IGNOU| BUSINESS MATHEMATICS AND STATISTICS (BCOC - 134| SOLVED PAPER – (DEC - 2023)| B.COM| ENGLISH MEDIUM
BACHELOR OF COMMERCE
(GENERAL) [B. COM. (G)]
Term-End Examination
December - 2023
BCOC-134
BUSINESS MATHEMATICS AND STATISTICS
Time: 3 Hours
Maximum Marks: 100
Note: Question No. 1 is compulsory. Attempt both Part A and Part B. All questions carry equal marks.
1. (a) Explain the following matrix with examples: 10
(i) Identity
Matrix
Ans:- The
identity matrix is a square matrix where all the elements on the main
diagonal (from top-left to bottom-right) are 1, and all other elements are 0.
The size of the identity matrix is determined by its number of rows (or
columns).
Example:-
3x3 identity
matrix:
(ii)
Rectangular Matrix
Ans:- A
rectangular matrix is a matrix that has a different number of rows and
columns. In other words, it is not a square matrix.
Example:-
A 3x2 rectangular
matrix:
(iii)
Orthogonal Matrix
Ans:- An
orthogonal matrix is a square matrix where the columns (or rows) are
orthogonal to each other, and the matrix has the property that its inverse is
equal to its transpose.
Example:-
An orthogonal 3x3
matrix:
(iv) Scalar
Matrix
Ans:- A
scalar matrix is a square matrix where all off-diagonal elements are 0, and
all diagonal elements are equal to a single scalar value.
Example:-
3x3 scalar matrix
with scalar value of 5:
(v) Transpose
of Matrix
Ans:-
Transpose of a matrix is a new matrix obtained by interchanging the rows and
columns of the original matrix.
Example:-
Transpose of a
2x3 matrix:
(b) Discuss
the limitations of statistics. 10
Ans:- The
main limitations of statistics are:-
(i) Statistics
deals not with individual objects or measurements but with aggregates and
groups. Statistics is concerned with the study of masses or groups, not
individual objects.
(ii) Statistics
deals only with quantitative characteristics that can be expressed numerically.
Qualitative aspects that cannot be quantified, such as intelligence, honesty or
efficiency, are outside the scope of statistical analysis.
(iii)
Statistical results are true only on average and do not represent the whole
story. Many factors influencing a phenomenon may not be fully captured in the
data, so statistical conclusions may not be completely accurate.
(iv) Statistics
can be misused or misinterpreted, especially by people who do not have proper
training and expertise. The data and methods used can be manipulated to give
misleading results.
(v) Statistical
rules and theories are not as precise as scientific rules. They are based on
probabilities and estimates, not absolute certainties.
(vi) Statistics
provides only one way to study a problem and may need to be complemented by
other qualitative approaches, especially for complex social and behavioural
phenomena.
In summary,
while statistics is a powerful tool, it has important limitations that must be
recognised and taken into account when using it to draw conclusions or make
decisions.
Part—A
Note: Answer any two of the following questions.
2. Solve by Cramer’s rule: 20
2x - y = 17
and 3x + 5y = 6
[COMING SOON]
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