Annual Exam Model Question Paper 2019 - 2020

9th Standard

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Maths

Time : 02:45:00 Hrs
Total Marks : 100

    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.

    14 x 1 = 14
  1. If U ={x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is

    (a)

    {1, 6, 7, 8, 9}

    (b)

    {1, 2, 3, 4}

    (c)

    {2, 3, 4, 5}

    (d)

    { }

  2. The number of elements of the set {x : x ∈ Z, x2 = I} is ________

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  3. if \(\frac { 1 }{ 7 } \) = \(0.\bar { 142857 } \) then the value of \(\frac { 5 }{ 7 } \)

    (a)

    \(0.\overline { 142857 } \)

    (b)

    \(0.\overline { 714285 } \)

    (c)

    \(0.\overline { 571428 } \)

    (d)

    0.714285

  4. If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

    (a)

    0.285741

    (b)

    0.428571

    (c)

    0.285714

    (d)

    0.574128

  5. The type of the polynomial 4–3x3 is

    (a)

    constant polynomial

    (b)

    linear polynomial

    (c)

    quadratic polynomial

    (d)

    cubic polynomial.

  6. (a-b) (a2+ab+b2)=_________

    (a)

    a+ b+ c- 3abc

    (b)

    a- b2

    (c)

    a+ b3

    (d)

    a3 - b3

  7. The perpendicular line from the centre of the circle to the chord divided the chord in the ratio________

    (a)

    1: 1

    (b)

    1: 2

    (c)

    2: 1

    (d)

    1: 3

  8. The point whose ordinate is 4 and which lies on the y-axis is............

    (a)

    ( 4, 0 )

    (b)

    (0, 4)

    (c)

    (1, 4)

    (d)

    (4, 2)

  9. The distance between the points (4, -1) and the origin is___________

    (a)

    \(\sqrt{24}\)

    (b)

    \(\sqrt{37}\)

    (c)

    \(\sqrt{26}\)

    (d)

    \(\sqrt{17}\)

  10. The mean of a,b,c,d and e is 28. If the mean of a, c and e is 24, then mean of b and d is

    (a)

    24

    (b)

    36

    (c)

    26

    (d)

    34

  11. The mean of the square of first 11 natural number is

    (a)

    26

    (b)

    46

    (c)

    48

    (d)

    52

  12. The value of \(\frac { 2tan30° }{ 1-{ tan }^{ 2 }30° } \) is equal to

    (a)

    cos600

    (b)

    sin600

    (c)

    tan600

    (d)

    sin300

  13. The perimeter of an equilateral triangle is 30 cm. The area is

    (a)

    \(10\sqrt { 3 } \) cm2

    (b)

    \(12\sqrt { 3 } \) cm2

    (c)

    \(15\sqrt { 3 } \) cm2

    (d)

    \(25\sqrt { 3 } \) cm 2

  14. The six faces of the dice are called equally likely if the dice is

    (a)

    Small

    (b)

    Fair

    (c)

    Six-faced

    (d)

    Round

  15. Part II

    Answer any 10 questions. Question no. 28 is compulsory.

    10 x 2 = 20
  16. Find the number of subsets and the number of proper subsets of the following sets.
    X = { x2 : x ∈N, x2 ≤ 100}.

  17. Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
    \(7\over 16\)

  18. Find any five rational numbers between
    (i) \(\frac { 1 }{ 4 } \) and \(1\over 5\)
    (ii) 0.1 and 0.11
    (iii) -1 and -2

  19. Give any two rational numbers lying between 0.5151151115…. and 0.5353353335…

  20. Simplify: (x-2y+3z)(x2+4y2+9z2+2xy+6yz-3xz)

  21. Draw the circumcircle for, An isosceles right triangle having 6 cm as the length of the equal sides.

  22. Show that the line segment joining the mid-points of two sides of a triangle is half of the third side
    (Hint: Place triangle ABC in a clever way such that A is (0,0), B is (2a,0) and C to be (2b,2c). Now consider the line segment joining the mid-points of AC and BC. This will make calculations simpler).

  23. Using section formula, show that the points A (7, -5), B (9, -3) and C (13, 1), are collinear.

  24. A car travels, at an uniform speed. At 2pm it is at a distance of 5 km at 6pm it is at a distance of 120 km. Using section formula, find at what distance it will reach 2 midnight.

  25. Find the mode for the set of values 17, 18, 20, 20, 21, 21, 22, 22.

  26. Find the value of sin 3x. sin 6x. sin 9x when x = 10°

  27. Find the value of cot 15°. cot 30°. cot 45°. cot 60°. cot 75°

  28. Find the surface 'area of a cube whose edge is
    (i) 27 cm
    (ii) 3 cm
    (iii) 6 cm
    (iv) 2.1 cm

  29. 1500 families were surveyed and following data was recorded about their maids at homes

    Type of maids Only part time Only full time Both
    Number of families 860 370 250

    A family is selected at random. Find the probability that the family selected has
    (i) Both types of maids
    (ii) Part time maids
    (iii) No maids

  30. Part III

    Answer any 10 questions. Question no. 42 is compulsory.

    10 x 5 = 50
  31. From the venn-diagram, list the following:

    (i) A
    (ii) B
    (iii) A ∩ B
    (iv) AU B
    (v) A-B
    (vi) B-A
    (vii) (A - B) ∩ (B - A)

  32. Draw: Venn diagram for each of the following:
    (i) \(A\cup (B\cap C)\)
    (ii) \(A\cap (B\cup C)\)
    (iii) \((A\cup B)\cap C\)
    (iv) \((A\cap B)\cup C\)
     

  33. Express the following decimal expression into rational numbers -21.\(21\overline {37}\)

  34. Represent the following numbers in scientific notation:
    (i) (300000)2 x (20000)4
    (ii) (0.000001)11 ÷ (0.005)3
    (iii) \(\left\{ (0.00003 \right\} ^{ 6 }\times (0.00005)^{ 4 }\} \div \{ (0.009)^{ 3 }\times (0.05)^{ 2 }\} \)

  35. Substract \(6\sqrt { 7 } \) from \(9\sqrt { 7 } \) . Is the answer rational or irrational?

  36. Multiply the following polynomials and find the degree of the resultant polynomial:
    p(x)=x2-9 q(x)=6x2+7x-2

  37. Expland the following using identities :(7x+2y)2

  38. Construct the ΔLMN such that LM=7.5cm, MN=5cm and LN=8cm. Locate its centroid.

  39. Plot the following points on a graph sheet by taking the scale as 1cm = 1 unit.
    Find how far the points are from each other?
    A (1,0) and D (4, 0). Find AD and also DA.
    Is AD=DA?
    You plot another set of points and verify your Result.

  40. Find the points which divide the line segment joining A(−11,4) and B(9,8) into four equal parts.

  41. The median of observation 11,12,14,18,x+12,x+4,30,32,35,41 arrenged in ascending order is 24.Find the values of x.

  42. Find the value of sin 64034'.

  43. The lengths of sides of a triangular field are 28 m, 15 m and 41 m. Calculate the area of the field. Find the cost of levelling the field at the rate of ₹ 20 per m2

  44. When a dice is rolled, find the probability to get the number greater than 4?

  45. Part IV

    Answer all the questions

    2 x 8 = 16
    1. Draw and locate the centroid of the triangle ABC where right angle at A, AB = 8 cm and AC = 6 cm.

    2. Find the values of the following:
      (i) (cos00 + sin450 + sin300)(sin900 - cos450 + cos600)
      (ii) tan2600 - 2tan2450 - cot2300 +2sin2300\(\frac { 3 }{ 4 } \) cosec2 450

    1. In a village of 100 families, 65 families buy Tamil newspapers and 55 families buy English newspapers. Find the number of families who buy
      (i) Both Tamil and English newspapers.
      (ii) Tamil newspapers only
      (iii) English newspapers only.

    2. Find the quotient and remainder when  5x3 - 9x2 + 10x + 2 is divided by x + 2 using synthetic division

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