MESL 1 Flashcards
In the matrix equation px = q, which is a necessary condition for the existence of at least one solution for the unknown vector x?
a. Matrix p must be singular
b. Augmented [pq] must have the same rank as matrix p
c. Matrix p must be square
d. Vector q must have only non-zero element
b. Augmented [pq] must have the same rank as matrix p
A non-homogeneous system of linear equations representing mathematically an over determined system will be _______.
a. Consistent having many solutions.
b. Inconsistent having no solution.
c. Consistent having a unique solution.
d. Inconsistent having a unique solution
c. Consistent having a unique solution.
A linear system is inconsistent if it has _______.
a. no solution
b. exactly two distinct solution
c. infinite number
d. unique solution
a. no solution
A branch of mathematics which uses the properties of numbers by using symbols or letter to represent variables and unknown quantities and numbers in arithmetic operations which usually involves the use and rearranging of equations.
a. Algebra
b. Calculus
c. Statistics
d. Geometry
a. Algebra
Logarithm of 1 to any base is equal to _______.
a. one
b. undefined
c. negative value
d. zero
d. zero
Napierian logarithm has a base closest to _______.
a. 0
b. 2.718
c. 3.1416
d. 1
b. 2.718
A statement that follows with little or no proof required from an already proven statement.
a. Hypothesis
b. Axiom
c. Corollary
d. Analysis
c. Corollary
In Mathematics, _______ is an expression or a proposition, often algebraic, asserting the equality of two quantities.
a. Coefficient
b. Graph
c. Term
d. Equation
d. Equation
_______ is a mathematical process to combine numbers and/or variables into an equivalent quantity, number or algebraic expression.
a. Subtraction
b. Addition
c. Factoring
d. Polynomial
b. Addition
A fraction where the numerator, denominator, or both contains a fraction.
a. Binomial Fraction
b. Complex Fraction
c. Proper Fraction
d. Improper fraction
b. Complex Fraction
A fraction which has a top number larger than (or equal to) the bottom number.
a. Improper fraction
b. complex fraction
c. Composite fraction
d. Compound Fraction
a. Improper fraction
An angular unit equivalent to 1/4000 of the circumference of a circle is called _______.
a. grad
b. radian
c. mil
d. degree
a. grad
A line that meets a plane but not perpendicular to it in relation to the plane is _______.
a. coplanar
b. parallel
c. oblique
d. collinear
c. oblique
In economics, what is the point at which total cost and total revenue are equal and there is no net loss or gain?
a. Payback period
b. Value added
c. Pay back
d. Breakeven
d. Breakeven
What is the difference between the present worth and the worth at some future time?
a. Credit
b. Discount
c. Debit
d. Profit
b. Discount
A financial report made at the end of the fiscal year which gives the past year’s financial transactions and the results.
a. Income report
b. Annual report
c. Business report
d. Profit report
b. Annual report
It is caused by a decrease in government, personal or investment spending which tends to have side effect of increased unemployment since there is a lower level of demand in the economy and which can lead to an economic depression.
a. inflation
b. deflation
c. appreciation
d. depreciation
b. deflation
The amount transferred to depreciation is a fixed ratio of the undepreciated balance for the item.
a. Discrete Periodic Cash Flow
b. Straight Line method of depreciation
c. Discounted Payback Period
d. Declining Balance Depreciation (DBD)
d. Declining Balance Depreciation (DBD)
What is a state of substance which possesses no definite volume and is compressible?
a. Gas
b. Vapor
c. Solid
d. Crystal
a. Gas
Fundamental substances of which all matter is composed.
a. Polymer
b. Elements
c. Compound
d. Molecules
b. Elements
In relation to the proton, the electron is _______.
a. about the same mass and of the same charge
b. much lighter and of opposite charge
c. about the same mass and of opposite charge
d. about the same mass and with no charge
b. much lighter and of opposite charge
What is the family of curves which intersect a given family of curves at an angle less than 90°?
a. intersecting curves
b. orthogonal
c. acute angle
d. isogonal
d. isogonal
How many independent elastic constant/s is/are required to express the stress-strain relationship for a linearly elastic isotropic material?
a. One
b. Two
c. Three
d. Four
c. Three
The deformation of a bar under its own weight or compared to that when subjected to a direct axial load equal to its own weight will be _______.
a. double
b. the same
c. triple
d. half
d. half
Two closed-coil springs are made from the same small diameter wire, one wound on 2.5 cm diameter core and the other on 1.25 cm diameter core. If each spring had ‘n’ coils, what is the ratio of their spring constants?
a. 1/8
b. 1
c. 1/4
d. 0
a. 1/8
For a harmonic oscillator, the graph between velocity and displacement is _______.
a. Circular
b. Elliptical
c. Hyperbolic
d. Linear
b. Elliptical
Kinetic theory of heat states that _______.
a. at absolute zero there is absolutely no vibration of molecules
b. at low temperature all bodies are in solid state
c. temperature should fall during freezing
d. temperature should rise during boiling
a. at absolute zero there is absolutely no vibration of molecules
A system comprising a single phase is called a _______.
a. closed system
b. homogeneous system
c. heterogeneous system
d. isolated system
b. homogeneous system
The normal stress is the same in all directions at a point in a fluid when _______.
a. the fluid is at rest, regardless of its nature
b. the fluid is frictionless and incompressible
c. the fluid is frictional
d. the fluid has zero viscosity and is rest
a. the fluid is at rest, regardless of its nature
Resultant pressure of the liquid in case of an immersed body acts through _______.
a. Center of pressure
b. Center of gravity
c. Center of buoyancy
d. Metacenter
a. Center of pressure
What is buoyant force?
a. Resultant force acting on a submerged body
b. Resultant force acting on the water
c. Resultant hydrostatic force on a body due to fluid surrounding it
d. Resultant force due to water on a body
c. Resultant hydrostatic force on a body due to fluid surrounding it
If a vessel containing liquid moves downward with constant acceleration g, then which of the following is correct?
a. the pressure in the liquid mass is greater than the hydrostatic pressure
b. the pressure throughout the liquid mass is greater than atmospheric
c. the pressure throughout the liquid mass is
atmospheric
d. there will be vacuum in the liquid
c. the pressure throughout the liquid mass is
atmospheric
Convective acceleration of the fluid is due to _______.
a. steady flow
b. laminar flow
c. non-uniform flow
d. uniform flow
c. non-uniform flow
At t=0, then the function f(t)=sint/t has
a. a maximum
b. a point of inflection
c. a continuity
d. a minimum
a. a maximum
A cubic polynomial with real coefficients ________.
a. may have up to four extrema and up to three zero crossing
b. can possibly have no extrema and no zero crossing
c. will always have an equal number of extrema and zero crossing
d. cannot have more than two extrema and more than three zero crossings
d. cannot have more than two extrema and more than three zero crossings
The function f(x) = is called _______.
a. Linear function
b. Identity function
c. Constant function
d. Polynomial function
b. Identity function
Which one of the following statements is not true?
a. In a negative skewed distribution,
mode>mean>median
b. In a symmetric distribution, the value of mean, mode and median are the same.
c. The measure of skewness is dependent upon the amount of dispersion.
d. In a positive skewed distribution mean>median>
mode
a. In a negative skewed distribution,
mode>mean>median
To take a longest possible jump, one should make an angle of _______.
a. 0° with the ground
b. 45° with the ground
c. 60° with the ground
d. 90° with the ground
b. 45° with the ground
Centers of mass of body _______.
a. Lies always outside the body
b. Can be inside or outside the body
c. Lies at geometrical center
d. Lies always inside the bod
b. Can be inside or outside the body
What is the ratio of moment of inertia of a triangle and a rectangle having same base and height with respect to their bases?
a. 1:2
b. 2:1
c. 1:4
d. 4:1
c. 1:4
The earth can be assured as uniform sphere. Suppose the earth shrinks by 1 % in diameter, the new day period will be _______.
a. reduce by about 2%
b. increase by about 1%
c. not change from 24 h
d. reduce by about 1%
b. increase by about 1%
If A and B are symmetric matrices of same order and are scalars, then which of the following is false?
a. A - A’ is symmetric
b. k1A + k2B is symmetric
c. AB + BA is symmetric
d. B - BA is skew-symmetric
a. A - A’ is symmetric
What is the product of two orthogonal matrices?
a. unit matrix
b. unitary matrix
c. unitary
d. None of these
c. unitary
What are the eigen values of a skew- symmetric matrix?
a. Either zero or pure imaginary
b. always zero
c. always real
d. always pure imaginary
a. Either zero or pure imaginary
A set of linear equations is represented by the matrix equation Ax = b. What is the necessary condition for the existence of a solution for this system?
a. b must be linearly dependent on the columns of
A
b. b must be linearly independent of the columns of A
c. A must be invertible
d. None of the above
a. b must be linearly dependent on the columns of
A
The convergence of the bisection method is _______.
a. triangular
b. cubic
c. quadratic
d. linear
d. linear
What is a proposition with little applicability except that it forms part of the proof of a larger theorem?
a. Hypothesis
b. Corollary
c. Lemma
d. Postulate
c. Lemma
A fraction that is less than one, with the numerator less than the denominator.
a. Improper fraction
b. Decimal fraction
c. Proper fraction
d. Mixed number
c. Proper fraction
In geometry, it is a line or plane which touches a given curve or solid at a single point.
a. a segment
b. a secant
c. a tangent
d. a sector
c. a tangent
A curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve is called _______.
a. an ellipse
b. directrix
c. a hyperbola
d. translated axis
a. an ellipse
A ______ is set of all points in a plane which are an equal distance away from a given point and given line.
a. a circle
b. an ellipse
c. a parabola
d. a hyperbola
c. a parabola
A periodic cost that remains more or less unchanged irrespective of the output level or sales revenue, such as depreciation, insurance, interest, rent, salaries, and wages.
a. Increment cost
b. Fixed cost
c. Variable cost
d. Differential cost
b. Fixed cost
What is a separate legal entity that has been incorporated either directly through legislation or through a registration process established by law?
a. Corporation
b. Enterprise
c. Partnership
d. Sole Proprietorship
a. Corporation
Period over which an asset (machine, property, computer system, etc) is expected to be usable, with normal repairs and maintenance, for the purpose it was acquired, rented, or leased.
a. Physical life
b. Write off period
c. Economic life
d. Perpetual life
c. Economic life
An annuity that has no end, or a stream of cash payments that continues forever is called _______.
a. Perpetuity
b. Ordinary annuity
c. Annuity due
d. Deferred annuity
a. Perpetuity
What is the price that can be obtained from the sale of property or second hand?
a. Market value
b. Book value
c. Salvage value
d. Fair value
c. Salvage value
A currency trade in a foreign exchange market for which the demand is consistently high in relation to its supply.
a. Certificate of deposit
b. Treasury bill
c. Money market
d. Hard currency
d. Hard currency
What is the estimated value at the end of the useful life?
a. Compounded annually
b. Economic life
c. Salvage value
d. Book Value
c. Salvage value
What is an artificial expense that spreads the purchase price of an asset or another property over a number of years?
a. Sinking fund
b. Depreciation
c. Bond
d. Amnesty
b. Depreciation
It is a series of equal payments accounting at equal interval of time where the first payment is made several periods, after the beginning of the payment.
a. Progressive annuity
b. Simple annuity
c. Delayed annuity
d. Deferred annuity
d. Deferred annuity
Which of the following statement is correct for an element?
a. the atomic number is equal to the number of protons in the atom
b. the mass number is equal to the number of electrons in the atom
c. the number of protons always equals the number of neutrons in the atom
d. the atomic number is equal to the number of
neutrons in the atom
a. the atomic number is equal to the number of protons in the atom
An “ overflow” can brimful of water is suspended from the hook of a spring balance. After a small block of wood is placed in water, the balance reading is _______.
a. unaffected
b. increased by weight of wood block
c. decreased by weight of wood block
d. decreased by weight of wood block
a. unaffected
The number of elastic constants for a completely an isotropic elastic material which follows Hooke’ s law is _______.
a. 1
b. 3
c. 5
d. 7
b. 3
A cantilever beam of rectangular cross-section is subject to a load W at its free end. If the depth of the beam is doubled and the load is halved, the deflection of the free end compared to original deflection will be _______.
a. one-sixteenth
b. one-eight
c. one fourth
d. half
a. one-sixteenth
A solid circular shaft is subjected to pure torsion. What would be the ratio of maximum shear to maximum normal at any point?
a. 2:3
b. 1:1
c. 1:2
d. 2:1
c. 1:2
Which of the following statements is correct?
a. The slope of vaporization curve is always positive
b. The slope of sublimation curve is negative for all pure substances
c. The slope of fusion curve is positive for all pure substances
d. The slope of vaporization curve is always
negative
d. The slope of vaporization curve is always
negative
What is a gas which obeys kinetic theory perfectly?
a. ideal gas
b. monoatomic gas
c. diatomic gas
d. real gas
a. ideal gas
Which of the following is not property of the system?
a. Specific volume
b. Heat
c. Temperature
d. Pressure
b. Heat
Which one of the following statements is true to a two-dimensional flow of ideal fluids?
a. Stream function may or may not exist
b. Stream function will exist but potential function may or may not exist
c. Potential function exists if stream function exists
d. Both potential function and stream function must exist for every flow
b. Stream function will exist but potential function may or may not exist
For an irrotational flow, the velocity potential lines and the streamlines are always _______.
a. orthogonal to each other
b. parallel to each other
c. inclined to the horizontal
d. coplanar
a. orthogonal to each other
All experiments far indicate that there can be a laminar flow in a pipe if the Reynolds number is _______.
a. 2000
b. 2300
c. 20000
d. 4300
a. 2000
The continuity equation deals with the law of conservation of ________.
a. energy
b. momentum
c. mass
d. none of these
c. mass
A flow is rotational if _______.
a. fluid particles do not rotate about their mass centers while moving along a streamline
b. fluid element undergoes net rotation in a plane about an axis normal to the plane
c. fluid element undergoes liner deformation
d. fluid flows in a circular path
b. fluid element undergoes net rotation in a plane about an axis normal to the plane
In a mass of continuum that is rotating like a rigid body, the vorticity is _______.
a. equal to the angular velocity of that rotation
b. twice the angular velocity vector of that rotation.
c. trice the angular velocity of that rotation
d. none of these
b. twice the angular velocity vector of that rotation
Consider a company that assembles computers. The probability of a faulty assembly of any computer is P. The company therefore, subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability _______.
a. (1-q) p
b. P + q
c. pq + (1-p) (1 -q)
d. (1-p) q
c. pq + (1-p) (1 -q)
When the acceleration and velocity are acting perpendicular to each other than the trajectory of motion is _______.
a. hyperbolic
b. straight line
c. circular
d. parabolic
c. circular
Two bodies of moment of inertia I1 and I2 where I1 is more than I2, and have same angular momentum, the body having higher kinetic energy is _______.
a. First body
b. Second body
c. Data insufficient
d. Both have same kinetic energy
b. Second body
Which of the following if false?
a. If A a unitary matrix, then A-1 is not unitary
b. If A is a nilpotent matrix, then A=0
c. If A and B are two unitary matrices, then the product of A and B is also unitary
d. If A is an orthogonal matrix, then A-1 is also
orthogonal
a. If A a unitary matrix, then A-1 is not unitary
A and B are the matrices of same order such that AB+A and BA = B, then A and B are _______.
a. unitary matrices
b. orthogonal matrices
c. nilpotent matrices
d. idempotent matrices
d. idempotent matrices
An array of m x n quantities which represents a single number system composed of elements in rows and columns is known as _______.
a. Determinant
b. Transposed matrix
c. Cofactor of a matrix
d. Matrix
d. Matrix
Who among the following is associated with a technique of solving a system of linear equations?
a. Cramer
b. Hermite
c. Sarrus
d. Cayley
a. Cramer
