SKM S J.M.PATEL COLLEGE OF COMMERCE GOREGAON (W)

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1 SEM-II TUTORIAL ASSIGNMENT NO:I Course/Subject: MATHEMATICAL & STATISTICAL TECHNIQUES Unit-II:INTEREST& ANNUITY 1. Calculate the simple & compound interest on the sum of Rs.50000/- deposited for p.a. 2. A sum of Rs.75000/- earned the interest of 15000/- over the period of 4 years what is the rate of simple interest? In how many years the sum will become double at the same rate? 3. A sum of Rs.25000/- deposited for the period of 8% p.a. Calculate the amount of interest earned when compounded, i) HLY ii) QLY. 4. Calculate the effective rate of interest when 10% is compounded a) HLY. b) QLY Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 1

2 SEM-II TUTORIAL ASSIGNMENT NO:II Course/Subject: MATHEMATICAL & STATISTICAL TECHNIQUES Unit-II:INTEREST& ANNUITY(F.V./P.V/ & ANNUITY) 1. Calculate the amount received at the end of 3 years when Rs.50000/- are 6% compounded YLY. (FV of PV) 2. Calculate the present value of the FV Rs.75000/- at the end of 4 8% compounded YLY. (PV of FV) 3. Calculate the Future value of the Annuity value Rs /- at the end of 4 compounded YLY. (FV of A) 4. What amount should be kept in the bank at the end of every year so as to get the maturity of Rs.1Lac after 4years when compounded 12%? (A of FV) 5. What amount should be deposited in the bank so as to receive Rs.15000/- at the end of every year over the period of 4 14% compounded YLY. (PV of A) 6. A mobile handset is purchased for Rs.45000/- by paying cash of Rs.10000/- The balance was repaid in 4 MLY installment 36%p.a. Calculate the EMI & total interest paid. (A of PV ) Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 2

3 SEM-II TUTORIAL ASSIGNMENT NO:III Course/Subject: MATHEMATICAL & STATISTICAL TECHNIQUES Unit-V:PROBABILITY DISTRIBUTIONS 1. A r.v. X follows binomial distribution with n=4 & p= 0.4, calculate a) P(X=2) b) P(X 1) c) P(X>2) 2. It is known that p=30% of the club members are lefty. What is the probability that out of randomly selected n=5 members x=3 are lefty? 3. The mean & variance of a binomial distribution are np=4 &npq=4/3 respectively, calculate P(X=3). Find n & p 4. In the class of 50 students p=40% are good at singing. What is the probability that out of randomly selected n=5 students only x=2 are good in singing? Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 3

4 SEM-II TUTORIAL ASSIGNMENT NO:IV Course/Subject: MATHEMATICAL & STATISTICAL TECHNIQUES Unit-V: PROBABILITY DISTRIBUTIONS (NORMAL DISTRIBUTION) 1. A continuous random variable X follows a normal distribution with mean 50 and S.D. of 10. Find the following probabilities for X, a) P (X 55) b) P(45 X 60) c) P(X 45). 2. The height of 250 soldiers in a military camp confirms a normal distribution with mean height of 155cms.and S.D. of 20cms. Find the proportion of soldiers with height above 170 cms. Also find the height of the shortest soldier in the group of tallest 20% soldiers. 3. The daily wages of 300 workers in a factory are normally distributed with the average wages of Rs.2500 and S.D. of wages equals to Rs.500. * Find the percentage of workers earning wages between Rs.3000 and Rs * Find the approximate no of workers earning wages below Rs3250/- * Also find the wages of the lowest paid worker in the group of highest paid 30% workers. Read the area values from the table. Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 4

5 SEM-II TUTORIAL ASSIGNMENT NO:V Unit-V: TIME SERIES 1. Obtain the trend values by the method of least square method & hence estimate the assets for the year 2012 Data- Annual assets Year: Assets: (in 00 Cr.) 2. Fit a trend equation & hence estimate the profits for the year 2015 Data- Annual assets Year: Profitss: (in 00 Cr.) 3. Data given below read the MLY sales of a company over period of 8 months. Obtain the estimates by 3 values moving average method. MONTH JAN FEB MAR APR MAY JUNE JULY AUG Sales(Lacks) Obtain the trend values by 4 values Moving Average method for the data given below. Year: Sales: (in 000 units) Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 5

6 SEM-II TUTORIAL ASSIGNMENT NO:V Unit-V: INDEX NUMBERS 1. Calculate the Fisher s price index number for the year Commodity Price in 2005 Price In 2007 Quantity in 2005 A B C Quantity In Compute Laspeyre s, Passche s and Fisher s Price index for the year 2005 from the following data. Commodity Price Quantity Price Quantity P Q R S Calculate the cost of living index (CLI) for the year (Use Family budget method) Commodity Price Quantity A B C Obtain the Cost of Living Index number for the year 2008 by Family Budget method. Commodity Price Quantity Price A B C D Calculate the real wages from the data given below. Base year 2005 Year CLI Income in Rs Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 6

7 SEM-II TUTORIAL ASSIGNMENT NO:VI Unit-III: CORRELATION & REGRESSION 1. The data given below are the marks of students in the subjects of Maths& Accounts. Calculate the Pearson s correlation coefficient r. Marks in Maths: Marks in Accounts: Calculate the coefficient of correlation r Data: No of pairs=10, x= 400 y=750 x 2 =18890, y 2 = 58500, xy= Calculate the Spearman s Rank correlation coefficient for the data given below. X: Y: Calculate the Spearman s coefficient of Rank correlation from the following data. X: Y: Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 7

8 SEM-II TUTORIAL ASSIGNMENT NO:VII Unit-III: CORRELATION & REGRESSION 1. Data given below read the MLY sales & Profits of a company over period of 8 months. Obtain the two regression equations & hence estimate the profits of the company when the Sales are of 30,000 units. Sales(000units) Profits(in Lacks) 2. Obtain the two regression equations & hence find X when Y=25. Data: No of pairs=10, x= 250 y=400 x 2 =8050, y 2 = 4100, xy= Obtain the two regression equations & hence estimate X when Y = 48on the basis of the following information: x = 40, y =45, 6x= 10, 6y = 9 and r = The two regression equations for a bi-variate data are given by 6x-5y-45=0 and 4x-3y-35=0. Find, a. means of x and y, b. Identify the regression equation of y on x and hence estimate the value of y when x=20. c. Correlation coefficient r d. SD(X) when SD(Y)=5 Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 8

9 SEM-II TUTORIAL ASSIGNMENT NO:VIII Unit-I: DERIVATIVES 1. Write all the Formulas on derivatives. 2. Find derivative w.r.t. x dy for the functions given below dx i) y= (e x + x)( 3x 2 +5x) ii) y= (2x 3 +4x+1)x(5x+2) iii) y= 2 (2x +5x+6) (3x+2) iv) y= 3 (x +2x+1) (5x+4) v) y= ( 2x 2 +5x+4) 3 (4x vi) y= 3 +7x+3) (5x+1) vii) y= 2 (3x +6x+5) (2x+3) Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 9

10 SEM-II TUTORIAL ASSIGNMENT NO:VIII Unit-I: DERIVATIVES 1. The demand function of a commodity is given by P= X 2 +2X+15, Find the AR and MR when the demand (X) is for 10 units. 2. If the fixed cost of production is 200 with variable cost Rs 20+x find the TC, AC & MC when output is of 50 units. 3. The total cost function of a commodity is given by C= 2x 2 +3x+15, Find the AC and MC when the output is of 10 units. 4. Calculate the price elasticity of demand for the commodity p 4 whose demand function is given by D at price p=4. p 2 5. A manufacturer sells x items at price Rs(330-x), find the output for maximum profit if his cost of production is given by C= x 2 +10x+20. Prepared by Asso.Prof.Dilip M Patil J.M.PATEL COLLEGE GOREGAON(W) Page 10

MTP_Foundation_Syllabus 2012_June2016_Set 1

MTP_Foundation_Syllabus 2012_June2016_Set 1 Paper- 4: FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Academics Department, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 1 Paper- 4: FUNDAMENTALS