Annual Exam Model Question Paper 2019 - 2020 Part-VII

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. The shaded region in the adjacent diagram represents

    (a)

    (A∪B)′

    (b)

    (A∩B)′

    (c)

    A′∩B′

    (d)

    A∩B

  2. Sets having the same number of elements are called ___________

    (a)

    overlapping sets

    (b)

    disjoints sets

    (c)

    equivalent sets

    (d)

    equal sets

  3. Which one of the following is an irrational number

    (a)

    \(\sqrt { 25 } \)

    (b)

    \(\sqrt { \frac { 9 }{ 4 } } \)

    (c)

    \(\frac { 7 }{ 11 } \)

    (d)

    \(\pi\)

  4. Rationalising the denominator  \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)

    (a)

    3

    (b)

    \(\cfrac { { 3 }^{ \frac { 2 }{ 3 } } }{ 3 } \)

    (c)

    \(\sqrt { 3 } \)

    (d)

    \(\sqrt [ 3 ]{ 3 } \)

  5. The Auto fare is found as minimum rs 25 for 3 kilometer and thereafter rs12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

    (a)

    c = 25 + n

    (b)

    c = 25 + 12n

    (c)

    c = 25 + (n–3)12

    (d)

    c = (n–3)12

  6. Divide x3-4x2+6x by "x" the result is _____________________

    (a)

    \(x^{ 2 }+4x-6\)

    (b)

    \(x^{ 2 }-4x-6\)

    (c)

    \(x^{ 2 }-4x+6\)

    (d)

    \(x^{ 2 }+4x+6\)

  7. Orthocentre of a triangle is the point of concurrency of _______

    (a)

    medians

    (b)

    altitudes

    (c)

    angle bisectors

    (d)

    perpendicular bisectors of side

  8. The distance between the points (-1, 2) and (3, 2) is____________

    (a)

    \(\sqrt{14}\)

    (b)

    \(\sqrt{15}\)

    (c)

    4

    (d)

    0

  9. If (1,−2), (3,6), (x,10) and (3,2) are the vertices of the parallelogram taken in order, then the value of x is

    (a)

    6

    (b)

    5

    (c)

    4

    (d)

    3

  10. Find the mean of the prime factors of 165.

    (a)

    5

    (b)

    11

    (c)

    13

    (d)

    55

  11. Let be the mid point and b be the upper limit of a class in a continuous frequency distribution.The lower limit of the class is

    (a)

    2m-b

    (b)

    2m+b

    (c)

    m-b

    (d)

    m-2b

  12. If cos A = \(\frac { 3 }{ 5 } \), them the value of tan A is

    (a)

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

    (b)

    \(\frac { 3 }{ 4 } \)

    (c)

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

    (d)

    \(\frac { 4 }{ 3 } \)

  13. The total surface area of a cuboid is

    (a)

    4a2 sq. units

    (b)

    6a2 sq. units

    (c)

    2(l + b)h sq. units

    (d)

    2(lb + bh + lh) sq. units

  14. If A is any event in S then its complement P(A′) is equal to

    (a)

    1

    (b)

    0

    (c)

    1-A

    (d)

    1-P(A)

  15. Part II

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

    14 x 2 = 28
  16. If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

  17. Write the following in the form of 5n:
    \(\frac{1}{5}\)

  18. Multiply \(\sqrt [ 3 ]{ 40 } \) and \(\sqrt [ 3 ]{ 16 } \) .

  19. Can you reduce the following to surds of same order \(\sqrt [ 4 ]{ 5 } \)

  20. If f(x) = x2 - 4x + 3, find the values of f(1), f(-1), f(2), f(3). Also find the zeros of the polynomial f(x).

  21. Find the supplement of the following angles.
    Right angle

  22. A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2,−3) and (2,1) respectively, then find the coordinates of C.

  23. A, Band C are vertices of \(\Delta\)ABC. D, E and F are mid points of sides AB, BC and AC respectively. If the coordinates of A, D and Fare (-3, 5), (5, 1) and (-5, -1) respectively. Find the coordinates of B, C and E.

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

  25. A set of numbers consists of five 4’s, four 5’s, nine 6’s,and six 9’s. What is the mode.

  26. If 3 cot\(\theta\) =, then find the value of  \(\cfrac { 3cos\theta -4sin\theta }{ 5sin\theta +4cos\theta } \)

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

  28. Find the area of an equilateral triangle whose perimeter is 150 m.

  29. In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

  30. Part III

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

    14 x 3 = 42
  31. If A = {b,c,e,g,h} , B = {a,c,d,g,i} and C = {a,d,e,g,h} , then show that \(A-(B\cap C)=(A-B)\cup (A-c)\).

  32. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : intersection of sets

  33. Express the following decimal expression into rational numbers \(3.1\overline { 7 } \)

  34. Rationalise the denominator and simplify \(\frac { \sqrt { 5 } }{ \sqrt { 6 } +2 } -\frac { \sqrt { 5 } }{ \sqrt { 6 } -2 } \)

  35. Simplify;\(\sqrt { 44 } +\sqrt { 99 } -\sqrt { 275 } \)

  36. Show that (x-3) is a factor of x+ 9x- x - 105

  37. Solve by cross-multiplication method
    (i) 8x − 3y = 12 ; 5x = 2y + 7
    (ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
    (iii) \(\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0\)

  38. Draw and locate the centroid of the triangle ABC where right angle at A, AB = 4cm and AC = 3cm

  39. Show that the point (11,2) is the centre of the circle passing through the points (1,2), (3,–4) and (5, -6)

  40. the mid-point formula to show that the mid-point of the hypotenuse of a right angled triangle is equidistant from the vertices (with suitable points).

  41. If the mean of the following data is 20.2, then find the value of p

    Marks 10 15 20 25 30
    No.of students 6 8 p 10 6

     

  42. i) If cosecA = sec340, find A (ii) If tanB = cot 470, find B.

  43. cube has the total surface area of 486 cm2. Find its lateral surface area.

  44. In an office, where 42 staff members work, 7 staff members use cars, 20 staff members use two-wheelers and the remaining 15 staff members use cycles. Find the relative frequencies.

  45. Part IV

    Answer all the questions

    4 x 5 = 20
  46. If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

  47. Factorise  2x3- x2 - 12x - 9 into linear factors
     

  48. In the given Fig. if AB = 2, BC = 6, AE = 6, BF = 8, CE = 7, and CF = 7, compute the ratio of the area of quadrilateral ABDE to the area of ΔCDF

  49. Draw an equilateral triangle of side 8 cm and locate its incentre .Also   draw the incircle

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