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 



DOWNLOAD QUESTION PAPPER CLICK HERE



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                 

                                                                                                                                                

                                                                                                                                          

                                                                                                                                                  

                                                                                                                                                                                

  

Comments

Popular posts from this blog

Guwahati university B.com all sem solved

Guwahati university B.com all sem solved

B.Com 6th Sem Question Papers & Solved Answers – Gauhati University 2025