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12th Standard English Medium Business Maths Reduced Syllabus Three Mark Important Questions - 2021(Public Exam )

12th Standard

    Reg.No. :
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Business Maths

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

    Part-A

    3 Marks

    25 x 3 = 75
  1. Find the rank of the matrix A = \(\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 4 & 5 \\ 2 & 3 & 4 \end{matrix}\begin{matrix} 1 \\ 2 \\ 0 \end{matrix} \right) \) 

  2. Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

  3. A total of Rs. 8,600 was invested in two accounts. One account earned \(4\frac { 3 }{ 4 } %\)% annual interest and the other earned \(6\frac { 1 }{ 2 } %\)annual interest. If the total interest for one year was Rs. 431.25, how much was invested in each account? (Use determinant method).

  4. Find the rank of each of the following matrices.
    \(\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right) \)

  5. Integrate the following with respect to x.
    \(\frac { 1 }{ x{ \left( \log x \right) }^{ 2 } } \)

  6. Integrate the following with respect to x.
    x3e3x

  7. Integrate the following with respect to x.
    \(\frac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } \)

  8. Using second fundamental theorem, evaluate the following:
    \(\int _{ -1 }^{ 1 }{ \frac { 2x+3 }{ { x }^{ 2 }+3x+7 } dx } \)

  9. Find the area bounded by y = x between the lines x = −1 and x = 2 with x -axis.

  10. The marginal cost function of manufacturing x shoes is 6 +10x − 6x2. The cost producing a pair of shoes is Rs. 12. Find the total and average cost function.

  11. The demand function p = 85 − 5x and supply function p = 3x − 35. Calculate the equilibrium price and quantity demanded. Also calculate consumer’s surplus.

  12. A manufacture’s marginal revenue function is given by MR = 275 − x − 0.3x2. Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units.

  13. Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x axis.

  14. Find the differential equation of the family of curves \(y=\frac { a }{ x } +b\) where a and b are arbitrary constants

  15. Solve the following:
    \(\frac { dy }{ dx } +ycosx=sinx\ cosx\).

  16. Construct a forward difference table for the following data

    x 0 10 20 30
    y 0 0.174 0.347 0.518
  17. Let X be a discrete random variable with the following p.m.f
    \(p(x) = \begin{cases}0.3 & \text { for } x =3 \\ 0.2, & \text { for } x = 5 \\ 0.3, & \text { for } x = 8 \\ 0.2, & \text { for} x = 10 \\ 0, & \text { otherwise } \\ \end{cases}\)
    Find and plot the c.d.f. of X.

  18. Consider a random variable X with probability density function \(f(x)= \begin{cases}4x^3 & \text { if } 0< x < 1 \\ 0, & \text { otherwise }\end{cases}\)
    Find E(X) and V(X).

  19. The probability that a student get the degree is 0.4 Determine the probability that out of 5 students
    (i) one will be graduate
    (ii) atleast one will be graduate

  20. The average daily procurement of milk by village society in 800 litres with a standard deviation of 100 litres. Find out proportion of societies procuring milk between 800 litres to 1000 litres per day.

  21. Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?

  22. Explain in detail about non-sampling error.

  23. A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant at 0.05 level of significance?

  24. Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method

    Cost are expressed in terms of rupees per unit shipped.

  25. The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-offs for various level of sales.

    Types of shampoo Estimated Sales (in Units)
    15000 10000 5000
    Egg shampoo 30 10 10
    Clinic Shampoo 40 15 5
    Deluxe Shampoo 55 20 3

    What will be the marketing manager’s decision if
    (i) Maximin and
    (ii) Minimax principle applied?

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