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12th Standard Business Maths Important 3 Mark Questions

12th Standard

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Business Maths and Statistics

Time : 01:30:00 Hrs
Total Marks : 90

    Answer all the following Questions.

    30 x 3 = 90
  1. If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank of BA.

  2. At marina two types of games viz., Horse riding and Quad Bikes riding are available on hourly rent. Keren and Benita spent Rs. 780 and Rs. 560 during the month of May.

    Name Number of hours Total amount spent
    (in Rs)
    Horse Riding Quad Bike Riding
    Keren 3 4 780
    Benita 2 3 560

    Find the hourly charges for the two games (rides). (Use determinant method).

  3. Evaluate \(\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx } \)

  4. Evaluate \(\int { \left( { x }^{ 2 }-2x+5 \right) } { e }^{ -x }dx\)

  5. The cost of over haul of an engine is Rs. 10,000 The operating cost per hour is at the rate of 2x − 240 where the engine has run x km. Find out the total cost if the engine run for 300 hours after overhaul.

  6. For the marginal revenue function MR = 6 − 3x2 − x3, Find the revenue function and demand function.

  7. Solve \(y d x-x d y-3 x^{2} y^{2} e^{x^{3}} d x=0\)

  8. Solve: \(\frac { 1+{ x }^{ 2 } }{ 1+y } =xy\frac { dy }{ dx } \)

  9. From the following table find the missing value

    x 2 3 4 5 6
    f(x) 45.0 49.2 54.1 - 67.4
  10. The following data relates to indirect labour expenses and the level of output

    Months Jan Feb Mar Apr May June
    Units of output 200 300 400 640 540 580
    Indirect labour expenses (Rs) 2500 2800 3100 3820 3220
    3640
     

    Estimate the expenses at a level of output of 350 units, by using graphic method

  11. Two unbiased dice are thrown simultaneously and sum of the upturned faces considered as random variable. Construct a probability mass function.

  12. If f (x) is defined by f(x)=ke-2x,  0\(\le\)x<\(\infty\) is a density function. Determine the constant k and also find mean.

  13. When counting red blood cells, a square grid is used, over which a drop of blood is evenly distributed. Under the microscope an average of 8 erythrocytes are observed per single square. What is the probability that exactly 5 erythrocytes are found in one square?

  14. The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e(–2.8) = 0.06]

  15. Explain in detail about sampling error.

  16. Explain the procedures of testing of hypothesis

  17. State the different methods of measuring trend.

  18. Construct the cost of living Index number for 2015 on the basis of 2012 from the following data using family budget method.

    Commodity Price Weight
    2012 2015
    Rice 250 280 10
    Wheat 70 280 5
    Corn 150 170 6
    Oil 25 35 4
    Dhal 85 90 3
  19. Determine an initial basic feasible solution to the following transportation problem using North West corner rule.

    Here Oi and Dj represent ith origin and jth destination.

  20. Solve the following assignment problem.

  21. If \(\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right] \) find x,y and z

  22. \(\int x^{3} \sin \left(x^{4}\right) d x\)

  23. The supply for a commodity is \(\mathrm{p}=x^{2}+4 x+5\), where x denotes supply. Find the producer's surplus when price is 10.

  24. Solve: \(\left(x^{2}-y x^{2}\right) d y+\left(y^{2}+x^{2} y^{2}\right) d x=0\)

  25. Using Lagrange's formula, find the value of y when x = 42 from the following table

    x 40 50 60 70
    y 31 73 124 159
  26. If a random variable. X has the probability distribution

    X 0 1 2 3 4 5
    P(X=x) a 2a 3a 4a 5a 6a

    then find F(4)

  27. Given the p.d.f of a continuous random variable X as follows \(f(x)= \begin{cases}k x(1-x) & \text { for } 0<x<1 \\ 0 & \text { otherwise }\end{cases}\). Find k and c.d.f.

  28. The average percentage of failure in a certain examination is 40. What is the probàbility that out of a group of 6 candidates atleast 4 passed in the examination?

  29. 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 interval.

  30. Compute Fisher's price index number for the following data.

    Commodity Base Year Current Year
    Price Quantity Price Quantity
    A 10 12 12 15
    B 7 15 5 20
    C 5 24 9 20
    D 16 5 14 5

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