11th Public Exam March 2019 Model Test

11th Standard

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Business Maths

Time : 02:30:00 Hrs
Total Marks : 90
    20 x 1 = 20
  1. If A and B are non-singular matrices then, which of the following is incorrect?

    (a)

    A2 = Iimplies A-1 = A

    (b)

    I-1 = I

    (c)

    If AX = B, then X = B-1 A

    (d)

    If A is square matrix of order 3 then |adj A|= |A|2

  2. If any three-rows or columns of a determinant are identical, then the value of the determinant is

    (a)

    0

    (b)

    2

    (c)

    1

    (d)

    3

  3. The term containing x3 in the expansion of (x - 2y)7 is

    (a)

    3rd

    (b)

    4th

    (c)

    5th

    (d)

    6th

  4. If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to 

    (a)

    9

    (b)

    11

    (c)

    5

    (d)

    7

  5. The focus of the parabola x2 = 16y is

    (a)

    (4,0)

    (b)

    (-4,0)

    (c)

    (0,4)

    (d)

    (0,-4)

  6. If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is

    (a)

    6

    (b)

    3

    (c)

    12

    (d)

    4

  7. The value of \(\sin15^o\) is

    (a)

    \(\frac{\sqrt{3}+1}{2\sqrt{2}}\)

    (b)

    \(\frac{\sqrt{3}-1}{2\sqrt{2}}\)

    (c)

    \(\frac{\sqrt3}{\sqrt2}\)

    (d)

    \(\frac{\sqrt3}{2\sqrt2}\)

  8. The value of \(\frac{2\tan30^o}{1+tan^230}\) is

    (a)

    \(\frac12\)

    (b)

    \(\frac{1}{\sqrt3}\)

    (c)

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

    (d)

    \(\sqrt3\)

  9. f(x) = - 5 , for all \(x\epsilon R\), is a

    (a)

    an identity function

    (b)

    modulus function

    (c)

    exponential function

    (d)

    constant function

  10. \(\lim _{ x\rightarrow 0 }{ \frac { { e }^{ x }-1 }{ x } } =\)

    (a)

    e

    (b)

    nx(n-1)

    (c)

    1

    (d)

    0

  11. Profit P(x) is maximum when 

    (a)

    MR = MC

    (b)

    MR = 0

    (c)

    MC = AC

    (d)

    TR = AC

  12. If R = 5000 units / year, C1 = 20 paise , C3 = Rs 20 then EOQ is 

    (a)

    5000

    (b)

    100

    (c)

    1000

    (d)

    200

  13. The present value of the perpetual annuity of Rs 2000 paid monthly at 10 % compound interest is

    (a)

    Rs 2,40,000

    (b)

    Rs 6,00,000

    (c)

    20,40,000

    (d)

    Rs 2,00,400

  14. Example of contingent annuity is

    (a)

    Life insurance premium

    (b)

    An endowment fund to give scholarships to a student

    (c)

    Personal loan from a bank

    (d)

    All the above

  15. Which of the following is positional measure?

    (a)

    Range

    (b)

    Mode

    (c)

    Mean deviation

    (d)

    Percentiles

  16. When calculating the average growth of economy, the correct mean to use is?

    (a)

    Weighted mean

    (b)

    Arithmetic mean

    (c)

    Geometric mean

    (d)

    Harmonic mean

  17. Example for positive correlation is

    (a)

    Income and expenditure

    (b)

    Price and demand

    (c)

    Repayment period and EMI

    (d)

    Weight and Income

  18. Scatter diagram of the variate values (X,Y) give the idea about

    (a)

    functional relationship

    (b)

    regression model

    (c)

    distribution of errors

    (d)

    no relation

  19. The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤20, x + 2y ≤ 20,x > 0 and y > 0 is

    (a)

    10

    (b)

    20

    (c)

    0

    (d)

    5

  20. In critical path analysis, the word CPM mean

    (a)

    Critical path method

    (b)

    Crash project management

    (c)

    Critical project management

    (d)

    Critical path management

  21. 7 x 2 = 14
  22. The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}\). Test whether the system is viable as per Hawkins Simon conditions.

  23. Evaluate the following using binomial theorem:(999)5

  24. Find the center and radius of the circle 5x2 + 5y2 +4x - 8y - 16 = 0

  25. Evaluate \(\cot\left(\frac{-15\pi}{4}\right)\)

  26. Differentiate the following functions with respect to x, \(x^{\frac{3}{2}}\)

  27. Find the maximum and minimum values of x3-6x2+7

  28. A cash prize of Rs 1,500 is given to the student standing first in examination of Business Mathematics by a person every year. Find out the sum that the person has to deposit to meet this expense. Rate of interest is 12% p.a

  29. Suppose one person is selected at random from a group of 100 persons are given in the following

      Psychologist Socialist Democrate Total
    Men 15 25 10 50
    Women 20 15 15 50
    Total 35 40 25 100

    What is the probability that the man selected is a Psychologist?

  30. Calculate the correlation coefficient from the following data
    N=9, ΣX=45, ΣY=108, ΣX2=285, ΣY2=1356, ΣXY=597

  31. A toy company manufactures two types of dolls A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is atmost half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of n2 and n6 per doll, how many of each should be produced weekly in order to maximize the profit. Formulate the above as mathematical LPP.

  32. 7 x 3 = 21
  33. If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A2-4A+5I2 = 0 and also find A-1.

  34. Find the 5th term in the expansion of (x - 2y)13.

  35. Find the equation of the parabola whose focus is (-3, 2) and the directrix is x+y=4.

  36. Find the values of the following  sin (-105)°

  37. Show that \(\underset { x\rightarrow 0 }{ lim } \frac { \log { \left( 1+{ x }^{ 2 } \right) } }{ \sin ^{ 3 }{ x } } =1\)

  38. If the demand law is given by p = 10e\(-\frac { x }{ 2 } \) then find the elasticity of demand.

  39. Find the yield on 20% stock at 80.

  40. Calculate GM for the following table gives the weight of 31 persons in sample survey.

    Weight (lbs): 130 135 140 145 146 148 149 150 157
    Frequency 3 4 6 6 3 5 2 1 1
  41. Compute the co-efficient of correlation batween the variates x and y from the given data:
    No. of pairs of x and y series=8.x-series A.M.=74.5, x-series assumed mean =69, x-series S.D=13.07, y-series S.D=15.85, sum of products of corresponding deviations of x and y series =2176.

  42. Solve the following LPP graphically.\(Maximize\quad Z=-{ x }_{ 1 }+2{ x }_{ 2 }\)
    Subject to the constraints \(-{ x }_{ 1 }+3{ x }_{ 2 }\le 10,\quad { x }_{ 1 }+{ x }_{ 2 }\le 6,\quad { x }_{ 1 }{ -x }_{ 2 }\le 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

  43. 7 x 5 = 35
  44. Suppose the inter-industry flow of the product of two industries are given as under.

    Production sector Consumption sector Domestic demand Total output
    X Y
    X 30 40 50 120
    Y 20 10 30 60

    Determine the technology matrix and test Hawkin's -Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands.

  45. If 22Pr+1:20Pr+2=11: 52, find r.

  46. Resolve into partial fraction \(\frac{9}{(x-1)(x+2^2)}\)

  47. Show that the equation 12x2 -10xy +2y2 +14x -5y +2 = 0 represents a pair of straight lines also find the separate equations of the straight lines

  48. Prove that \(\frac { 4tan\ x(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 } x+{ tan }^{ 4 } x } =tanx\)

  49. If cosA =\(\frac{4}{5}\)and cosB =\(\frac{12}{13}\),\(\frac{3\pi}{3}\)\(\pi\), find the value of cos(A+B).

  50. Show that f(x) = \(\begin{cases} 5x-4,\quad if0 is continous at x = 1

  51. Find the absolute (global) maximum and absolute minimum of the function
     f(x)=3x5–25x3+60x+1 in the interval [–2,2]

  52. Find the marginal productivities for Capital (K) and Labour (L) if P = 10K-K2 + KL when K = 2 and L = 6.

  53. Rani sold Rs.8000 worth 7% stock at 96 and invested the amount realised in the shares of FV Rs.100 os a 10% stock by which her income increased by Rs.80. Find the purchase price of 10% stock.

  54. An unbiased die is thrown twice. Let the event A be odd number on the first throw and B the event odd number on the second throw. Check whether A and B events are independent.

  55. Find out the coefficient of correlation in the following case and interpret.

    Height of father (in inches) 65 66 67 67 68 69 71 73
    Height of son (in inches) 67 68 64 68 72 70 69 70
  56. Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity of the project given below and determine the Critical path of the project and duration to complete the project.

    Activity 1-2 1-3 1-5 2-3 2-4 3-4 3-5 3-6 4-6 5-6
    Duration ( in week) 8 7 12 4 10 3 5 10 7 4
  57. Solve graphically: Minimize Z = 20x1 + 40x2 . Subject to the constraints
    \(36{ x }_{ 1 }+6{ x }_{ 2 }\ge 108,\quad 3{ x }_{ 1 }+12{ x }_{ 2 }\ge 36,\quad 20{ x }_{ 1 }+10{ x }_{ 2 }\ge 100\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

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