11th First Revision Test Question Answer 2019

11th Standard

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Business Maths

Time : 02:30:00 Hrs
Total Marks : 90
    20 x 1 = 20
  1. adj (AB) is equal to

    (a)

    adj A adj B

    (b)

    adj AT adj BT

    (c)

    adj B adj A

    (d)

    adj BT adj AT

  2. If A is an invertible matrix of order 2, then det (A-1) be equal to

    (a)

    det (A)

    (b)

    \({{1}\over{det(A)}}\)

    (c)

    1

    (d)

    0

  3. The value of n, when nP2 = 20 is

    (a)

    3

    (b)

    6

    (c)

    5

    (d)

    4

  4. The last term in the expansion of (3 +\(\sqrt{2}\) )8 is

    (a)

    81

    (b)

    16

    (c)

    8\(\sqrt{2}\)

    (d)

    27\(\sqrt{3}\)

  5. If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

    (a)

    1/2

    (b)

    -1/2

    (c)

    2

    (d)

    -2

  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 \(\cos(-480^o)\) is

    (a)

    \(\sqrt3\)

    (b)

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

    (c)

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

    (d)

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

  8. If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\) then tan(2A+B) is equal to

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    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. \(\frac{d}{dx}(a^x)=\)

    (a)

    \(\frac { 1 }{ x\log { \begin{matrix} a \\ e \end{matrix} } } \)

    (b)

    aa

    (c)

    \(x\log { \begin{matrix} a \\ e \end{matrix} } \)

    (d)

    \({ a }^{ x }\log { \begin{matrix} a \\ e \end{matrix} } \)

  11. The demand function is always

    (a)

    Increasing function

    (b)

    Decreasing function

    (c)

    Non-decreasing function

    (d)

    Undefined function

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

    (a)

    5000

    (b)

    100

    (c)

    1000

    (d)

    200

  13. An annuity in which payments are made at the beginning of each payment period is called

    (a)

    Annuity due

    (b)

    An immediate annuity

    (c)

    perpetual annuity

    (d)

    none of these

  14. 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

  15. Let a sample space of an experiment be S = { E1,E2,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

    (a)

    0

    (b)

    1

    (c)

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

    (d)

    \(\frac { 1 }{ 3 } \)

  16. Probability of an impossible event is

    (a)

    1

    (b)

    0

    (c)

    0.2

    (d)

    0.5

  17. Correlation co-efficient lies between

    (a)

    0 to ∞

    (b)

    -1 to +1

    (c)

    -1 to 0

    (d)

    -1 to ∞

  18. The coefficient of correlation describes

    (a)

    the magnitude and direction

    (b)

    only magnitude

    (c)

    only direction

    (d)

    no magnitude and no direction

  19. In the context of network, which of the following is not correct

    (a)

    A network is a graphical representation

    (b)

    A project network cannot have multiple initial and final nodes

    (c)

    An arrow diagram is essentially a closed network

    (d)

    An arrow representing an activity may not have a length and shape

  20. Given an L.P.P maximize Z=2x1+3x2 subject to the constrains x1+x2≤1, 5x1+5x2≥0 and x1≥0, x2≥0 using graphical method, we observe

    (a)

    No feasible solution

    (b)

    unique optimum solution

    (c)

    multiple optimum solution

    (d)

    none of these

  21. 7 x 2 =14
  22. Find |AB| if \(A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix}and \begin{bmatrix} 3&0\\1&-2 \end{bmatrix}\)

  23. If nPr = 360, find n and r.

  24. Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

  25. In any quadrilateral ABCD, prove that sin (A + B) + sin (C + D) = 0

  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. Find the number of shares which will give an annual income of Rs 3,600 from 12% stock of face value Rs 100.

  29. A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

  30. From the following data calculate the correlation coefficient Σxy=120, Σx2=90, Σy2=640

  31. Draw a network diagram for the project whose activities and their predecessor relationships are given below

    Activity A B C D E F
    Predecessor activity - - D A B C
  32. 7 x 3 = 21
  33. Find the inverse of the following matrices \(\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5 \end{matrix} \right] \)

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

  35. Find the slope of the lines which make an angle of 45° with the line 3x - y + 5 = 0.

  36. Prove that  \(2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 } \)

  37. Differentiate the following with respect to x .
    x3 ex

  38. For the production function P = \(4L^{ \frac { 3 }{ 4 } }K^{ \frac { 1 }{ 4 } }\) verify Euler’s theorem

  39. A sum of Rs.1000 is deposited at the beginning of each quarter in a S.B. account that pays C.I 8% compounded quarterly. Find the account at the end of 3 years.

  40. From the following data compute the value of Harmonic Mean.

    Marks 10 20 30 40 50
    No. of students 20 30 50 15 5
  41. Find the co-variance and co-efficient of correlation for the following data:
    n=10, \(\sum\)x=50, \(\sum\)y=-30, \(\sum\)x2=290, \(\sum\)y2=300 and \(\sum\)xy=-115.

  42. Solve the following LPP graphically.  \(\\ \therefore \quad Maximize\quad Z=3{ x }_{ 1 }+4{ x }_{ 2 }\) 
    subject to the constraints \({ x }_{ 1 }+{ x }_{ 2 }\le 4\quad \quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

  43. 7 x 5 = 35
    1. Two commodities A and B are produced such that 0.4 tonne of A and 0.7 tonne of B are required to produce a tonne of A. Similarly 0.1 tonne of A and 0.7 tonne of B are needed to produce a tonne of B. Write down the technology matrix. If 6.8 tonnes of A and 10.2 tonnes of B are required, find the gross production of both of them.

    2. By the principle of mathematical induction, prove the following.
      4+8+12+......+4n=2n(n+1), for all \(n\in N\).

    1. Resolve into partial factors : \(\frac { { x }^{ 2 }+x+1 }{ { x }^{ 2 }+2x+1 } \)

    2. The profit Rs.y accumulated in thousand in x months is given by y = -x2  +10x - 15. Find the best time to end the project.

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

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

    1. If \(y={ \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ m }\) , then show that (1 + x)2 y2 + xy1 - m2 = 0.

    2. A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5+\(\frac { x }{ 50 } \) where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.

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

    2. a bank pays 8% interest compounded quarterly. Determine the equal deposits to be made at the end of each quarter for 3 years so as to receive Rs.300 at the end of 3 years.

    1. Calculate the geometric mean of the data given below giving the number of families and the income per head of different classes of people in a village of Kancheepuram District.

      Class of people No. of Families Income per head in 1990 (Rs)
      Landlords 1 1000
      Cultivators 50 80
      Landless labourers 25 40
      Money- lenders 2 750
      School teachers 3 100
      Shop-keepers 4 150
      Carpenters 3 120
      Weavers 5 60
    2. The heights ( in cm.) of a group of fathers and sons are given below

      Heights of fathers: 158 166 163 165 167 170 167 172 177 181
      Heights of Sons: 163 158 167 170 160 180 170 175 172 175

      Find the lines of regression and estimate the height of son when the height of the father is 164 cm .

    1. Draw a network diagram for the following activities.

      Activity code A B C D E F G H I J K
      Predecessor activity - A A A B C C C,D E,F G,H I,J
    2. A manufacturer produces two types of steel trunks. He has two machine A and B. For completing, the first type of the trunk requires 3 hours on machine A and 2 hours on machine B, whereas the second type of the trunk requires 3 hours on machine A and 3 hours on machine B. Machines A and B can work at the most for 18 hours and 14 hours per day respectively. He earns a profit of Rs.30 andRs.40 per trunk of the first type and second type respectively. How many trunks of the each type must he make each day to make maximum profit?

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