11-STD 3rd Revision Exam Answers 2019

11th Standard

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Business Maths

Time : 02:30:00 Hrs
Total Marks : 90
    20 x 1 = 20
  1. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

    (a)

    1

    (b)

    3

    (c)

    4

    (d)

    2

  2. The inventor of input-output analysis is

    (a)

    Sir Francis Galton

    (b)

    Fisher

    (c)

    Prof. Wassily W. Leontief

    (d)

    Arthur Caylay

  3. The possible out comes when a coin is tossed five times

    (a)

    25

    (b)

    52

    (c)

    10

    (d)

    \(\frac { 5 }{ 2 } \)

  4. Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

    (a)

    7!

    (b)

    3!

    (c)

    8!

    (d)

    5!

  5. The double ordinate passing through the focus is

    (a)

    focal chord

    (b)

    latus rectum

    (c)

    directrix

    (d)

    axis

  6. The equation of directrix of the parabola y2 = - x is

    (a)

    4x+ 1 =0

    (b)

    4x - 1 = 0

    (c)

    x - 4=0

    (d)

    x + 4 = 0

  7. The value of sin 15o cos 15o is

    (a)

    1

    (b)

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

    (c)

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

    (d)

    \(\frac{1}{4}\)

  8. If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is 

    (a)

    \(\frac{16}{15}\)

    (b)

    0

    (c)

    \(\frac{56}{65}\)

    (d)

    \(\frac{64}{65}\)

  9. Let \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\), then f(5) is

    (a)

    -1

    (b)

    2

    (c)

    5

    (d)

    7

  10. \(\frac{d}{dx}(5e^x-2logx)\) is equal to

    (a)

    5ex - \(\frac{2}{x}\)

    (b)

    5ex - 2x

    (c)

    5ex - \(\frac{1}{x}\)

    (d)

    2 logx

  11. Marginal revenue of the demand function p= 20–3x is

    (a)

    20–6x

    (b)

    20–3x

    (c)

    20+6x

    (d)

    20+3x

  12. The demand function is always

    (a)

    Increasing function

    (b)

    Decreasing function

    (c)

    Non-decreasing function

    (d)

    Undefined function

  13. The annual income on 500 shares of face value 100 at 15% is

    (a)

    Rs 7,500

    (b)

    Rs 5,000

    (c)

    Rs 8,000

    (d)

    Rs 8,500

  14. Rs 5000 is paid as perpetual annuity every year and the rate of C.I 10 %. Then present value P of immediate annuity is

    (a)

    Rs 60,000

    (b)

    Rs 50,000

    (c)

    Rs 10,000

    (d)

    Rs 80,000

  15. The mean of the values 11,12,13,14 and 15 is

    (a)

    15

    (b)

    11

    (c)

    12.5

    (d)

    13

  16. If two events A and B are dependent then the conditional probability of P(B/A) is

    (a)

    \(P(A)P(B/A)\)

    (b)

    \(\frac { P(A\cup B) }{ P(B) } \)

    (c)

    \(\frac { P(A\cap B) }{ P(A) } \)

    (d)

    \(P(A)P(A/B)\)

  17. Example for positive correlation is

    (a)

    Income and expenditure

    (b)

    Price and demand

    (c)

    Repayment period and EMI

    (d)

    Weight and Income

  18. The variable whose value is influenced or is to be predicted is called

    (a)

    dependent variable

    (b)

    independent variable

    (c)

    regressor

    (d)

    explanatory variable

  19. Maximize: z=3x1+4x2 subject to 2x1+x2≤40, 2x1+5x2≤180, x1,x2≥0 in the LPP, which one of the following is feasible corner point?

    (a)

    x1=18, x2=24

    (b)

    x1=15, x2=30

    (c)

    x1=2.5, x2=35

    (d)

    x1=20, x2=19

  20. In constructing the network which one of the following statement is false?

    (a)

    Each activity is represented by one and only one arrow. (i.e) only one activity can connect any two nodes

    (b)

    Two activities can be identified by the same head and tail events

    (c)

    Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity

    (d)

    Arrows should not cross each other

  21. 7 x 2 = 14
  22. Find the minors and cofactors of all the elements of the following determinants.
    \(\begin{bmatrix} 1&-3&2\\4&-1&2\\3&5&2 \end{bmatrix}\)

  23. Find the values of A and B if \(\frac { 1 }{ \left( { x }^{ 2 }-1 \right) } =\frac { A }{ x-1 } +\frac { B }{ x+1 } \)

  24. Find the cartesian equation of the circle whose parametric equation are x = 3 cos\(\theta\), y = 3 sin\(\theta\) \(0\le \theta \le 2\pi \) 

  25. Prove that \(\cos18^o-\sin18^o=\sqrt{2}.\sin27^o\)

  26. Determine whether the following functions are odd or even?
    f(x)=x+x2

  27. A certain manufacturing concern has the toal cost function C = \({1\over5}x^2-6x+100\).Find when the tatal cost is minimum.

  28. What is the amount of perpetual annuity of Rs 50 at 5% compound interest per year?

  29. The price of a commodity increased by 5% from 2004 to 2005, 8% from 2005 to 2006 and 77% from 2006 to 2007. Calculate the average increase from 2004 to 2007?

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

  31. A producer has 30 and 17 units of labour and capital respectively which he can use to produce two types of goods X and Y. To produce one unit of X, 2 unit of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Yare priced at HOO and H20 per unit respectively, how should the producer use his resources to maximize the total revenue? Formulate the LPP for the above.

  32. 7 x 3 = 21
  33. Find the minor and cofactor of each element of the determinant\(\left| \begin{matrix} 1 & -2 \\ 4 & 3 \end{matrix} \right| \)

  34. Find the term independent of x in the expansion of \({ \left( x-\frac { 2 }{ { x }^{ 2 } } \right) }^{ 15 }\)

  35. For what value of k does 12x2+7xy+ky2+13x-y+3=0 represents a pair of straight lines?

  36. Convert the following into the product of trigonometric functions
    cos75+ cos 45o

  37. Differentiate the following with respect to x. \(\left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right) ^{ 2 }\)

  38. Find the elasticity of supply for the supply law \(x={p\over p+5}\) when p=20 and interpret your result.

  39. A man wishes to pay back his depts of Rs.3783 due after 3 years by 3 equal yearly instalments. Find the amount of each instalments,money being worth 5% p.a. compounded annually

  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. Find the regression co-efficient of x on y from the following data. \(\sum\)X=20, \(\sum\)Y=40, \(\sum\)XY=300, \(\sum\)X2=150, \(\sum\)Y2=345, N=5. Find the value of x when y=5

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

  43. 7 x 5 = 35
  44. Find adjoint of \(A=\left[ \begin{matrix} 1 & -2 & -3 \\ 0 & 1 & 0 \\ -4 & 1 & 0 \end{matrix} \right] \)

  45. Resolve into partial fractions for the following:
    \(\frac { x-2 }{ (x+2)(x-1)^{ 2 } } \)

  46. Using the principle of mathematical induction, prove that 1.3 + 2.32 + 3.33 + ... + n.3n =\(\frac { (2n-1){ 3 }^{ n+1 }+3 }{ 4 } for\quad all\quad n\in N\)

  47. As the number of units produced increases from 500 to 1000 and the total cost of production increases from. Rs 6000 to Rs 9000. Find the relationship between the cost (y) and the number of units produced (x) if the relationship is linear

  48. Prove that cos 20° cos 40° cos 60° cos 800=\(\frac { 1 }{ 16 } \)

  49. If  \(sin\left( { sin }^{ -1 }\left( \frac { 1 }{ 5 } \right) +{ cos }^{ -1 }(x) \right) =1\)  then find the value of x

  50. Draw the graph of f(x) = ax\(a\ne 1\) and a > 0

  51. Find the stationary values and stationary points for the function f(x) = 2x3 +9x2 +12x+1

  52. What is the maximum slope of the tangent to the curve y = - x3 + 3x2 +  9x - 27 and at what point is it?

  53. Equal amounts are invested in 12% stock at 95 (brokerage). If 12% stock brought at Rs.120 more by way of dividend income than the other, find the amount invested in each stock?

  54. A, B and C was 50% , 30% and 20% of the cars in a service station respectively. They fail to clean the glass in 5% , 7% and 3% of the cars respectively. The glass of a washed car is checked. What is the probability that the glass has been cleaned?

  55. Calculate coefficient of correlation from the following data:

    X 12 9 8 10 11 13 7
    Y 14 8 6 9 11 12 3
  56. A company is producing three products P1, P2 and P3, with profit contribution of Rs.20, Rs.25 and Rs.15 per unit respectively. The resource requirements per unit of each of the products and total availability are given below.​​​​​​​

    Product P1 P2 P3 Total availability
    Man hours/unit 6 3 12 200
    Machine hours/unit 2 5 4 350
    Material/unit 1kg 2kg 1kg 100kg

    Formulate the above as a linear programming model.

  57. 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) 7 6 11 3 9 2 4 9 6 3

     

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