BCom FY BCom Sem 1 2023 2024 Dec 2024 MATHEMATICAL & STATISTICAL TECHNIQUES I Question Paper - Mumbai University | munotes

Questions asked in this paper

• Note: 1) Figures to the right indicate full marks

1. Q1 Attempt any four from the following: 20 marks
   • 1) Find a market value of 12% share if Rs. 6400 were invested to purchase share with face value of Rs. 100 and total dividend of Rs. 480 was
   • 2) Seema invested Rs. 2,08,832 to purchase equity shares of company at market price of Rs, 260 through a brokerage form charging 0.4% brokerage. Find number of shares
   • 3) Praniti invested Rs. 9945 to purchase share of a company with face value of Rs. 10each, at market price of Rs. 65. She received dividend of 20% as well. Afterwards, shesold these share at market price of Rs. 90. She had to pay brokerage of 2% for both purchase and sales of share. Find her net profit
   • 4) Mr Kale invest an amount of Rs. 50,000 on 14th Feb, 2021 when NAV was Rs 125.6, with an entry load of 2.5%. Find the number of units purchased. If current NAV is Rs 140.4, find current value of his investment
   • 5) Nikhil invested Rs 15,000 on 5th,of every month for 6 months in Systematic Investment Plan Scheme of a Mutual Fund. The Navy on these dates where RS 42.36, 47.68, 40.25,
   • 49.87, 52.48 and 39.16 respectively. There was same entry load of 2.25% for all these months. Find average price of unit
2. Q2 Attempt any, four from the following: 20 marks
   • 1) Solve: x ii)
   • 2) How many different numbers of 4-digit can be formed using the digits 1,2,3,4,5 such that
   • (a) Repetition of digits is allowed (b) Repetition of digits is not allowed
   • 3) An organization consists of 2 managers, 5 officers, and 10 clerks. A selection of 4 persons is to be done. Find how many selections will have 1 officer and 3 clerks?
   • 4) A manufacturer produces bulbs and tubes. Each of these must be processed through two machines. Mland M2. A package of bulbs require 1 hour of work on machine M1 and 3 hours of work on M2.A package of tubes require 2 hours on machine M1 and 4 hours machine M2. He earns a profit of Rs. 13.5 per package of bulbs and Rs. 55 per package of tubes. If maximum availability of Machine M1 is 10 hours and that of Machine M2 is 12 hours. Formulate the LPP to maximize the profit
   • 5) Solve the L.P.P. graphically, Maximize Z = 5x + 10y
3. Q3 Attempt any four from the following: 20 marks
   • 1) Calculate mean for the following data
   • 2) Calculate standard deviation and coefficient of variation for the following data
   • 3) Calculate quartile deviation and coefficient of quartile deviation for the following data Daily Wages in Rs | 100 | 300 | | 600 VCD/ SEMI MATHEMATICAL AND STATISTICAL TECH-I 3 MARR
   • 4) Draw cumulative frequency curve and hence locate median graphically
   • 5) Write Merits & Demerits of Range. \
4. Q4 Attempt any four from the following: (20) }
   • 1) Three unbiased coins are tossed. Find the probability of getting (a) exactly 2 heads
   • (b)no tail ‘ 2) Acard is drawn from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is (a) a black card (b) a heart card
   • 3) For the following probability distribution function, find k, P(x > 3), P(x < 4)
   • 4) Find mean and variance for the following:
   • 5) Explain: i) Random Variable ii) Discrete Random Variable iii) Complimentary Event
5. Q5 Attempt any four from the 20 marks
   • 1) Explain briefly decision making under uncertainty
   • 2) Solve the given decision problem using Minimax regret
   • 3) Given the pay-off matrix, solve the decision using EMV criterion Courses of Action
   • 4) Given the pay-off matrix, solve the decision using EOL criterion
   • 5) Draw a decision tree for the given pay-off table Courses of Action SEM I MATHEMATICAL AND STATISTICAL TECH-I 3 HRS 100 MARKS Note: 1) Figures to the right indicate full marks
   • 2) Use of simple calculator is allowed
6. Q1 Attempt any four from the following: 20 marks
   • 1) Find a market value of 12% share if Rs. 6400 were invested to purchase share with face value of Rs. 100 and total dividend of Rs. 480 was obtained
   • 2) Seema invested Rs. 2,08,832 to purchase equity shares of company at market price of Rs. 260 through a brokerage form charging 0.4% brokerage. Find number of shares
   • 3) Praniti invested Rs. 9945 to purchase share of a company with face value of Rs. 10each, at market price of Rs. 65. She received dividend of 20% as well. Afterwards, shesold these share at market price of Rs. 90. She had to pay brokerage of 2% for both purchase and sales of share. Find her net profit
   • 4) Mr Kale invest an amount of Rs. 50,000 on 14th Feb, 2021 when NAV was Rs 125.6, with an entry load of 2.5%. Find the number of units purchased. If current NAV is Rs 140.4, find current value of his investment
   • 5) Nikhil invested Rs 15,000 on Sth of every month for 6 months in Systematic Investment Plan Scheme of a Mutual Fund. ‘The Navy on these dates where RS 42.36, 47.68, 40.25,
   • 49.87, 52.48 and 39.16 respectively. There was same entry load of 2.25% for all these months. Find average price of unit
7. Q2 Attempt any four from the following: 20 marks
   • 1) Solve: x ii)
   • 2) How many different numbers of 4-digit can be formed using the digits 1,2,3,4,5 such that
   • (a) Repetition of digits is allowed (b) Repetition of digits is not allowed
   • 3) An organization consists of 2 managers, 5 officers, and 10 clerks. A selection of 4 persons is to be done. Find how many selections will have | officer and 3 clerks?
   • 4) A manufacturer produces bulbs and tubes. Each of these must be processed through two machines. Mland M2. A package of bulbs require 1 hour of work on machine M1 and 3 hours of work on M2.A package of tubes require 2 hours on machine M1 and 4 hours machine M2. He earns a profit of Rs. 13.5 per package of bulbs and Rs. 55 per package of If maximum availability of Machine M1 is 10 hours and that of Machine M2 is 12: hours. Formulate the LPP to maximize the profit
   • 5) Solve the L.P.P. graphically, Maximize Z = 5x +10y
8. Q3 Attempt any four from the following: 20 marks
   • 1) Calculate mean for the following data
   • 2) Calculate standard deviation and coefficient of variation for the following data
   • 3) Calculate quartile deviation and coefficient of quartile deviation for the following data Daily Wages in Rs | 100 | 200 | 300 [| 500 | 600 VCD/ SEMI MATHEMATICAL AND STATISTICAL TECH-I 3 MARRS
   • 4) Draw cumulative frequency curve and hence locate median graphically
   • 5) Write Merits & Demerits of Range
9. Q4 Attempt any four from the following: 20 marks
   • 1) Three unbiased coins are tossed. Find the probability of getting (a) exactly 2 heads
   • (b)no tail
   • 2) A card is drawn from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is (a) a black card (b) a heart card
   • 3) For the following probability distribution function, find k, P(x > 3), P(x < 4)
   • 4) Find mean and variance for the following:
   • 5) Explain: i) Random Variable ii) Random Variable iii) Complimentary Event
10. Q5 Attempt any four from the following: 20 marks
    • 1) Explain briefly decision making under uncertainty
    • 2) Solve the given decision problem using Minimax regret Courses of Action
    • 3) Given the pay-off matrix, solve the decision using EMV criterion Courses of Action States of Nature
    • 4) Given the pay-off matrix, solve the decision using EOL criterion Courses of Action
    • 5) Draw a decision tree for the given pay-off table Courses of Action

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