New ! Business Maths and Statistics MCQ Practise Tests



All Chapter 1 Marks

12th Standard

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Business Maths

Time : 00:30:00 Hrs
Total Marks : 40
    Choose The Correct Answer:
    40 x 1 = 40
  1. The rank of the diagonal matrix\(\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right) \)

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    5

  2. For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 2, 5x + 5y + 9z = 4 _______.

    (a)

    there is only one solution

    (b)

    there exists infinitely many solutions

    (c)

    there is no solution

    (d)

    None of these

  3. If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

    (a)

    3

    (b)

    ± 3

    (c)

    ± 6

    (d)

    6

  4. If A, B are two n x n non-singular matrices, then ___________

    (a)

    AB is non-singular

    (b)

    AB is singular

    (c)

    (AB)-1 = A-1 B-1

    (d)

    (AB)-1 does not exit

  5. \(\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } } \) is _______.

    (a)

    \(\sqrt { { x }^{ 2 }-{ 36 } } +c\)

    (b)

    log\(\left| x+\sqrt { { x }^{ 2 }-36 } \right| +c\)

    (c)

    log\(\left| x-\sqrt { { x }^{ 2 }-36 } \right| +c\)

    (d)

    \(log\left| { x }^{ 2 }+\sqrt { { x }^{ 2 }-36 } \right| +c\)

  6. \(\Gamma (n)\) is _______.

    (a)

    (n −1)!

    (b)

    n!

    (c)

    \(n\Gamma (n)\)

    (d)

    (n −1)\(\Gamma \)(n)

  7. \(\int { { e }^{ x } } \) (1-cot x +cot2 x) dx = _______________ +c

    (a)

    ex cot x

    (b)

    - ex cot x

    (c)

    ex cosec x

    (d)

    -ex cosec x

  8. \(\int { \left( \frac { x }{ m } +\frac { m }{ x } \right) } \) dx = __________ +c

    (a)

    \(\frac { { x }^{ 2 } }{ 2m } +m\log { \left| x \right| } \)

    (b)

    \(\frac { x }{ { m }^{ 2 } } +m\log { \left| x \right| } \)

    (c)

    \(-\frac { 1 }{ { mx }^{ 2 } } +m\log { \left| x \right| } \)

    (d)

    \(\frac { 1 }{ m } -\frac { m }{ { x }^{ 2 } } \)

  9. If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x2 − 81 , then the maximum profit at x is equal to ________.

    (a)

    3

    (b)

    6

    (c)

    9

    (d)

    5

  10. Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

    (a)

    1sq.units

    (b)

    3 sq.units

    (c)

    2 sq.units

    (d)

    4 sq.units

  11. The area lying above the X-axis and under the parabola y = 4x - x2 is ______ sq. units

    (a)

    \(\frac{16}{3}\)

    (b)

    \(\frac{8}{3}\)

    (c)

    \(\frac{32}{3}\)

    (d)

    \(\frac{64}{3}\)

  12. The area bounded by the curve y = 4ax and the lines y2 = 2a and Y-axis is _______ sq. units.

    (a)

    \(\frac{2a}{3}\)

    (b)

    2a2

    (c)

    \(\frac{a^2}{3}\)

    (d)

    \(\frac{2a^2}{3}\)

  13. The order and degree of the differential equation \(\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 } \) are respectively ______.

    (a)

    2 and 3

    (b)

    3 and 2

    (c)

    2 and 1

    (d)

    2 and 2

  14. A homogeneous differential equation of the form  \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.

    (a)

    x = v y

    (b)

    y = v x

    (c)

    y = v

    (d)

    x = v

  15. Solution of \(\frac { dx }{ dy } \)+mx = 0 where m<0 is _______

    (a)

    x = cemy

    (b)

    x = ce-my

    (c)

    x = my + c

    (d)

    x = c

  16. The differential equation of the family of lines y=mx is ______

    (a)

    \(\frac { dy }{ dx } \)=m

    (b)

    y dx - x dx

    (c)

    \(\frac { d^{ 2 }y }{ dx^{ 2 } } \)=0

    (d)

    y dx + x dy=0

  17. Δf(x) = _______.

    (a)

    f(x+ h)

    (b)

    f(x) − f(x+h)

    (c)

    f(x + h) − f(x)

    (d)

    f (x) − f(x−h)

  18. If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x) _______.

    (a)

    2x −3

    (b)

    2x +3

    (c)

    x + 3

    (d)

    x − 3

  19. ∆f(x + 3h) ______________

    (a)

    f(x + 3h) - f(x + 4h)

    (b)

    f(x + 4h) - f(x + 3h)

    (c)

    f(x + h) - f(x)

    (d)

    f(x + 2h) - f(x + 3h)

  20. If y is to be estimated for the values of x which lies unside the given set of the values of it is called __________

    (a)

    Interpolation

    (b)

    extrapolation

    (c)

    Forward Interpolation

    (d)

    backward Interpolation

  21. A probability density function may be represented by ________.

    (a)

    table

    (b)

    graph

    (c)

    mathematical equation

    (d)

    both (b) and (c)

  22. Which one is not an example of random experiment?

    (a)

    A coin is tossed and the outcome is either a head or a tail

    (b)

    A six-sided die is rolled

    (c)

    Some number of persons will be admitted to a hospital emergency room during any hour

    (d)

    All medical insurance claims received by a company in a given year

  23. If the p.d.f of a continuous random variable. X is \(f(x)=\left\{\begin{array}{l} \frac{x}{2}, 0 then E(3X2-2X) = _________

    (a)

    \(\frac{2}{3}\)

    (b)

    \(\frac{4}{3}\)

    (c)

    \(\frac{10}{3}\)

    (d)

    \(\frac{7}{3}\)

  24. If X is a discrete random variable. then P(X≥a)=________.

    (a)

    P(X

    (b)

    1-P(X≤a)

    (c)

    1-P(X

    (d)

    0

  25. In a parametric distribution the mean is equal to variance is ________.

    (a)

    binomial

    (b)

    normal

    (c)

    poisson

    (d)

    all the above

  26. Which of the following cannot generate a Poisson distribution?

    (a)

    The number of telephone calls received in a ten-minute interval

    (b)

    The number of customers arriving at a petrol station

    (c)

    The number of bacteria found in a cubic feet of soil

    (d)

    The number of misprints per page

  27. The variance of a binomial distribution is ___________

    (a)

    equal to its mean

    (b)

    less than its mean

    (c)

    greater than its mean

    (d)

    none

  28. If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to ________

    (a)

    \(\frac{5}{16}\)

    (b)

    \(\frac{11}{16}\)

    (c)

    \(\frac{10}{16}\)

    (d)

    \(\frac{1}{2}\)

  29. A __________ of statistical individuals in a population is called a sample.

    (a)

    Infinite set

    (b)

    finite subset

    (c)

    finite set

    (d)

    entire set

  30. The standard error of sample mean is  ______.

    (a)

    \(\frac { \sigma }{ \sqrt { 2n } } \)

    (b)

    \(\frac { \sigma }{ { n } } \)

    (c)

    \(\frac { \sigma }{ \sqrt { n } } \)

    (d)

    \(\frac { { \sigma }^{ 2 } }{ \sqrt { n } } \)

  31. The point estimate variance of 21, 25, 20, 16, 12, 10, 17, 18, 13 and 11 is _______

    (a)

    23.5

    (b)

    2.35

    (c)

    4.85

    (d)

    48.5

  32. The point estimate variance of 6.33, 6.37, 6.36, 6.32, 6.37 is

    (a)

    0.0022

    (b)

    0.00055

    (c)

    0.0055

    (d)

    0.055

  33. The components of a time series which is attached to short term fluctuation is ________.

    (a)

    Secular trend

    (b)

    Seasonal variations

    (c)

    Cyclic variation

    (d)

    Irregular variation

  34. A typical control charts consists of ________.

    (a)

    CL, UCL

    (b)

    CL, LCL

    (c)

    CL, LCL, UCL

    (d)

    UCL, LCL

  35. The causes leading to vast variation in the specification of a product are usually due to _____

    (a)

    random process

    (b)

    assignable causes

    (c)

    non-traceable causes

    (d)

    all the above

  36. Choose the odd one out

    (a)

    Secular trend

    (b)

    seasonal variation

    (c)

    Simple averages

    (d)

    cyclic variations

  37. The transportation problem is said to be unbalanced if _______.

    (a)

    Total supply ≠ Total demand

    (b)

    Total supply = Total demand

    (c)

    m = n

    (d)

    m+n–1

  38. In a non – degenerate solution number of allocations is _______.

    (a)

    Equal to m+n–1

    (b)

    Equal to m+n+1

    (c)

    Not equal to m+n–1

    (d)

    Not equal to m+n+1

  39. The optimum_______schedule remains, unaltered if we add or subtract a constant from all the elements of the row or which of the cost________matrix.

    (a)

    transportation

    (b)

    assignment

    (c)

    unique

    (d)

    optimal

  40. The least cost method is more economical than North West Corner Rule, since it starts with the ___________

    (a)

    least cost

    (b)

    minimum cost

    (c)

    maximum cost

    (d)

    lower beginning cost

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