GUWAHATI UNIVERSITY B,COM 3RD SEMESTER QUESTION PAPPER OF BUSINESS MATHEMATICS DOWNLOAD 2023
GUWAHATI UNIVERSITY B,COM 3RD SEMESTER QUESTION PAPPER OF BUSINESS MATHEMATICS DOWNLOAD 2023
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2023
COMMERCE
(Regular Core) Paper: COM-RC-2026
(Business Mathematics and Statistics)
Full Marks: 80
Time: Three hours
The QUEigures in the
margin indicate full marks for the questions.
Answer either in English or in Assamese.
Write the answers to
the two Groups in separate books.
GROUP-A
(Business Mathematics)
Marks: 30
1. Answer the
following questions: 1×4=4
(a) Find the value of
x if
(b) Find the mean proportional between 50 and 128.
(c) In case of
compound interest, what is the formula for 'Amount' if interest is compounded
quarterly?
(d) Fill in the blank:
Where x denotes the
volume of output. D/dx (TC) =
2. Answer the
following questions: 2X3=6
(a) If
Find : 6A - 4B
(b) Evaluate
(c) Find d/dx (x * log(x))
OR
Evaluate
3. Answer any two of the following questions: 5×2=10
(a) Show that
(b) A certain sum of money invested at C.I. amounts to
₹2,420 at the end of 2 years and to ₹2,662 at the end of 3 years. Find the rate
of C.I. and the sum invested.
(c) A and B together
can do a piece of work in 15 days. They work together for 8 days, when A leaves
and B finishes the work in 15 days more. In how many days can A alone finish
the work?
(d) Find:
(i) the average profit function, and
(ii) the marginal profit function for the following total
profit function (𝝅)
Where 𝝅
= 2Q2 2 - 15Q + 20
Evaluate them at Q = 3 and Q = 5.
4. Answer any one question: 10X1 = 10
(a) Solve the following system
of equations by Cramer's rule
x + y + z = 3
2x - 3u + 5z = 4
x + 2y - 4z = - 1
(b) (i) The producer, the wholesaler and
the retailer make 10%, 15% and 25% profit respectively. What is the production
cost of a pen which a customer buys from the retailer for Rs.12.65? 6
(ii) If
Then find the matrix C so that A + B + C = 0 , where 0
represents null matrix. 4
(c) (i) Prove that 5
(ii) If
5
Then verify that
A2 + 3A + 4I = 0
Where 0 is the 2 x 2 null matrix and I is the 2 x 2 unit
matrix.
GROUP-B
(Business Statistics)
Marks: 50
Answer Question Numbers 1, 2 & 3 and any three from the rest.
1... Answer the following questions: 1×4=4
(a) Cost of living
index numbers are also known as ------------- (Fill in the blank)
(b) Select the correct answer:
(i) If the correlation coefficient between x
and y is negative then the regression coefficient of x on y is
(a) positive
(b) Negative
(c) Not certain
(ii) Standard
deviation is dependent on the change of
(a) Origin
(b) Scale
(c) Origin and scale
(d) None of the above
(c) At what point do the two lines of regression intersect?
2. Answer the following questions: 2×3=6
(a) Given, byx = -0.9
and bxy = -0.4. Find r.
(b) If Mean = 26,
Median =22. Find Mode.
(c) A.M and G.M of
two observations are 10 and 8. Find there Н.М.
3. Answer any two of the following questions: 5X2
= 10
(a) Determine mode for the following distribution:
Marks:
0-9 10-19 20-29
30-39 40-49
No. of students: 27
34 28 48 13
(b) Given
Find r(X, Y)
(c) What is a regression line? When are the two regression
lines identical? Mention any two properties of regression coefficient. 2 + 1 + 2 = 5
(d) Define arithmetic mean. Discuss the relative merits and
demerits of arithmetic mean.
4. Answer any three questions:
10
X 3 = 30
(a) (i) Calculate mean, standard deviation and variance for
the following distribution: 3 + 3 + 1 =
7
Marks: 10-20 20-30
30-40 40-50 50-60
60-70 70-80
80-90 90-100
No. of students: 5 6 15 10
5 4 2 2 1
(ii) Mention the characteristics of a good average. 3
(b) (i) Fit a straight line trend to the time series data
given below and obtain the trend value for the year 2018:
5+1=6
Year: 2015 2016
2017 2018 2019
Sales (2000): 35 56 79 80 40
(ii) Write a
brief note on the usefulness of index number. 4
(c) (i) For the data given below find the two regression
lines: 7
Mean X Y
36 85
S.D. 11 8
Correlation coefficient:
0.66
Find the value of X
when Y=75.
(ii) Given two regression equations as follows: 3
4X-5Y+31 = 0 and
20X-9Y-107 = 0
Find X and Y.
(d) (i) From the
following data of marks obtained by 10 students in Statistics and Mathematics,
compute rank correlation coefficient. 6
Marks in
Statistics: 80
38 95 30
74 84 91
60 66
40
Marks in Mathematics:
85 50 92
58 70 65
88 56 52
46
(ii) Prove that correlation coefficient is
independent of change of origin and scale. 4
(e) Define time reversal test and factor
reversal test. Show that Fisher's index number satisfies both time reversal
test and factor reversal test.
(f) (i) Explain with examples:
(a) Positive and negative correlation
(b) Linear and
non-linear correlation
(ii) Compute cost of living index number from the data given
below:
6
Group Group Weights Group Indices
Food 40 525 Clothing 16 325 Fuel and lighting 20 180
House rent 15 240
Misc. 9 200
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