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Important Questions - Part-VI

9th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 60

    Part - A

    40 x 1 = 40
  1. The set does not have a proper subset is __________

    (a)

    Finite set

    (b)

    Infinite set

    (c)

    Null set

    (d)

    Singleton set

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

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  3. If A is a proper subset ofB, then A ∩ B = __________

    (a)

    A

    (b)

    B

    (c)

    Ø

    (d)

    A U B

  4. For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is

    (a)

    P-(Q\(\cup \)R)

    (b)

    (P\(\\ \cap \)Q)-R

    (c)

    (P-Q)\(\cup \)(P-R)

    (d)

    (P-Q)\(\\ \cap \)(P-R)

  5. If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is

    (a)

    10

    (b)

    15

    (c)

    25

    (d)

    30

  6. Which one of the following has a terminating decimal expansion?

    (a)

    \(\frac { 5 }{ 64 } \)

    (b)

    \(\frac { 8 }{ 9 } \)

    (c)

    \(\frac { 14 }{ 15 } \)

    (d)

    \(\frac { 1 }{ 12 } \)

  7. The decimal form of -\(\frac { 3 }{ 4 } \) is_______________

    (a)

    - 0.75

    (b)

    - 0.50

    (c)

    -0.25

    (d)

    - 0.125

  8. Which of the following are irrational numbers?
    \(\sqrt { 2+\sqrt { 3 } } \)
    \(\sqrt [ 3 ]{ 5+\sqrt { 7 } } \)
    \(\sqrt { 8-\sqrt [ 3 ]{ 8 } } \)
    \(\sqrt { 4+\sqrt { 25 } } \)

    (a)

    (ii), (iii) and (iv)

    (b)

    (i), (ii) and (iv)

    (c)

    (i), (ii) and (iii)

    (d)

    (i), (iii) and (iv)

  9. Which one of the following is not a rational number?

    (a)

    \(\sqrt { \frac { 8 }{ 18 } } \)

    (b)

    \(\frac { 7 }{ 3 } \)

    (c)

    \(\sqrt{0.01}\)

    (d)

    \(\sqrt{13}\)

  10. Which of the following is not an irrational number?

    (a)

    \(\sqrt { 2 } \)

    (b)

    \(\sqrt { 5 } \)

    (c)

    \(\sqrt { 3 } \)

    (d)

    \(\sqrt { 25 } \)

  11. Which of the following is a monomial?

    (a)

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

    (b)

    \(a+b\)

    (c)

    \(a+b+c\)

    (d)

    \(a+b+c+d\)

  12. 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)

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

  13. If p(a)= 0 then (x-a) is a ___________ of p(x)

    (a)

    divisor

    (b)

    quotient

    (c)

    remainder

    (d)

    factor

  14. Zero of (7+4x) is_______

    (a)

    \(\cfrac { 4 }{ 7 } \)

    (b)

    \(\cfrac { -7 }{ 4 } \)

    (c)

    7

    (d)

    4

  15. Quadratic polynimial may have maximum of______linear factors

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  16. The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is

    (a)

    k = 3

    (b)

    k = 2

    (c)

    k = 4

    (d)

    k = -3

  17. ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles are

    (a)

    6

    (b)

    8

    (c)

    4

    (d)

    12

  18. If the diagonal of a rhombus are equal, then the rhombus is a

    (a)

    Parallelogram but not a rectangle

    (b)

    Rectangle but not a square

    (c)

    Square

    (d)

    Parallelogram but not a square

  19. What is the name of a regular polygon of six sides?

    (a)

    Square

    (b)

    Equilateral triangle

    (c)

    Regular hexagon

    (d)

    Regular octagon

  20. The angle subtend by a semicircle at the centre is_________

    (a)

    60o

    (b)

    90°

    (c)

    1200

    (d)

    180o

  21. If sum of two opposite angles of a cyclic quadrilateral is_________

    (a)

    45°

    (b)

    90°

    (c)

    180°

    (d)

    360°

  22. The distance between the longest chord of a circle and the centre is________

    (a)

    1

    (b)

    0

    (c)

    2

    (d)

    5

  23. The point whose abscissa is 5 and lies on the x-axis is__________

    (a)

    (-5, 0)

    (b)

    (5,5)

    (c)

    (0,5)

    (d)

    (5,0)

  24. A point which lies in the III quadrant is__________________

    (a)

    (5, 4)

    (b)

    (5, - 4)

    (c)

    (-5, - 4)

    (d)

    (-5,4)

  25. A point on the y-axis is ________________

    (a)

    (1, 1)

    (b)

    (6,0)

    (c)

    (0,6)

    (d)

    (-1, -1)

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

    (a)

    \(\sqrt{24}\)

    (b)

    \(\sqrt{37}\)

    (c)

    \(\sqrt{26}\)

    (d)

    \(\sqrt{17}\)

  27. If the coordinates of one end of a diameter of a circle is (3,4) and the coordinates of its centre is (−3,2), then the coordinate of the other end of the diameter is

    (a)

    (0,−3)

    (b)

    (0,9)

    (c)

    (3,0)

    (d)

    (−9,0)

  28. The mid-point of the line joining (−a,2b) and (−3a,−4b) is

    (a)

    (2a,3b)

    (b)

    (−2a, −b)

    (c)

    (2a,b)

    (d)

    (−2a, −3b)

  29. The algebraic sum of the deviations of a set of n values from their mean is

    (a)

    0

    (b)

    n-1

    (c)

    n

    (d)

    n+1

  30. The median of the first 10 whole numbers is

    (a)

    4

    (b)

    4.5

    (c)

    5

    (d)

    5.5

  31. For which set of number do the mean,median and mode all have the same valuas?

    (a)

    2,2,2,4

    (b)

    1,3,3,3,5

    (c)

    1,1,2,5,6

    (d)

    1,1,2,1,5

  32. The mean of the first 10 whole number is

    (a)

    4

    (b)

    4.5

    (c)

    5

    (d)

    5.5

  33. The mean of set of numbers is \(\bar{x}\) If each number is multiplied by z, the mean is

    (a)

    \(\bar{X}+z\)

    (b)

    \(\bar{X}-z\)

    (c)

    \(z\bar{X}\)

    (d)

    \(\bar{X}\)

  34. Find the mean of the prime factors of 165

    (a)

    5

    (b)

    11

    (c)

    13

    (d)

    55

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

    (a)

    cos600

    (b)

    sin600

    (c)

    tan600

    (d)

    sin300

  36. Given that sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and cos \(\beta\) = \(\frac { 1 }{ 2 } \), then the value of \(\alpha\) + \(\beta\) is

    (a)

    00

    (b)

    900

    (c)

    300

    (d)

    600

  37. The lateral surface area of a cube of side 12 cm is

    (a)

    144 cm2

    (b)

    196 cm2

    (c)

    576 cm2

    (d)

    664 cm2

  38. If the lateral surface area of a cube is 600 cm2, then the total surface area is

    (a)

    150 cm2

    (b)

    400 cm2

    (c)

    900 cm2

    (d)

    1350 cm2

  39. The probability based on the concept of relative frequency theory is called

    (a)

    Empirical probability

    (b)

    Classical probability

    (c)

    Both (1) and (2)

    (d)

    Neither (1) nor (2)

  40. A letter is chosen at random from the word “STATISTICS”. The probability of getting a vowel is

    (a)

    \(\frac { 1 }{ 10 } \)

    (b)

    \(\frac { 2 }{ 10 } \)

    (c)

    \(\frac { 3 }{ 10 } \)

    (d)

    \(\frac { 4 }{ 10 } \)

  41. Part - B

    25 x 2 = 50
  42. In a party of 60 people, 35 had Vanilla ice cream, 30 had Chocolate ice cream. All the people had at least one ice cream. Then how many of them had,
    (i) both Vanilla and Chocolate ice cream.
    (ii) only Vanilla ice cream.
    (iii) only Chocolate ice cream.

  43. Identify the following sets as finite or infinite.
    Y = The set of all straight lines passing through a point.

  44. In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics only

  45. State the formula to find \(n\left( A\cup B\cup C \right) \)

  46. Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
    \({17\over 200}\)

  47. Express the following in the form 2n:
    32

  48. Express the following in the form 2n:
    \(\sqrt{2}\)

  49. Express the following in the form 3n: 27

  50. Find the total savings of a boy who saves Rs. (4x - 6y), Rs. (6x + 2y) , Rs. (4y - x) and Rs. (y - 2x) for four consecutive days

  51. Factorise the following expressions: 2y3+y2-2y-1

  52. Factorise the following: m4-7m2+1

  53. Find the complement of the following angles (1°= 60′ minutes, 1′ = 60′′ seconds)
     27°

  54. In the given diagram PQRS is a parallelogram.
    ㄥS = 4x - 60, ㄥQ = 30 - x. Find the angles of P and R.

  55. Draw an equilateral triangle of side 6.5 cm and locate its incentre. Also draw the incircle

  56. The radius of a circle 15 em and the length of one of its chord is 24 cm. Find the distance of the chord from the centre.

  57. Find the distance between the following pairs of points. (3,– 9) and (–2, 3)

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

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

  60. Find the mode of the given data:3.1,3.2,3.3,2.1,1.3,3.3,3.1

  61. In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree (that is \( )  measures 42° and the distance to the tree is 60 metres. Find the height of the tree.

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

  63. The volume of a cuboid is 1800 cm3. If its length is 15 cm and height 12 cm, then find the breadth of the cuboid.

  64. The outer dlmensions of a closed wooden box are 10 cm by 8 cm by 7 cm, Thickness of the wood is 1 cm3. Find the total cost of wood required to make box if 1 cm3 of wood costs Rs.2.00?

  65. A manufacturer tested 7000 LED lights at random and found that 25 of them were defective. If a LED light is selected at random, what is the probability that the selected LED light is a defective one.

  66. An urn contains 10 red and 8 white balls. One ball is drawn at random. Find the probability, that the ball drawn is white.

  67. Part - C

    15 x 3 = 45
  68. Given that A = {1,3,5,7} B = {1,2,4,6,8}. Find (i) AΔB and (it) BΔA

  69. In a mathematics class,20 children forgot to bring their rulers,17 children forgot to bring their pencil and 5 children forgot to bring both ruler and pencil. Then find the number of children
    (i) who forgot to bring only pencil .
    (ii) who forgot to bring only ruler .
    (iii) in the class

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

  71. Write in scientific notation:(500000)5X(3000)3

  72. Expland the following using identities :(4a+3b) (4a-3b)

  73. Solve the system of linear equations x + 3y = 16 and 2x − y = 4 by substitution method.

  74. The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.

  75. In the given figure, ㄥCAB=25°, find ㄥBDC, ㄥDBAand ㄥCOB

  76. Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot the points and find the coordinates of the fourth vertex.

  77. If (x,3), (6,y), (8,2) and (9,4) are the vertices of a parallelogram taken in order, then find the value of x and y.

  78. Find the Arithmetic Mean of the following data using Step Deviation Method:

    Age 15-19 20-24 25-29 30-34 35-39 40-44
    No. of persons 4 20 38 24 10 9
  79. The mean of five positive integers is twice their median. If four of the integers are 3, 4, 6, 9 and median is 6, then find the fifth integer

  80. If sec \(\theta\) = \(\frac { 13 }{ 5 } \), then show that \(\frac { 2sin\theta -3cos\theta }{ 4sin\theta -9cos\theta } \) = 3

  81. The length, breadth and height of a hall are 25 m, 15 m and 5 m respectively. Find the cost of renovating its floor and four walls at the rate of \(\triangle\)80 per m2.

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

  83. Part - D

    10 x 5 = 50
  84. If U = {x :x \(\in \)  Z, -3 \(\le \) x \(\le \) 9 },A = {x : x = 2P +1, \(\in \) Z, -2 \(\le \) P\(\le \) 3}, B ={x : x = q + 1, q \(\in \) Z, 0 \(\le \) q \(\le \) 3}, verify De Morgan's law's for complementation.

  85. Find any  seven rational numbers between \(\frac { 5 }{ 8 } \) and \(\frac { 5 }{ 6 } \)

  86. Represent \(-\frac { 2 }{ 11 } ,-\frac { 5 }{ 11 } and-\frac { 9 }{ 11 } \)on the number line.

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

  88. Find the angle of the given cyclic quadrilateral ABCD in the figure.

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

  90. Show that the point (3, -2), (3, 2), (-1, 2) and (-1, -2) taken in order are the vertices of a square.

  91. Find the mode of the following data

    Marks 0-10 10-20 20-30 30-40 40-50
    Number of students 22 38 46 34 20
  92. Find the mean,median and mode of the following distribution

    Weight (in kgs) 25-34 35-44 45-54 55-64 65-74 75-84
    Number of students 4 8 10 14 8 6
  93. Find the area of a quadrilateral ABCD whose sides are AB = 8cm, BC = 15 cm, CD = 12 cm, AD = 25 cm and = 90°.

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