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12th Standard English Medium Business Maths Reduced Syllabus Creative Three Mark Question with Answerkey - 2021(Public Exam )

12th Standard

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Business Maths

Time : 02:30:00 Hrs
Total Marks : 75

    Part-A

    3 Marks(Creative)

    25 x 3 = 75
  1. Show that the equations 2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5 are consistent and have a unique solution.

  2. Solve: 2x - 3y - 1 = 0, 5x + 2y - 12 = 0 by Cramer's rule.

  3. Two products A and B currently share the market with shares 60% and 40% each respectively. Each week some brand switching latees place. Of those who bought A the previous week 70% buy it again whereas 30% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 20% switch over to A. Find their shares after one week and after two weeks.

  4. If f' (x) = 3x2 - \(\frac { 2 }{ { x }^{ 3 } } \) and f(1) = 0, find f(x)

  5. Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis

  6. Find the area of the region bounded by the line x - y =1, x-axis and the lines x = -2 and x = 0.
    x - y = 1

    x 0 1
    y -1 0
  7. Form the differential equation for \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \)=1 where a & b are arbitrary constants.

  8. Solve: cos2x dy + y.etanx dx = 0

  9. Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(ex-x-1).

  10. A man plans to invest some amount in a small saving scheme with a guaranteed compound in crest compounded continuously at the ratio of 12 percent for 5 years. How much should he invest if he wants an amount of Rs. 25000 at the end of 5 year period? (e-0.6 = 0.5488)

  11. Using graphic method, find the value of y when x=27.

    x 10 15 20 25 30
    y 35 32 29 26 23
  12. If y75 = 2459, y50 = 2018, y85 = 1180, and y90 =402, find y82

    x 75 80 85 90
    y 2459 2018 1180 402
  13. The probability distribution of a discrete random variable. X is given by

    X -2 2 5
    P(X=x) \(\frac{1}{4}\) \(\frac{1}{4}\) \(\frac{1}{2}\)

    then find 4E(X2)- Var (2X)

  14. A player tosses two unbiased coins. He wins Rs. 5 if two heads appear, Rs. 2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.

  15. If the probability density function of a random variable. X is given by f(x) = \(\frac{2x}{9}\),0

  16. Two cards are drawn from a pack of 52 playing cards. Find the probability distribution of the number of aces.

  17. An urn contains 4 white and 6 red balls. Four balls are drawn at random from the urn. Find the probability distribution of the number of white balls.

  18. The standard deviation of a binomial distribution (q +p)16 is 2. Find its mean.

  19. Obtain K, μ and σ2 of of the normal distribution whose probability distribution function is f(x) = \(K{ e }^{ -2x^{ 2 }+4x-2 }\), -∞

  20. Alpha particles are emitted by a radio active source at an average rate of 5 in a 20 minutes interval. Using Poisson distribution find the probability that there will be atleast 2 emission in a particular 20 minutes interval (e-5 = 0.0067).

  21. A random sample of 500 apples was taken from large consignment and 45 of them were found to be bad. Find the limits at which the bad apples lie at 99% confidence level.

  22. The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with the S.D. of 110 hours. If II is the mean life time of all the bulbs produced by the company, test the hypothesis that μ = 900 hours at 5% level of significance.

  23. Fit a straight line trend for the following data using the method of least squares.

    x 0 1 2 3 4
    y 1 1 3 4 6
  24. From the data given below, construct a cost of living index number by family budget method for 1986 with 1976 as the base year.

    Commodity P Q R S T U
    Quantity in 1976 50 25 10 20 30 40
    Price in 1976 (Rs) 10 5 8 7 9 6
    Price in 1986 (Rs) 6 4 3 8 10 12

     

  25. Find the initial basic feasible solution for the following transportation problem by Vogel's approximation method.

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