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Public Exam Model Question Paper 2019 - 2020

11th Standard

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Business Maths

Time : 02:45:00 Hrs
Total Marks : 90

    Part I

    Answer all the questions.

    Choose the most suitable answer from the given four alternatives and write the option code with the corresponding answer.

    20 x 1 = 20
  1. If A is 3 x 3 matrix and |A|= 4, then |A-1| is equal to

    (a)

    \({{1}\over{4}}\)

    (b)

    \({{1}\over{16}}\)

    (c)

    2

    (d)

    4

  2. If \(\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}\) and Aij is cofactor of aij, then value of \(\triangle\) is given by

    (a)

    a11 A31 + a12 A32 + a13 A33

    (b)

    a11 A11 + a12 A21 + a13 A31

    (c)

    a21 A11 + a22 A12 + a23 A13

    (d)

    a11 A11 + a21 A21 + a31 A31

  3. If nC3 = nC2, then the value of nC4 is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

  4. If nPr = 720 (nCr), then r is equal to

    (a)

    4

    (b)

    5

    (c)

    6

    (d)

    7

  5. The slope of the line 7x + 5y - 8 = 0 is

    (a)

    7/5

    (b)

    -7/5

    (c)

    5/7

    (d)

    -9/7

  6. The eccentricity of the parabola is

    (a)

    3

    (b)

    2

    (c)

    0

    (d)

    1

  7. The value of \(\frac{3\tan10^o-\tan^310}{1-3\tan^210}\) is

    (a)

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

    (b)

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

    (c)

    \(\frac{\sqrt3}2\)

    (d)

    \(\frac{1}{\sqrt2}\)

  8. \(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is

    (a)

    \(\frac{3}{5}\)

    (b)

    \(\frac{5}{3}\)

    (c)

    \(\frac{4}{5}\)

    (d)

    \(\frac{5}{4}\)

  9. The graph of y = ex intersect the y-axis at

    (a)

    (0,0)

    (b)

    (1,0)

    (c)

    (0,1)

    (d)

    (1,1)

  10. The range of f(x) = |x|, for all \(x\epsilon R\), is

    (a)

    (0, \(\infty \))

    (b)

    (0, \(\infty \))

    (c)

    (-\(\infty \)\(\infty \))

    (d)

    (1, \(\infty \))

  11. The demand function is always

    (a)

    Increasing function

    (b)

    Decreasing function

    (c)

    Non-decreasing function

    (d)

    Undefined function

  12. if q = 1000 + 8p1 - p2 then, \(\frac { \partial q }{ \partial { p }_{ 1 } } \) is

    (a)

    -1

    (b)

    8

    (c)

    1000

    (d)

    1000 - p2

  13. A person brought a 9% stock of face value Rs 100, for 100 shares at a discount of 10%, then the stock purchased is

    (a)

    Rs 9000

    (b)

    Rs 6000

    (c)

    Rs 5000

    (d)

    Rs 4000

  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. When an observation in the data is zero, then its geometric mean is

    (a)

    Negative

    (b)

    Positive

    (c)

    Zero

    (d)

    Cannot be calculated

  16. The events A and B are independent if

    (a)

    \(P\left( A\cap B \right) =0\)

    (b)

    \(P\left( A\cap B \right) =P(A)\times P(B)\)

    (c)

    \(P\left( A\cup B \right) =P(A)+P(B)\)

    (d)

    \(P\left( A\cup B \right) =P(A)\times P(B)\)

  17. The correlation coefficient

    (a)

    r=±\(\sqrt { { b }_{ xy }\times { b }_{ yx } } \)

    (b)

    r=\(\frac { 1 }{ { b }_{ xy }\times { b }_{ yx } } \)

    (c)

    r=bxy x byx

    (d)

    r=±\(\sqrt { \frac { 1 }{ { b }_{ xy }\times { b }_{ yx } } } \)

  18. The regression coefficient of X on Y

    (a)

    bxy=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

    (b)

    byx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

    (c)

    bxy=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)

    (d)

    bxy=\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma y^{ 2 }-(\Sigma y)^{ 2 } } } } \)

  19. One of the conditions for the activity (i, j) to lie on the critical path is

    (a)

    Ej-Ei=Lj-Li=tij

    (b)

    Ei-Ej=Lj-Li=tij

    (c)

    Ej-Ei=Li-Lj=tij

    (d)

    Ej-Ei=Lj-Li≠tij

  20. In a network while numbering the events which one of the following statement is false?

    (a)

    Event numbers should be unique

    (b)

    Event numbering should be carried out on a sequential basis from left to right

    (c)

    The initial event is numbered 0 or 1

    (d)

    The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow

  21. Part II

    Answer any 7 questions. Question no. 30 is compulsory.

    7 x 2 = 14
  22. Show that \(\left[ \begin{matrix} 8 & 2 \\ 4 & 3 \end{matrix} \right] \)is non – singular.

  23. If P(n) is the statement "23n -1 is a multiple of 7" then show that P (5) is true.

  24. Find the equation of the circle with centre at (3, –1) and radius is 4 units.

  25. If \(\cos x=-\frac{1}{2}\) and \(\pi <x<3\frac { \pi }{ 2 } \), find the value of \(4\tan^2x-3cosec^2x\)

  26. Evaluate \(\underset { x\rightarrow \frac { 1 }{ 2 } }{ lim } \frac { { 4x }^{ 2 }-1 }{ 2x-1 } \)

  27. A tour operator charges Rupees 136 per passenger with a discount of 40 paisa for each passenger in excess of 100. The operator requires at least 100 passengers to operate he tour. Determine the number of passenger that will maximize the amount of money the tour perator receives.

  28. A person pays Rs 64,000 per annum for 12 years at the rate of 10% per year. Find the annuity [(1.1)12 = 3.3184]

  29. A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

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

  31. Develop a network based on the following information:

    Activity: A B C D E F G H
    Immediate predecessor: - - A B C,D C,D E F
  32. Part III

    Answer any 7 questions. Question no. 40 is compulsory.

    7 x 3 = 21
  33. Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

  34. Find the inverse of the following matrices \(\left[ \begin{matrix} -3 & -5 & 4 \\ -2 & 3 & -1 \\ 1 & -4 & -6 \end{matrix} \right] \)

  35. Evaluate the following using binomial theorem:(101)4

  36. If the lines x+ y = 6 and x + 2y = 4 are diameters of the circle , and the circle passes through the point (2,6)  then find its equation.

  37. Find \(\frac{dy}{dx}\)  of the following functions:
    x = a (\(\theta\) - sin \(\theta\)), y = a (1 - cos \(\theta\))

  38. A company has to supply 1000 item per month at a uniform rate and for each time, a production run is started with the cost of Rs 200. Cost of holding is Rs 20 per item per month. The number of items to be produced per run has to be ascertained. Determine the total of setup cost and average inventory cost if the run size is 500, 600, 700, 800. Find the optimal production run size using EOQ formula.

  39. What amount should be deposited annually so that after 16 years a person receives Rs 1,67,160 if the interest rate is 15% [(1.15)16 = 9.358]

  40. Calculate mean deviation about median for the following data:

    Class 0-10 10-20 20-30 30-40 40-50
    Frequency 5 8 15 16 6
  41. If two regression co-efficient are 2 and 0.45, what will be the co-efficient of correlation?

  42. A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are Rs 5 and Rs 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.

  43. Part IV

    Answer all the questions.

    7 x 5 = 35
    1. Data on readership of a magazine indicates that the proportion of male readers over 30 years old is 0.30 and the proportion of male reader under 30 is 0.20. If the proportion of readers under 30 is 0.80. What is the probability that a randomly selected male subscriber is under 30?

    2. Solve the following LPP by graphical method Minimize z = 5x1+4x2 Subject to constraints 4x1+ x2 ≥ 40 ; 2x1+3x2 ≥ 90 and x1, x2 > 0.

    1. Differentiate (sec x -1) (sec x +1)

    2. A company buys in lots of 500 boxes which is a 3 month supply. The cost per box is Rs 125 and the ordering cost in Rs 150. The inventory carrying cost is estimated at 20% of unit value.
      (i) Determine the total amount cost of existing inventory policy
      (ii) How much money could be saved by applying the economic order quantity?

    1. Differentiate the following with respect to x \(\sqrt { \frac { (x-1)(x-2) }{ (x-3)({ x }^{ 2 }+x+1) } } \)

    2. A computer while calculating the correlation co-efficient between two variables x and y from 25 pairs of observations, obtained the following results. \(\sum\)x=125, \(\sum\)x2=650, \(\sum\)y=100, \(\sum\)y2=460, xy=508. It was later found out that it had copied down two pairs as while the correct values are 

      x y
      6 14
      8 6
      x y
      8 12
      6 8

      Obtain the correlation co-efficient for the correct value.

    1. Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

    2. If  z = 4x6 - 8x3 - 7x + 6xy + 8y + x3y5, find 
      (i) \({\partial^2z\over \partial y^2}\) (ii)\(\partial^2 z\over \partial x\partial y\)(iii) \(\partial^2z\over \partial y\partial x\)

    1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

    2. Equal amounts are invested in 10% stock at 89 and 7% stock at 90 (1% brokerage paid in both transactions). If 10% stock bought Rs 100 more by way of dividend income than the other, find the amount invested in each stock.

    1. If \(A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right] \), then show that ATA-1=\(\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .\)

    2. Prove that:  \(\frac { \sin { \left( 180-\theta \right) } \cos { \left( 90+\theta \right) } \tan { \left( 270-\theta \right) \cot { \left( 360-\theta \right) } } }{ \sin { \left( 360-\theta \right) \cot { \left( 360+\theta \right) \sin { \left( 270-\theta \right) \csc { \left( -\theta \right) } } } } } =-1\)

    1. Resolve into partial fractions for the following:
      \(\frac { 1 }{ ({ x }^{ 2 }+4)(x+1) } \)

    2. As the number of units manufactured increases from 6000 to 8000, the total cost of production increases from Rs. 33,000 to Rs. 40,000. Find the relationship between the cost (y) and the number of units made (x) if the relationship is linear.

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