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

12th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Part-A

    Multiple Choice Questions

    50 x 1 = 50
  1. The rank of the unit matrix of order n is ________.

    (a)

    n −1

    (b)

    n

    (c)

    n +1

    (d)

    n2

  2. 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

  3. ഽ2xdx is _______.

    (a)

    2x log 2 + c

    (b)

    2x + c

    (c)

    \(\frac { 2^{ x } }{ log2 } +c\)

    (d)

    \(\frac { log2 }{ { 2 }^{ x } } +c\)

  4. \(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.

    (a)

    \(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } +c\)

    (b)

    \(2\sqrt { 1+{ e }^{ x } } +c\)

    (c)

    \(\sqrt { 1+{ e }^{ x } } +c\)

    (d)

    \({ e }^{ x }\sqrt { 1+{ e }^{ x } } +c\)

  5. The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is ________.

    (a)

    9x2 + 54x

    (b)

    9x2 − 54x

    (c)

    54x - \(\frac { { 9x }^{ 2 } }{ 2 } \)

    (d)

    54x - \(\frac { { 9x }^{ 2 } }{ 2 } \) + k

  6. When x0 = 2 and P0 = 12 the producer’s surplus for the supply function Ps = 2x2 + 4 is ________.

    (a)

    \(\frac{31}{5}\)units

    (b)

    \(\frac{31}{2}\) units

    (c)

    \(\frac{32}{3}\) units

    (d)

    \(\frac{30}{7}\) units

  7. The degree of the differential equation \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3\) ______.

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  8. The differential equation formed by eliminating A and B from y = e−2x(A cos x + B sin x) is ______.

    (a)

    y− 4y+ 5 = 0

    (b)

    y2+ 4y – 5 = 0

    (c)

    y2−4y1−5= 0

    (d)

    y+ 4y+ 5 = 0

  9. Δf(x) = _______.

    (a)

    f(x+ h)

    (b)

    f(x) − f(x+h)

    (c)

    f(x + h) − f(x)

    (d)

    f (x) − f(x−h)

  10. If c is a constant then Δc = _______.

    (a)

    c

    (b)

    Δ

    (c)

    Δ2

    (d)

    0

  11. Probability which explains x is equal to or less than particular value is classified as ________.

    (a)

    discrete probability

    (b)

    cumulative probability

    (c)

    marginal probability

    (d)

    continuous probability

  12. Given E(X)=5 and E(Y)=−2, then E(X−Y) is ________.

    (a)

    3

    (b)

    5

    (c)

    7

    (d)

    -2

  13. A variable that can assume any possible value between two points is called ________.

    (a)

    discrete random variable

    (b)

    continuous random variable

    (c)

    discrete sample space

    (d)

    random variable

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

    (a)

    table

    (b)

    graph

    (c)

    mathematical equation

    (d)

    both (b) and (c)

  15. If c is a constant in a continuous probability distribution, then p(x = c) is always equal to ________.

    (a)

    zero

    (b)

    one

    (c)

    negative

    (d)

    does not exist

  16. E[X-E(X)]2 is ________.

    (a)

    E(X)

    (b)

    E(X2)

    (c)

    V(X)

    (d)

    S.D(X)

  17. An expected value of a random variable is equal to it’s ________.

    (a)

    variance

    (b)

    standard deviation

    (c)

    mean

    (d)

    covariance

  18. A discrete probability function p(x) is always non-negative and always lies between ________.

    (a)

    0 and \(\infty \)

    (b)

    0 and 1

    (c)

    –1 and +1

    (d)

    –∞ and +∞

  19. If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is ________.

    (a)

    0.4987

    (b)

    0.1915

    (c)

    0.3072

    (d)

    0.3098

  20. If X ~ N(μ, σ2), the maximum probability at the point of inflexion of normal distribution is ________.

    (a)

    \({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }^{ { e }^{ \frac { 1 }{ 2 } } }\)

    (b)

    \({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }^{ { e }^{ \left( -\frac { 1 }{ 2 } \right) } }\)

    (c)

    \({ \left( \frac { 1 }{ \sigma \sqrt { 2\pi } } \right) }^{ { e }^{ \left( \frac { 1 }{ 2 } \right) } }\)

    (d)

    \({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }\)

  21. If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.

    (a)

    (2/3)6

    (b)

    (2/3)5(1/3)

    (c)

    (1/3)6

    (d)

    4(2/3)6

  22. The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are ________.

    (a)

    0.5443

    (b)

    0.4543

    (c)

    0.5543

    (d)

    0.4573

  23. Which of the following statements is/are true regarding the normal distribution curve?

    (a)

    it is symmetrical and bell shaped curve

    (b)

    it is asymptotic in that each end approaches the horizontal axis but never reaches it

    (c)

    its mean, median and mode are located at the same point

    (d)

    all of the above statements are true.

  24. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?

    (a)

    0.683

    (b)

    0.954

    (c)

    0.271

    (d)

    0.340

  25. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of  Rs.180,000 and a standard deviation of Rs. 10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs. 165,000 and Rs. 175,000 per annum?

    (a)

    0.819

    (b)

    0.242

    (c)

    0.286

    (d)

    0.533

  26. In a large statistics class the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students are between 165 cm and 181 cm in height?

    (a)

    0.954

    (b)

    0.601

    (c)

    0.718

    (d)

    0.883

  27. The time until first failure of a brand of inkjet printers is normally distributed with a mean of 1,500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1000 hours?

    (a)

    0.0062

    (b)

    0.0668

    (c)

    0.8413

    (d)

    0.0228

  28. The weights of newborn human babies are normally distributed with a mean of 3.2 kg and a standard deviation of 1.1 kg. What is the probability that a randomly selected newborn baby weighs less than 2.0 kg?

    (a)

    0.138

    (b)

    0.428

    (c)

    0.766

    (d)

    0.262

  29. If P(Z > z) = 0.8508 what is the value of z (z has a standard normal distribution)?

    (a)

    –0.48

    (b)

    0.48

    (c)

    -1.04

    (d)

    1.04

  30. In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is ________.

    (a)

    16/81

    (b)

    1/16

    (c)

    2/27

    (d)

    1/81

  31. A random sample is a sample selected in such a way that every item in the population has an equal chance of being included ______.

    (a)

    Harper

    (b)

    Fisher

    (c)

    Karl Pearson

    (d)

    Dr. Yates

  32. Which one of the following is probability sampling

    (a)

    purposive sampling

    (b)

    judgment sampling

    (c)

    simple random sampling

    (d)

    Convenience sampling

  33. In ________ the heterogeneous groups are divided into homogeneous groups.

    (a)

    Non-probability sample

    (b)

    a simple random sample

    (c)

    a stratified random sample

    (d)

    systematic random sample

  34. _______ is a relative property, which states that one estimator is efficient relative to another.

    (a)

    efficiency

    (b)

    sufficiency

    (c)

    unbiased

    (d)

    consistency

  35. If probability \(P[|\hat{\theta}-\theta|<\varepsilon] \rightarrow 1\) as \(n \rightarrow \infty\), for any positive \(\varepsilon \) then \(\hat{\theta}\) is said to ________ estimator of \(\theta\).

    (a)

    efficient

    (b)

    sufficient

    (c)

    unbiased

    (d)

    consistent

  36. An estimate of a population parameter given by two numbers between which the parameter would be expected to lie is called an………..interval estimate of the parameter.

    (a)

    point estimate

    (b)

    interval estimation

    (c)

    standard error

    (d)

    confidence

  37. A time series is a set of data recorded ________.

    (a)

    Periodically

    (b)

    Weekly

    (c)

    successive points of time

    (d)

    all the above

  38. A time series consists of ________.

    (a)

    Five components

    (b)

    Four components

    (c)

    Three components

    (d)

    Two components

  39. 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

  40. The component of a time series attached to long term variation is trended as ________.

    (a)

    Cyclic variation

    (b)

    Secular variations

    (c)

    Irregular variation

    (d)

    Seasonal variations

  41. The seasonal variation means the variations occurring with in ________.

    (a)

    A number of years

    (b)

    within a year

    (c)

    within a month

    (d)

    within a week

  42. Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to: ________.

    (a)

    110

    (b)

    108

    (c)

    100

    (d)

    109

  43. Which of the following Index number satisfy the time reversal test?

    (a)

    Laspeyre’s Index number

    (b)

    Paasche’s Index number

    (c)

    Fisher Index number

    (d)

    All of them

  44. The quantities that can be numerically measured can be plotted on a ________.

    (a)

    p - chart

    (b)

    c – chart

    (c)

    x bar chart

    (d)

    np – chart

  45. Variations due to natural disorder is known as ________.

    (a)

    random cause

    (b)

    non-random cause

    (c)

    human cause

    (d)

    all of them

  46. \(\overset {-}{X}\) chart is a ________.

    (a)

    attribute control chart

    (b)

    variable control chart

    (c)

    neither Attribute nor variable control chart

    (d)

    both Attribute and variable control chart

  47. 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

  48. If number of sources is not equal to number of destinations, the assignment problem is called______.

    (a)

    balanced

    (b)

    unsymmetric

    (c)

    symmetric

    (d)

    unbalanced

  49. The solution for an assignment problem is optimal if _______.

    (a)

    each row and each column has no assignment

    (b)

    each row and each column has atleast one assignment

    (c)

    each row and each column has atmost one assignment

    (d)

    each row and each column has exactly one assignment

  50. A type of decision –making environment is _______.

    (a)

    certainty

    (b)

    uncertainty

    (c)

    risk

    (d)

    all of the above

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