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# Online Assignment for Business Math Set 5

QN1. The matrix is an arrangement of numbers in___
a. m rows & n columns
b. n rows & m columns
c. both a & b
d. none of the above.

QN2. The value of the determinant is _____
a.100.
b.364.
c.14.
d.340.

QN3. Zero matrix is also called____.
a. Diagonal matrix
b.Scalar matrix
c.Unit matrix
d.Null matrix

QN4. The rank of the given matrix is
a.1
b.2
c.3
d.0

QN5. The order of is
a.3×3
b.2×3
c.3×2
d.4×4

QN6. If A is is
a.0
b.l
c.2
d.3

QN7. The given matrix is a. a scalar matrix.
b. a unit matrix.
c. a square matrix
d. a rectangular matrix.

QN8.1f A=  QN9. If A is a singular matrix |A| is____
a.1
b.0
c. any positive value.
d. any negative value

QN10. If a. square matrices.
b. null matrices.
c. row matrices.
d. zero matrices.

QN11. If A, B are two matrices and K is a scalar then QN12. If A,B and C are matrices the associative property is___ QN13. Zero matrix is otherwise known as____
a. null matrix.
b. square matrix.
c.unit matrix.
d.triangular matrix.

QN14. If Aand B are matrices of same order then QN15. If A,B and C are matrices of the same order then QN16. The determinant value of the following matrix a.47
b.40
c.57
d.-57

QN17. When the number of rows and the number of columns of a matrix are equal, the matrix is___
a.square matrix
b.row matrix
c.column matrix
d.none of these.

QN18. If all the elements of a matrix are zeros, then the matrix is a___
a.unit matrix
b.square matrix
c.zero matrix
d.none of these.

QN19. A diagonal matrix in which all the diagonal elements are equal is a ___
a.scalar matrix
b.column matrix
c.unit matrix
d.None of these.

QN20. If any two rows and columns of a determinant are identical, the value of the determinant is___
a.1
b.0
c.-1
d.Unaltered

QN21. .If there is only one column in a matrix, it is called___
a.Row matrix
b.column matrix
c.square matrix
d.rectangular matrix.

QN22.When all the elements of a matrix are zeros, the matrix is called____
a.unit matrix
b.square matrix
c.null matrix
d.Row matrix.

QN23.When the number of rows is not equal to the number of columns then the matrix is said to be____
a.unit matrix
b. Rectangular matrix
c .null matrix
d.row matrix.

QN24.The Value of determinant of a. -27.
b. 27.
c. 24.
d. -24.

QN25. .If the number of rows of a matrix is greater than the number of columns then the matrix is called as___
a. a row matrix
b.a column matrix
c.a rectangular matrix
d.a square matrix.

QN26. Inverse of a matrix exists if and only if___
a.determinant value exists
b.determinant value is zero
c.determinant value is one
d.determinant value is negative

QN27.A square matrix A is an orthogonal matrix x, if___ QN28. (3 8 9 -2 ) is a row matrix of order___
a.4×4
b.1×4
c.1×1
d.4×1.

QN29.If  QN30.Cramer’s Rule is also known as___
a. Inverse Matrix Method
b. Matrix Method
c. Determinant Method
d. Inverse Method

QN31. The___is the order of the largest square submatrix.
a. Rank of a matrix
b. Size of a matrix
c. Both a & b
d. None of the above.

QN32. O.R. Stands for___
a. Operations research
b. Open Report
c. Own Record

QN33. If a matrix has 4 rows and 3 columns, then the size will be denoted by
a.3×4
b.3×3
c.4×3
d.4×4

QN34. I stands for
a. Simple Interest
b. Compound Interest
c. Rate of interest
d. No.of.years.

QN35.C.I. stands for .
a. Compound Interest
b. Simple Interest
c. Rate Of Interest
d. No.of.years.

QN36. Principal (or) Present Value is denoted by
a. A
b. n
c. P
d. None of the above.

QN37. The Lender’s are also known as____
a. Creditor’s
b. Debtor’s
d. None of the above.

QN38.The borrowers are also known as___
a. Debtor’s
b. Creditor’s
c. Both a & b
d. None of the above.

QN39. Compound Interest is always___the Simple Interest.
a. Lesser than
b. Equal to
c. Greater than
d. None of the above.

QN40.Simple interest will be the income for___
a.lender.
b.borrower.
c.both .
d.neither lender nor borrower.

QN41.The simple interest on Rs 5,000 at 10% for 3 years is
a.500.
b.1000.
c.1500.
d.2000.

QN42.The formula for the face value A is given by___ QN43.Under annuity due, payment is due at the
a.beginning of the time
b.end of the time.
c.at the middle of the time.
d.each .

QN44.The compound interest for Rs 20000 for 3 years at 10 % is
a.2500.
b.2200.
c.6000.
d.2500.

QN45.The simple interest for Rs 10000 for 2 years at 10% is
a.200.
b.3000.
c.4000.
d.2000.

QN46. 51-46+3(5) =
a. 40
b. 20
c. 41
d.52

QN47. 3x- 4+7 = 0, then x =?
a. -1
b. +1.
c. 0.
d. 2.

QN48.Under compound interest the formula for A is given by
a.A=P(1+ni).
b.A=P(1+i).
c.A=Pnr/100. d.A=P(1+i)n.

QN49.Banker’s discount is given by the formula___.
a.Anr/100.
b.Pnr/100.
c.Anr.
d.Pnr.

QN50.Face value of a bill of exchange is given by the formula___ QN51.When the payments are to be made at the end of each interval the annuity is called___
a.immediate annuity.
b.annuity due.
c.both( a) and( b).
d.present annuity.

QN52. In calculation of interest ‘n’ stands for
a. Rate of interest
b. Amount
c. Principal
d. No.of.years

QN53.The formula for finding the compound interest is___
a.A=P(1+ni).
b.A=P(1+i).
c.A=Pnr/100.
d.A=P(1+i)n.

QN54.Under simple interest, the interest for n years is
a.A=P(1+ni).
b.A=P(1+i).
c.A=Pnr/100.
d.A=P(1+i)n.

QN55.Under simple interest, amount or value at the end is
a.A=P+I.
b.A=P(1+i).
c.A=Pnr/100.
d.A=P(1+i)n.

QN56.Under simple interest, the rate of interest is given by
a. R = 100r-(100-nr).
b. r = 100 I/Pn.
c. Anr/100.
d. A=P(1+i)n.

QN57.The present value under annuity due is____ QN58.The Amount due under immediate annuity is___ QN59.Formula for Bankers gain is___ QN60.In Graphical solution the feasible region is____
a.where all the constraints are satisfied simultaneously.
b.any one constraint is satisfied
c.only the first constraint is satisfied
d.any one of the above condition.

QN61.An LPP has___.
a.one optimal solution
b.two optimal solutions
c.Three optimal solutions
d.none of these.

QN62.An LPP deals with problems involving only___
a.single objective
b.multiple objective
c.two objective
d.none of these.

QN63.Which of the following is not associated with any LPP?
a.Feasible Solution
b.Optimum Solution
c.Basic solution

QN64.Which of the following is not true about feasibility?
a.It cannot be determined in a graphical solution of an LPP.
b.It is independent of the objective function.
c.It implies that there must be a convex region satisfying all the constraints.
d.Extreme points of the convex region give the optimum solution.

QN65.In Graphical solution the feasible solution is any solution to a LPP which satisfies____
a.only objective function.
b.non-negativity restriction.
c.only constraint.
d.all the three.

QN66.In Graphical solution the redundant constraint is___
a.which forms the boundary of feasible region.
b.which do not optimizes the objective function.
c.which does not form boundary of feasible region.
d.which optimizes the objective function.

QN67.Optimal solution in an LPP is___
a.which maximizes or minimizes the objective function.
b.which maximizes the objective function.
c.which minimizes the objective function.
d.which satisfies the non negativity restrictions.

QN68.Unbounded solution in an LPP is___
a.where the objective function can be decreased indefinitely.
b.which maximizes the objective function.
c.where the objective function can be increased or decreased indefinitely
d.where the objective function can be increased indefinitely.

QN69.The two forms of LPP are ___
a.standard form and canonical form
b.standard form and general form
c.matrix form and canonical form
d.matrix form and standard form.

QN70.In the canonical form of LPP if the objective function is of maximization, then all the constraints other than non-negativity conditions are ___
a.greater than type.
b.lesser than type.
c.greater than or equal to type.
d.lesser than or equal to type.

QN71.In the canonical form of LPP if the objective function is of minimization then all the constraints other than non-negativity conditions are___
a. greater than type.
b. lesser than type.
c. greater than or equal to type.
d. lesser than or equal to type.

QN72.In an LPP the solution for the problems involving more than 2 variables can be solved using___
a. graphical method.
b. simplex method.
c. hungarian method.
d. all the above

QN73.In the standard form of LPP if the objective functions is of minimization then all the constraints___
a. equations .
b. inequalities.
c. greater than or equal to type.
d. lesser than or equal to type.

QN74.In the standard form of LPP if the objective function is of minimization then the right hand side of the constraints should be ____
a. positive.
b. negative.
c. non-negative.
d. zero.

QN75.The non-negative variable which is added to LHS of the constraint to convert the inequality â‰¤ into equation is called___
a. random variable.
b. decision variable.
c. surplus variable.
d. slack variable.

QN76.The non-negative variable which is added to LHS of the constraint to convert the inequality â‰¥ into equation is called___
a.random variable.
b.decision variable
c.surplus variable
d.slack variable.

QN77.The test of optimality in simplex method is QN78.The Key column in simplex method is selected when the column of Zj-Cj is
a. most negative.
b. largest negative.
c. positive.
d. zero.

QN79.The Key row is selected when the column of Zj-Cj is finding the ratio which is
a. maximum.
b. minimum.
c. largest positive.
d. most negative.

QN80.In simplex method the LPP has unbounded solution if the variable in the key column is____
a. maximum.
b. minimum.
c. positive.
d. negative.

QN81.In graphical method the LPP has unbounded solution if the solution space has
a. no upper boundary.
b. no lower boundary.
c. no boundary in the first quadrant.
d. none of the above.

QN82.In a linear programming minimization model the objective function is to be___
a.minimized
b.maximized.
c.minimized or maximized.
d.standardized.

QN83.Which of the following is associated with any L.P.P?
a.feasible solution
b.optimum solution
c.basic solution
d.all the above.

QN84.Linear programming is___
a.a constraint optimization model
b.a constraint decision making model.
c.a mathematical programming model.
d.all the above.

QN85.Which of the following is not true about feasibility?
a.it cannot be determined in a graphical solution of an L.P.P.
b.it is independent of the objective function.
c.it implies that there must be a convex region satisfying all the constraints.
d.extreme points of the convex region gives the optimum solution.

QN86.Graphical method can be used only when the decision variables is___.
a.more than 3
b.more than 1
c.two
d.one

QN87.The region on the graph sheet with satisfies the constraints including the non negativity restrictions is called the____space
a.solution.
b.interval
c.concave.
d.convex.

QN88.The ___ is the method available for solving an L.P.P.
a.graphical method.
b.least cost method.
c.MODI method
d.hungarian method.

QN89. The graphical method is applicable to solve an L.P.P when there is___
a.Only one variable
b.Two variables
c.More than two variables
d.None of the above.

QN90.The objective of network analysis is to___
a.Minimize total project duration.
b.Minimize total project cost.
c.Minimize product delays,interruption and conflicts
d.All the above.

QN91. Network models have advantage in terms of project___
a.Planning
b.Scheduling
c.Controlling
d.All the above.

QN92.The slack for an activity is equal to___
a.LF-LS.
b.EF-ES.
c.LS-ES.
d.None of the above.

QN93.The another term commonly used for activity slack time is___
a.Total float
b.Independent float
c.Free float
d.All the above.

QN94.Generally the PERT technique deals with the project of
a.Repetatative nature
b.Non-repetative nature
c.Determinstic nature
d.None of the above.

QN95.In PERT the span of time between the optimistic and pessismistic time estimates of an activity is___ QN96.If an activity has zero slack,it implies that___
a.It lies on the critical path.
b.It is a dummy acitivity.
c.The project is progressing well.
d.None of the above.

QN97.A dummy activity is used in the network diagram when___
a.Two parallel activities have the same tail and head events.
b.The chain of acitivities may have a common event yet he independent by themselves. c.Both a & b
d.None of the above.

QN98.While drawing the network diagram for each activity project we should look___
a.What acitivities preceede this acitivity .
b. What acitivities follow this acitivity.
c.What activity can concurrently take place with this activity.
d.All the above.

QN99.In the PERT network each activity time assumes
a Beta distribution because
a.It is a unimodal distribution that provides information regarding the uncertainity of time estimates of activities.
b.It has got finite non-negative error.
c.It need not be symmetrical about model value
d.All the above

QN100.The critical path satisfy the condition that QN101.Float or slack analysis is useful for___
a.Projects behind the schedule only
b.Projects ahead of the schedule only
c.Both a & b
d.None of the above.

QN102.The acitivity that can be delayed without affecting the execution of the immediate succeeding activity is determined by____
a.Total float
b.Independent float
c.Free float
d.None of the above.

QN103.In time cost trade off function analysis___
a.Cost decreases linearily as time increases
b.Cost at normal time is zero
c.Cost increses linearily as time increases
d.None of the above.

QN104.Activity -on-arrow (AOA) diagram is prefeered over Activity -on-node (AON) diagram because___
a.AOA diagrams are simple to construct.
b.AOA diagrams give a better sense of the flow of time throughout a project.
c.AOA diagrams do not involve dummy activites
d.ALL the above.

QN105.Resource leveling is the process of ___the utilization of resources in a project.
a. Emerging
b.Smoothing out.
c. Minimize
d. Maximize

QN106.Crashing is the process of reducing the total time that it takes to complete a project by expanding___
b. No.of.days
c. Both a & b
d. None of the above

QN107. ____is the time consuming job (or) task that is a key subpart of the total project
a.Activity
b.Event
c.Node
d.All the above.

QN108.Earliest finish time that an activity can be finished without___of precedence requirements.
a. Planning
bViolation
c. Both a&b
d. None of the above

QN109. ____is the point in time that marks the beginning or ending of an activity.
a.Event
b.Node
c.Activity
d.Dummy activity

QN110. If an activity has a zero slack, it implies that
a. It lies on the critical path
b. It is a dummy activity
c. Both a & b
d. None of the above

QN111.Network is the graphical display of a project that contains both___and___
a.Activities and events
b.Activities and dummy activities
c. Both (a) &(b)
d.Neither (a) nor (b).

QN112.A small circle or rectangle that is known as___serves as a junction point in the project network
a.Event
b.Node
c.Slack
d.Variables

QN113.Latest finish time that an activity can be finished without___the entire project.
a.Delaying.
b. Planning
c. Both a&b
d. None of the above

QN114.The amount of time that is expected to complete the activity is called___
a.Latest time
b.Earliest time
c.Most likely time.
d.Both a & b .

QN115.PERT is a tool for___and control time.
a. Delaying. b.Planning.
c. Both a&b
d. None of the above

QN116.The CPM is used for completing the project that involves___of repetitive nature.
a.Activities
b.Node
c.Event.
d.Dummy activity

QN117.Project___phase allocates resources to work packages.
a. Planning
b.Scheduling
c.Controlling
d.Both b&c.

QN118. ___phase identify manpower that will be responsible for each task.
a. Planning
b.Scheduling
c.Controlling
d.All the above.

QN119.A ____is an endeavour to create a unique product service.
a.Project
b.Network
c.Activity
d.Node.

QN120. Transportation problem is a special class of___
a.LPP
b.assignment problem
c.none of the two
d.both 1 and 2.

QN121.The Objective function of Transportation problem is to___
a.maximize the total cost.
b.minimize or maximize the total cost.
c.minimize the total cost.
d.total cost should be zero.

QN122. In Transportation problem the preferred method of obtaining either optimal or very close to the optimal solution is___
a..north west corner rule
b.least cost method
c.vogel’s approximation method
d.simplex method.

QN123.In Transportation problem the improved solution of the initial basic feasible solution is called___
a.basic solution
b.optimal solution
c.degenerate solution
d.non-degenerate solution.

QN124.In Transportation problem optimal solution can be verified by using___
a.north west corner rule
b.least cost method
c.MODI method
d.matrix method.

QN125.The cells in the Transportation problem can be classified as___
a.assigned cells and empty cells
b.allocated cells and un allocated cells
c.occupied and unoccupied cells
d.assigned and unoccupied cells

QN126.In North West corner rule the allocation is done in___
a.upper right corner
b.middle cell in the transportation table
c.cell with the lowest cost
d.Upper left corner.

QN127.In Least cost method the allocation is done by selecting____
a.upper left corner.
b.upper right corner.
c.middle cell in the transportation table.
d.cell with the lowest cost.

QN128. Transportation problem is said to be balanced if a.total supply is not equal to total demand. b.total supply is greater than total demand. c.total supply is lesser than total demand. d.total supply is equal to total demand.

QN129.Transportation problem is said to be unbalanced if___
a.total supply is not equal to total demand
b.Tot al supply is greater than total demand
c.total supply is lesser than total demand
d. All the above

QN130.The basic feasible solution to a transportation problem is said to be optimal if it___
a.maximizes or minimizes the transportation cost
b.maximizes the transportation cost
c.minimizes the transportation cost
d.has degenerate solution.

QN131.The necessary and sufficient condition for the existence of a feasible solution to a transportation problem is a solution that satisfies all the conditions of___
a.supply
b.demand.
c.supply and demand
d.either supply or demand

QN132.Purpose of MODI method is to get
a.degenerate solution
b.non-degenerate solution
c.optimal.
d.basic feasible solution.

QN133.In transportation problem the solution is said to non-degenerate solution if occupied cells is___.
a. greater than m+n-1.
b. lesser than m+n-1.
c. greater than or equal to m+n-1.
d. lesser than or equal to m+n-1.

QN134.In transportation problem the solution is said to degenerate solution if occupied cells is
a.greater than m+n-1.
b.lesser than m+n-1.
c.greater than or equal to m+n-1.
d.lesser than or equal to m+n-1.

QN135.In transportation problem if total supply > total demand we add___
a.dummy row with cost 0
b.dummy column with cost 0
c.dummy row with cost 1
d.dummy column with cost 1.

QN136.In transportation problem if total supply < total demand we add___
a.dummy row with cost 0
b.dummy column with cost 0
c.dummy row with cost 1
d.dummy column with cost 1

QN137.In North West corner rule if the demand in the column is satisfied one must move to the____
a.left cell in the next column
b.right cell in the next row
c.right cell in the next column
d.left cell in the next row

QN138.In North West corner rule if the supply in the row is satisfied one must move
a.down in the next row
b.up in the next row
c.right cell in the next column
d.left cell in the next row.

QN139.The objective of the transportation problem which is to be maximized is to
a.maximize the total profit
b.minimize the total loss
c.neither maximize nor minimize
d.optimal cost.

QN140.In Maximization case of transportation problem we convert into minimization by subtracting all the elements from the___
a.zero
b.one.
c.highest element
d.lowest element.

QN141.The application of assignment problems is to obtain___
a.only minimum cost
b.only maximum profit
c.minimum cost or maximum profit
d.assign the jobs.

QN142.The assignment problem is said to be unbalanced if___
a.number of rows is greater than number of columns
b.number of rows is lesser than number of columns
c.number of rows is equal to number of columns
d.both 1 and 2.

QN143.The assignment problem is said to be balanced if___
a.number of rows is greater than number of columns
b.number of rows is lesser than number of columns
c.number of rows is equal to number of columns
d.if the entry of row is zero.

QN144.The assignment problem is said to be balanced if it is___
a.square matrix
b.rectangular matrix
c.unit matrix
d.triangular matrix.

QN145.In assignment problem if number of rows is greater than column then___ a.dummy column is added
c.row with cost 1 is added
d.column with cost 1 is added.

QN146.In assignment problem if number of column is greater than row then___
a.dummy column is added
b. dummy row added .
c. row with cost 1 is added.
d. column with cost 1 is added.

QN147.The transportation technique or simplex method cannot be used to solve the assignment problem because of___
a.degeneracy
b.non-degeneracy
c.square matrix
d.any one of the above.

QN148.The objective of Transportation problem is to allocate___
a.number of origins to equal number of destinations at minimum cost
b.number of origins to equal number of destination at maximum cost
c.only to maximize cost
d.only to maximize the profit.

QN149. In transportation problem ‘NWC’ stands for___
a. North West Corner
b. Net Working Capital
c. Naval Weapons Center
d. Nuclear Weapons Convention