303d business mathematics

8/4/2019 303D Business Mathematics

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Dr. G.R. Damodaran college of Science Coimbatore 641 014

GRD School of Commerce and International Business

Degree: B Com [CA]

Subject: Business Mathematics-303DSemester: III

1.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.

Answer: A

2.An LPP has ________.

a.one optimal solution.

b.two optimal solutions.

c.Three optimal solutions.d.none of these.

Answer: D3.An LPP deals with problems involving only ______.a.single objective.

b.multiple objective.

c.two objective.

d.none of these.

Answer: A

4.Which of the following is not associated with any LPP?

a.Feasible Solution.

b.Optimum Solution.c.Basic solution.

d.Quadratic equation.

Answer: D

5.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.Answer: A

6.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.

Answer: B7.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.


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Answer: C8.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.

Answer: A

9.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.

Answer: C

10.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.Answer: A

11.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.

Answer: D12.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.


d.lesser than or equal to type.Answer: C

13.In an LPP the solution for the problems involving more than 2 variables can be solvedusing _____________.

a.graphical method.

b.simplex method.

c.hungarian method.

d.all the above

Answer: B

14.In the standard form of LPP if the objective functions is of minimization then all the

constraints ____________.a.equations .

b.inequalities.


d.lesser than or equal to type.

Answer: A


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15.In the standard form of LPP if the objective function is of minimization then the righthand side of the constraints should be ___________.a.positive.

b.negative.c.non-negative.

d.zero.

Answer: C

16.The non-negative variable which is added to LHS of the constraint to convert the

inequality < into equation is called ______________.a.random variable.

b.decision variable.

c.surplus variable.

d.slack variable.

Answer: D

17.The non-negative variable which is added to LHS of the constraint to convert theinequality > into equation is called _________.

a.random variable.b.decision variable.c.surplus variable.

d.slack variable.

Answer: C

18.The test of optimality in simplex method is _________.

a.Zj-Cj >0.

b.Zj-Cj


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a.no upper boundary.b.no lower boundary.c.no boundary in the first quadrant.

d.none of the above.Answer: A

23.Transportation problem is a special class of ____________.

a.LPP.

b.assignment problem.

c.none of the two.d.both 1 and 2.

Answer: A

24.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.

Answer: C25. In Transportation problem the preferred method of obtaining either optimal or veryclose to the optimal solution is _____________.

a.north west corner rule.

b.least cost method.

c.vogels approximation method.

d.simplex method.

Answer: C

26.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.

Answer: B

27.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.

Answer: C

28.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.Answer: C

29.In North West corner rule the allocation is done in ______________.

a.upper left corner.

b.upper right corner.

c.middle cell in the transportation table.


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d.cell with the lowest cost.Answer: A30.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.

Answer: D

31. 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.

Answer: D

32.In Transportation problem is said to be unbalanced 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.

Answer: A

33.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.Answer: C

34.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.

Answer: C35.Purpose of MODI method is to get __________.

a.degenerate solution.

b.non-degenerate solution.

c.optimal.

d.basic feasible solution.

Answer: C

36.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.

Answer: C


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37.In transportation problem the solution is said to degenerate solution if occupied cellsisa.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.

Answer: B

38.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.

Answer: B

39.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.Answer: A

40.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.

Answer: C41.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.Answer: A

42.The objective of the transportation problem which is to be maximized is toa.maximize the total profit.

b.minimize the total loss .

c.neither maximize nor minimize.

d.optimal cost.

Answer: A

43.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.

Answer: C

44.The application of assignment problems is to obtain _________.


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a.only minimum cost.b.only maximum profit.c.minimum cost or maximum profit.

d.assign the jobs.Answer: D

45.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.

Answer: B

46.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.

Answer: C47.The assignment problem is said to be balanced if it is _________.a.square matrix.

b.rectangular matrix.

c.unit matrix.

d.triangular matrix.

Answer: A

48.In assignment problem if number of rows is greater than column then _________.

a.dummy column is added .

b.dummy row added .c.row with cost 1 is added.

d.column with cost 1 is added.

Answer: A

49.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.Answer: B

50.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.

Answer: A51.The objective of assignment problem is to assign _________.

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.


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Answer: A52.A Competitive situation is called_________.a.game.

b.saddle point.c.strategy.

d.outcome.

Answer: A

53.Strategy of a player is the decision _________.

a.course of action.b.rule.

c.pay off.

d.action.

Answer: B

54.Strategy are classified into_________.

a.pure and mixed.b.pure and complex.

c.mixed.d.pure .Answer: A

55.Saddle point is the position in_________.

a.pay off matrix.

b.game .

c.player A.

d.player B.

Answer: A

56.Game is called Two person zero sum game if_________.a.gain of one player equal to loss of the other.

b.gain of one player is not equal to loss of the other.

c.gain of player A is always greater than the loss of Player B.

d.gain of player B is always greater than the loss of Player A.

Answer: A

57.Strategy is called pure if _________.a.player may be able to choose only one strategy.

b.the player knows in advance of the play that is to be adopted.c.the player do not knows in advance of the play that is to be adopted.

d.the player may not be able to choose any strategy.

Answer: B

58.Saddle point is the point of intersection of _________.

a.pure strategy.

b.mixed strategy.

c.complex strategy.

d.impure strategy.Answer: A

59.The gains resulting from a game is called_________.

a.pay off.

b.strategy.

c.value of the game.


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d.fair game.Answer: A60.Minimax of the game is_________.

a.minimum of row.b.maximum of row.

c.minimum of column maxima.

d.maximum of row minima.

Answer: D

61.Maximin of the game is_________.a.minimum of row.

b.maximum of row.

c.minimum of column maxima.

d.maximum of row minima.

Answer: C

62.Game is stable when there is _________.a.no saddle point.

b.saddle point.c.strategy.d.outcome.

Answer: B

63.Game is said to be fair if _________.

a.minimax= maximin =0.

b.minimax= maximin =value of the game.

c.minimum row = maximum of column .

d.minimum column = maximum of row.

Answer: A64.Game is said to be strictly determinable if _________.

a.minimax = maximin =0.

b.minimax= maximin =value of the game.

c.minimum row = maximum of column.

d.minimum column = maximum of row.

Answer: B65.__________ method is used to simplify the game with mixed strategy

a.Row minima.b.Column maxima.

c.Dominance.

d.any one of the above methods.

Answer: C

66.Game can be solved graphically only if the pay off matrix is in the form of

_________.

a.mx2.

b.2xn.c.mx2 or 2xn.

d.mxn.

Answer : C

67.Games without saddle point require players to play _________.

a. pure strategy.


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b. mixed strategy.c. optimal strategy.d. any one of the above strategy.

Answer: B68.Pure strategy game is one in which each player has _________.

a.only one optimal strategy.

b.mixed strategy.

c.many optimal strategy.

d.no optimal strategy.Answer: A

69.Dominance property helps in reducing the pay off matrix involving _________

a.mixed stratergy.

b.Pure stratergy

c.both pure and mixed strategy.

d.none of the above.Answer: C

70.Value of the game is denoted by _________.a...b..

c..

d. .

Answer: C

71.The Value of the game for the given pay off 6 -3 is _________.-3 0

a.-3/4.

b.3/4.c.1/4.

d.2/4.

Answer: A

72.The Value of the game for the given pay off 2 5 is_________.

4 1

a.3.b.-3.

c.5.

d.-5.

Answer: A

73.The optimal strategy for the given pay off 2 5 is_________.4 1

a. ( 1/4 1/2 ) (1/2 1/2).b.( 1/4 1/2 ) (2/3 1/2).

c.( 1/2 1/2 ) ( 1/4 1/2 ).d.( 1/2 1/2 ) (2/3 1/3) .

Answer: D

74.The optimal strategy for the given pay off 6 -3 is_________.

-3 0

a. ( 1/4 3/2 ) (1/4 1/2).

b.( 1/4 3/2 ) (1/4 3/4).


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c.( 1/2 1/2 ) ( 1/4 1/2 ).d.( 1/2 1/2 ) (2/3 2/3).Answer: B

75.For the given pay off matrix 1 3 10 -4 -3 _________.

1 5 -1

a.saddle point do not exists.

b.saddle point exists.

c.player plays mixed strategy.d.player plays pure strategy.

Answer: B

76.The given game -5 2 is _________.

-7 -4

a.strictly determinable game.

b.determinable game.c.fair game.

d.unfair game.Answer: A77.The given game 0 2 is _________.

-1 4

a.strictly determinable game .

b.determinable game.

c.fair game.

d.unfair game.

Answer: C

78.The optimum minimax strategies for each player for the given pay off matrix of thegame -5 2 0 7 is _________.

5 6 4 8

4 0 2 -3

a.A2, B2.b.A1, B3.c.A2, B3.d.A2, B2.Answer: C79.The optimum strategies for the game -5 2 is _________.

-7 -4

a.A2, B2.b.A1, B1.c.A2, B1.d.A1, B2.Answer: B


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80.Two players A and B match coins. If the coins match then A wins two units of value.If the coins do not match then B wins two units of value. For the given situation the payoff matrix is _________.

a.2 -2

-2 2 .

b.2 -2

0 2 .

c.2 -2

0 0 .

d.2 0

0 -2 .Answer: A

81.The value of the determinant is _________.

a.100.b.364.

c.14.

d.340.

Answer: B

82.The value of the determinant 5 -2 is _________.6 1

a.17.b.-7.

c.7.d.0.

Answer: A

83.The value of the determinant 1 2 5

0 0 0 is _________.

3 - 4 9

a.0.

b.25.c.-25.d.6.

Answer: A

84.The value of the determinant 3 6 7 is_________.

4 -1 8

6 3 7a.6.

b.25.

c.-25.


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d.0.Answer: D85.The rank of the given matrix 1 2 5 is_________.

0 0 03 - 4 9

a.1.

b.2.

c.3.

d.0.Answer: B

86.Find the value of an if [3 4 7] 1 = [18]?

2

a

a.1.

b.2.c.-1.

d.-2.Answer: A

87.The order of 3 1 3

6 5 6 is _________.

9 6 9

a.3x3.

b.2x3.

c.3x2.d.4x4.

Answer: A

88.If A = 3 2 3

0 4 0

3 8 3 then (A) is_________.

a.0.

b.1.

c.2.

d.3.

Answer: C89.The given matrix is 1 0 0_________.

0 1 0

a.a scalar matrix.

b.a unit matrix.

c.a square matrix.

d.a rectangular matrix.

Answer: B

90.If A = 2 3 and B = 5 -2 then (A+B)` is _________.-1 4 -1 6


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a.7 -21 10 .

b.7 -21 10 .

c.10 -2

7 1 .

d.1 7

-2 10 .

Answer: A

91.If A = 2 3 and B = 5 -2 then (A-B) is _________.

-1 4 -1 6

a.7 1-9 0 .

b.-3 5

7 8 .

c.-3 7

5 8 .

d. 7 -91 0 .

Answer: D

92.If A = 1 2 2A = _________.

3 4

a.2 -43 4 .

b.7 -2

3 4 .

c.2 4

6 8 .

d. 1 7

-2 10 .Answer: C

93.If A is a singular matrix |A| is _________.

a.1.

b.0.

c.any positive value.


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d.any negative value.Answer: B94.If A = 2 1 and B = 3 2

4 3 1 -1 thenAB is _________.

a.7 3

15 5 .

b.7 3

-15 5 .c.7 - 3

- 5 5 .

d.- 7 3

-15 5 .

Answer: A

95.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.

Answer: D

96.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.

Answer: C97.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

.

Answer: A98.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.

Answer: D

99.The present value of a bill of exchange is found as _________.

a.A=P(1+ni).

b.P=100A/100+nr.

c.A=Pnr/100.d.A=P(1+i)n.

Answer: B

100.The compound interest for Rs 10,000 for 2 years at 10% p.a is as _________.

a.Rs. 2000.

b.Rs. 2100.


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c.Rs. 2200.d.Rs. 12,000.Answer: B

101.The present value under annuity due is _________.a.A/i [1-(1+i)-n].

b.A+A/i [1-(1+i)-n].

c.A/i [1+i)-n

-1].

d.A/i (1+i)[ 1+i)-n

-1].

Answer: A102.The Amount due under immediate annuity is _________.

a.A/i [1-(1+i)-n].

b.A+A/i [1-(1+i)-n

].

c.A/i [1+i)-n

-1].

d.A/i (1+i)[ 1+i)-n

-1].

Answer: D103.Formula for Bankers gain is _________.

a.Anr/100.b.An2r2/100(100+nr).c.100A/100+nr.

d.Anr/100+nr.

Answer: B

104.The series 4, 2, 1 .takes the form of_________.

a.A.P.

b.H.P.

c.G.P.

d.A.MAnswer: C

105.The series 90, 80, 70_________.

a.A.P.

b.H.P.

c.G.P.

d.A.M.Answer: A

106.The 14th term of the series 1+6+11+ . is , _________.a.71.

b.17.

c.27.

d.37.

Answer: A

107.The 7h

term of the series 64-32+16- is _________.

a.1.

b.0.c.-1.

d.2.

Answer: C

108.Which term of the series is 2+5+8+ is 239 ?

a.80.


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b.79.c.78.d.75.

Answer: A109.1+2+3++200 =_________.

a.10000.

b.20000.

c.20100.

d.40200.Answer: C

110.The first term of an A.P is denoted by_________.

a.A.

b.a.

c.d.

d.D.Answer: B

111.In Arithmetic progression the common difference is denoted by_________.a.A.b.a.

c.d.

d.D.

Answer: C

112.In geometric progression the ratio is denoted by_________.

a.r.

b.R.

c.a.d.a.

Answer: A

113.The sum of three numbers in A.P is 24. Find the first number a=_________.

a.8.

b.7.

c.6.d.5.

Answer: A114.The sum of n natural numbers is _________.

a.n(n+1)/2.

b.n+1/2.

c.n(n+1)/2.

d.n-1/2.

Answer: A

115.The sum of first 100 natural numbers is_________.a.5050.

b.1050.

c.5010.

d.1010.

Answer: A


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116.a+(a+d)+(a+2d)+.+(a+(n-1)d)= _________.a.n/2[a+(n-1)d].b.n/2[a+(n+1)d].

c.n/2[2a+(n-1)d].d.n/2[a+2(n-1)d].

Answer: C

117.The first and the seventh terms of a G.P are 2 and 1/8 , then common ratio r

is_________.

a.2.b.1/2.

c.3.

d.1/3.

Answer: B

118.In an arithmetic series the seventh and the ninth terms are 16 and 20 respectively.

Find the common difference d is_________.a.6.

b.5.c.3.d.2.

Answer: D

119.Find the number of terms in the G.P 0.03+0.06+0.12++1.92?

a.6.

b.5.

c.4.

d.7.

Answer: D120.If sum of the 3 numbers in AP is15 then the first term is _______.

a.5.

b.15.

c.-5.

d.-15.

Answer: A

121.The sum of the series 0.7+0.07+.+ is_________.a.9/7.

b.4/7.

c.7/9.

d.7/4.

Answer: C

122.The sum of 3 numbers in G.P is 35 then the first term is _________.

a.3.

b.10.c.-10.

d.-1/3.

Answer: B

123.The next term of the series 50, 40, 30, is _________.

a.20.


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b.30.c.-30.d.-20.

Answer: A124.When r


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a.square matrices.b.null matrices.c.unit matrices.

d.row matrices.Answer: A

If A and B are matrices of same order then _________.

a.A+B=B+A.

b.A+BB+A.

c.A+BB+A.

Answer: A

129.If A,B and C are matrices of the same order then _________.

a.(A+B)+C=A+(B+C).

b.(A+B)+C A+(B+C.

c.(A+B)+C> A+(B+C.d.(A+B)+C < A+(B+C ).

Answer: A130.If A, B are two matrices and K is a scalar then _________.a.K(A+B) KA+KB.b.K(A+B)=KA+KB.

c.K(A+B)KA+KB.

Answer: B

131.If A,B and C are matrices the associative property is_________.

a.(AB)CA(BC).c. (AB)CA(BC).

d. (AB)C=A(BC).

Answer: D

132.Zero matrix is otherwise known as_________.

a.null matrix.

b.square matrix.c.unit matrix.

d.triangular matrix.Answer: A

134.Simple interest will be income for_________.

a.lender.

b.borrower.

c.both .

d.neither lender nor borrower.

Answer: A

135.The simple interest on Rs 5,000 at 10% for 3 years is _________.a.500.

b.1000.

c.1500.

d.2000.

Answer: C


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136.The formula for the face value A is given by_________.a.(B.DxT.D)/(B.D-T.D).b.100T.D/nr.

c.100r/100-nr.d.Pnr/100.

Answer: B

137.In what time will a sum of Rs 1234 amount to Rs5678 at 8% compound interest

payable quarterly?

a.18.72.b.19.27.

c.19.72.

d.19.

Answer: B

138.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 .Answer: A

139.The compound interest for Rs 10000 for 2 years at 10 % is _________.

a.2000.

b.2200.

c.2100.

d.2500.

Answer: C

140.The element at 2 nd Row and 2 nd Column is denoted by_________.a.a 12 .

b.a 32 .

c.a 22 .

d.a 11.Answer: C

141.Order of the matrix A = [aij]3 x 3 is_________.a.2 x 3.

b.3 x 3.c.1 x 3.

d.3 x 1.

Answer: B

142.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.

Answer: A

143.If all the elements of a matrix are zeros, then the matrix is a_________.

a.unit matrix .

b.square matrix.


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c.zero matrix.d.none of these.Answer: C

144.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.

Answer: A145.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.Answer: B

146.If there is only one column in a matrix, it is called_________.a.Row matrix .b.column matrix.

c.square matrix.

d.rectangular.

Answer: B

147.The first term of G.P is 4 while its sum to infinity is 5 then the value of r

is_________.

a.0.2.

b.0.02.c.0.4.

d.0.6.

Answer: A

148.The first term of arithmetic series is 5 , number of terms is 15 and their sum is 390

Then the common difference is _________.

a.52.b.42.

c.41.d.40.

Answer : A

149.The first and the last terms of an A.P are -4 and 146 and the sum of the A.P is 7171

then the number of terms is_________.

a.101.

b.100.

c.105.

d.108.Answer: D

150.Sum of the three numbers in arithmetic series is 12, then the first number

is_________.

a.23.

b.20.


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c.21.d.12.Answer: D

151.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.

Answer: C152.When the number of rows is equal to the number of columns then the matrix is said

to be _________.

a.unit matrix.

b.square matrix.

c.null matrix.

d.row matrix.Answer: B

153.The Value of determinant of 3 6 74 -1 8 is _________.6 3 7

a.0.

b.4.

c.2.

d.5.

Answer: A

154. The rank of 3 1 3

6 5 6 is _________.9 6 9

a.1.

b.2.

c.3.

d.0.

Answer: B155.If A=2 3and B =5 -2

-1 4 1 -3 then A+B = _______.

a. 7 1

2 7 .

b.7 1

0 1 .

c.-3 5

-2 7 .

d.-3 10 1 .

Answer: B

156.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.


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b.a column matrix.c.a rectangular matrix.d.a square matrix.

Answer: C157.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.Answer: A

158.A square matrix A is an orthogonal matrix x, if ________.

a.AA`=I.

b.AA-1

=I.

c.A=A-1

.

d.A=A`.Answer: B

159. 3 8 9 -2 is a row matrix of order________.a.4x1.b.1x4.

c.1x1.

d.4x4.

Answer: B

160. If A= 1 2

3 4 then 3A=________.

a. 3 69 12 .

b. 2 2

6 4 .

c. 2 46 8 .

d. 7 10

15 22 .

Answer: A

161.The 10th term of 6, 4, 2 . is ________.

a.24.

b.26.

c.-12.

d.-14.Answer: C

162.The 9th

term of the series 5, 10, 20 is________.

a.45.

b.80.

c.1280.


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d.2560.Answer: C163.The nth term of an AP is given by________.

a.a+(n-1)d.b.a+1.

c.arn.

d.arn-1

.

Answer: A

164.Which term of the series 2+5+8+..is 239?a.81.

b.80.

c.79.

d.78.

Answer: B

165.The sum of the fourth and twelfth term of an A.P is 20. What is the sum of the first15 terms of the AP?

a.300.b.150.c.120.

d.170.

Answer: B

166.The simple interest on R 5,000 at 10% for 3 years is ________.

a.Rs 500.

b.Rs1,000.

c.Rs1,500.

d.Rs6,500.Answer: C

167.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.

Answer: D

168.The present value of perpetuity of Rs 5000 at 20%p.a is________.a.Rs 6000.

b.Rs. 25000.

c.Rs. 100000.

d.Rs .150000.

Answer: C

169.Bankers discount is given by the formula________.

a.Anr/100.

b.Pnr/100.c.Anr.

d.Pnr.

Answer: A

170.Face value of a bill of exchange is given by the formula ________.

a.100A/100+nr.


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b.(B.DxT.D)/B.D-T.D).c.(B.DxT.D)/B.D+T.D).d.(B.D+T.D)/B.D-T.D).

Answer: B171.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 1) and 2).d.present annuity.

Answer: A

172.y=ax2+bx+c is a________.

a.linear equation.

b.quadratic equation.

c.simultaneous equation.d.transcendental equation.

Answer: B173.In a linear programming minimization model the objective function is to be________.

a.minimized.

b.maximized.

c.minimized or maximized.

d.standardized.

Answer: A

174.Which of the following is not associated with any L.P.P?

a.feasible solution.b.optimum solution.

c.basic solution.

d.quadratic equation

Answer: D

175.Linear programming is________.

a.a constraint optimization model.b.a constraint decision making model.

c.a mathematical programming model.d.all the above.

Answer: D

176.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.

Answer: A177.Graphical method can be used only when the decision variables is________.

a.more than 3.

b.more than1.

c.two.

d.one.


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Answer: C178.In an LPP the Objective function is to be ________.a.minimized.

b.maximized.c.minimized or maximized.

d.maximin.

Answer: C

179.The non-negative variables which are added to the left hand side of the constraints in

< form to make them into = form are________.a.decision variables.

b.slack variables.

c.surplus variables.

d.random variable.

Answer: B

180.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.

Answer: A

181.The __________ is the method available for solving an L.P.P.

a.graphical method.

b.least cost method.

c.MODI method.

d.hungarian method.Answer: A

182.The initial solution of a transportation problem can b obtained by applying any

known method. However, the only condition is that ________.

a.the solution be optimal.

b.the rim conditions are satisfied.

c.the solution not be degenerate.d.nondegenerate.

Answer: B183.One disadvantage of using north west corner rule to find initial solution to the

transportation problem is that ________.

a.it is difficult to use.

b.it does not take into account cost of transportation.

c.it leads to a degenerate initial solution.

d.transportation cost is maximum.

Answer: B

184.The solution of a transportation problem with m rows and n-columns is feasible ifnumber of positive allocations are

a.m+n.

b.mxn.

c.m+n-1.

d.m+n+1.


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Answer: C185.When total supply is equal to total demand in a transportation problem, the problemis said to be

a.balanced.b.unbalanced.

c.degenerate.

d.non-degenerate.

Answer: A

186.Which of the following methods is used to verify the optimality of the currentsolution of the transportation problem?

a.least cost method.

b.vogels method.

c.north west corner rule.

d.MODI method.

Answer: D187.The method used for solving an assignment problem is called________.

a.reduced matrix method.b.MODI method.c.hungarian method.

d.graphical method.

Answer: C

188.The purpose of dummy row or column in an assignment problem is to________.

a.obtain balance between total activities and total resources.

b.prevent a solution from becoming degenerate.

c.provide a means of representing a dummy problem.

d.any one of the above.Answer: A

189.The assignment problem is said to be a balanced one if________.

a.number of rows is equal to columns.

b.number of rows is greater than columns.

c.number of columns is greater to rows.

d.any one of the above.Answer: A

190.An optimal assignment requires that the maximum number of lines that can be drawnthrough squares with zero opportunity cost be equal to number of ________.

a.rows or columns.

b.rows and columns.

c.rows+columns-1.

d.rows.

Answer: C

191.Game theory models are classified by the ________.

a.number of players.b.sum of all payoffs.

c.number of strategies.

d.all the above.

Answer: D

192.In a mixed strategy game________.


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a.no saddle point exists.b.saddle point exists.c.each player selects same strategy.

d.each player selects different strategy.Answer: A

193.Game theory is the study of ________.

a.selecting optimal strategies.

b.resolving conflict between players.

c.both 1and 2.d.either 1 or 2.

Answer: A

194.The size of the payoff matrix of a game can be reduced by using the principle

of________.

a.game inversion.

b.rotation reduction.c.dominance.

d.convex combination.Answer: C195.A saddle point exists________.

a.maximin=minimax.

b.minimin=maximin.

c.maximin=maximax.

d.minimum=maximum.

Answer: A

196.When some of the gains of one player is equal to the sum of losses to another player

in a game, this situation is known as________.a.biased game.

b.zero-sum game.

c.fair game.

d.determinable game.

Answer: B

197.Games which involve more than 2 players________.a.conflicting games.

b.negotiable games.c.zero-sum game.

d.n person games.

Answer: D

198.When maximin and minimax values of the game exists then________.

a.solution exists.

b.no solution exists.

c.solution is mixed.

d.saddle point exists.Answer: D

199.The payoff value for which each player in a game always select the same strategy is

called the ________.

a.saddle point.

b.equilibrium point.


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c.both 1 and 2.d.maxim in.Answer: C

200.A mixed strategy game can be solved by________.a.algebraic method.

b.dominance method.

c.graphical method.

d.all the above.

Answer: D

Staff Name: Mrs. M. Mallika and Mrs. S.Nirmala

303d business mathematics

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