Business Mathematics
Previous year question paper with solutions for Business Mathematics Dec-2018
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Question paper 1
(SECTION-A)
1. (a) Show that every square matrix can be expressed as sum of a symmetric and a skew-symmetric matrix.
Answer:
let A be any square matrix
Then A can be expressed as
Adding and subtracting A’ on R.H.S
Hence Q is a skew-symmetric matrix
Hence A=P+Q
Hence every square matric can be expressed as a sum of a symmetric and skew-symmetric matrix
(b) find the inverse of the matrix:
Answer:
2. Solve the system of equations
Cramer’s rule as well as by matric and compare the results. Answer:
Using crammer’s rule
2. Solve the system of equations
Cramer’s rule as well as by matric and compare the results.Answer:
By Matrix method
3. (a) Use definition of limits to show that :
4
Answer:
4
X-a
For a given
small we find a positive numbers depending upon 
such that 
(b) State and prove Euler’s theorem for homogenous function of two variables.
Answer:
. Statement If
Differentiating (1) partially t’x’
Adding (2) and (3) we get
4. Find the maximum and minimum values of
Answer:
(SECTION-B)
5. Solve the following LPP by simplex method :
Subject to :
Answer:
6. A company has 4 machines on which to be 3 jobs Each job can be assigned to one and only one machine the cost of each machine is given as :
Machines
A
B
C
D
I
18
24
28
32
II
8
13
17
19
III
10
15
19
22
What are the job assignment which will minimize the cost
Answer:
I
18
24
28
32
Ii
8
13
17
19
Iii
10
15
19
22
iv
0
0
0
0
Dummy
Reduction(Row)
0
6
10
14
0
5
9
11
0
5
9
12
0
0
0
0
Column Reduction
Total cost =18+13+19=50
7. Given below the unit costa array with supplies and demands:
Sink
I
II
III
IV
Supply
I
8
10
7
6
50
II
12
9
4
7
40
III
9
11
10
8
30
Demands
25
32
40
23
Find the optimal solution to above problem.
Answer:
8. Define game and given its characteristic Define a two game with suitable example
Answer:
Game theory :
Game theory is a branch of mathematics concerned with the analysis of conflict situation It involves determining a strategy for a given situation and the costs or benefits realized by using the strategy.
Characteristics
-
There is a conflict between two or more players resulting in a win for some and a loss for others.
-
There is a way to start the game
-
During each move, single slayers are forced to make choices or the choices are assigned by random devices
Two-person game :
A two-person game is characterized by the strategies of each player and the payoff matrix
The two-person game is also called zero-sum game because one player wins whatever the other player loses
???????-
SECTION-C
Answer in brief of the following :
-
Define 1.1 and onto function.
Answer:
Let x and y be tur non-empty sets
Is said to be one-one if every let if x has a unique image in y.
Onto
If every let f y has an ore image in x then
-
ii. Define Linear function with proper example.
Answer:
Liners f×n:
When A liners quation is represented in slope
Intercept form
Can be regarded as a linear
iii. Solve:
Answer:
iv. Define Adjoint of a matrix
Answer:
Adjoint of A matrix
The transpose of the co factor matrix of matrix is adjoint of a matrix.
v. Verify Euler’s for
Answer:
vi. Define log x using first principles.
Answer:
vii. Write limitation of graph method to solve an LPP.
Answer:
Limitations of graphic method
- This method is limited to lineal programming models containing only two decision variables
- Factors such as uncertainty and time are not taken into consideration
viii. Define pay off matrix.
Answer:
An m n matrix which gives the passible outcome of a two person zero sum game when plays A has m passible moves and [layer B n moves the analysis of the aim of game theory the so called augment pay off matrix is defined as follows
ix. Explain least cost method to solve transportation problem.
Answer:
Least cost entry method : The least cost method is another method used to obtain the initial feasible soln for the transportation problem here the allocation begins with the cell which has the minimum cost the loves cost cells are chosen over the higher to have the least cost of transportation
x. Explain the balanced assignment problem.
Answer:
Balanced assignment problem is assignment problem where number of facilities is qual to the numbers of jobs.