New ! Business Maths and Statistics MCQ Practise Tests



All Chapter 2 Marks

12th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 80
    Answer The Following Question:
    40 x 2 = 80
  1. Find the rank of the matrix \(\left( \begin{matrix} 5 & 3 & 0 \\ 1 & 2 & -4 \\ -2 & -4 & 8 \end{matrix} \right) \)

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

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

  4. If A and B are non-singular matrices, prove that AB is non-singular.

  5. Evaluate \(\int { \frac { x }{ \sqrt { { x }^{ 2 }+1 } } dx } \)

  6. Evaluate \(\int { x } \sqrt { { x }^{ 2 }+1 } \ dx\)

  7. If f'(x) = 8x3 -2x2, f(2) = 1, find f(x)

  8. If \(\int _{ 0 }^{ 1 }{ \left( { 3x }^{ 2 }+2x+k \right) } dx=0\)find k.

  9. Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.

  10. Using Integration, find the area of the region bounded the line 2y + x = 8, the x axis and the lines x = 2, x = 4.

  11. The marginal cost function is MC = \(\frac{100}{x}\). Find the cost function C(x) if C(16) = 100.

  12. Find the consumer's surplus for the demand function p = 25 - x -x2 when Po = 19

  13. Solve: \(\frac { dy }{ dx } \) = y sin 2x

  14. Solve \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -4\frac { dy }{ dx } +5y\) = 0

  15. Find the differential equation for y = mx + \(\frac { a }{ m } \) where m is arbitrary constant.

  16. Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

  17. Find (i) Δeax
    (ii) Δ2ex
    (iii) Δ log x

  18. Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.

  19. Find the missing term from the following data.

    x 20 30 40
    y 51 - 34
  20. If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.

  21. Construct cumulative distribution function for the given probability distribution.

    X 0 1 2 3
    P(X = x) 0.3 0.2 0.4 0.1
  22. Explain the distribution function of a random variable.

  23. A random variable X has the probability mass function

    X -2 3 1
    P(X=x) \(\frac{k}{6}\) \(\frac{k}{4}\) \(\frac{k}{12}\)

    then find k

  24. Find the mean for the probability density function \(f(x)=\begin{cases} \frac { 1 }{ 24 } ,-12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)

  25. Write the conditions for which the poisson distribution is a limiting case of binomial distribution.

  26. Mention the properties of poisson distribution.

  27. If the mean of the binomial distribution with 9 trial is 6, then find the variance.

  28. Students of a class were given an aptitude test. Marks were found to be normally distributed with mean 60 and S.D. 5. Find the percentage of students who scored more than 60 marks.

  29. Define critical value.

  30. What is single tailed test.

  31. Out of 1500 school students, a sample of 150 selected to test the accuracy of solving a problem in B.M. and of them 10 did a mistake. Calculate the standard error of sample proportion.

  32. A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)

  33. What is the need for studying time series?

  34. State the test of adequacy of index number.

  35. Using the method ofleast squares, fit a straight line trend for Σx = 10, Σy = 16.9, Σx2 = 30, Σxy = 47.4 and n = 7.

  36. Calculate the seasonal indices by the method of simple average for the following data.

    Year I quarter II quarter III quarter IV quarter
    1985 68 62 61 63
    1986 65 58 66 61
    1987 68 63 63 67
  37. What is transportation problem?

  38. What is the difference between Assignment Problem and Transportation Problem?

  39. Determine an initial basic feasible solution to the following transportation problem using feast cost method.

  40. For the given pay-off matrix, find the optimal decision under the minimax principle.

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