot falls of a ledge of a 5th floor window, just as it passes the third floor window, someone accidentally drops a glass of water from the window. Which of the following is true?
The flower pot hits the ground at the same time as the glass
The glass hits the ground before the flower pot
The flower pot hits the ground first and with a higher speed than the glass
The flower pot and the glass hits the ground at the same time
Whenever a net force acts on a body, it produces an acceleration in the direction of the resultant force, an acceleration which is directly proportional to the resultant force and inversely proportional to the mass of the body. This theory is popularly known as
Newton’s First Law of Motion
Faraday’s Law of Force
Newton’s Second Law of Motion
Hooke’s Law
Any two points along a streamline in an ideal fluid in steady state flow, the sum of pressure, the potential energy per unit volume and the kinetic energy per unit volume has the same value. This concept is known as the
Pascal’s theorem
Bernoulli’s Energy Theorem
Fluid Theorem
Hydraulic Theorem
Inelastic collision is a collision in which the total kinetic energy after the collision is less than before collision
Equal to zero
Equal
Less than
Greater than
The property by virtue of which a body tends to return to its original size of shape after a deformation and when the deformation forces have been removed
Elasticity
Malleability
Ductility
Plasticity
When two waves of the same frequency, speed and the amplitude traveling in opposite directions superimposed,
Destructive interference always results
Standing waves are produced
Constructive interference always results
The phase difference is always zero
What is the name of a vector that represents the sum of two vectors?
Scalar
Tensor
Resultant
Reaction
The standard acceleration due to gravity is
32.2 ft/s^2
980 ft/s^2
9.81 ft/s^2
23.3 ft/s^2
Ivory soap floats in water because
All matter has mass
The specific gravity of ivory soap is less than that of water
The density of ivory soap is unity
The specific gravity of ivory soap is less than that of water
