Important Questions Part-IX

9th Standard

Reg.No. :
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Maths

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

Part - A

40 x 1 = 40
1. If A∪B = A∩B, then ________.

(a)

A ≠ B

(b)

A = B

(c)

A ⊂ B

(d)

B ⊂ A

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

(a)

0

(b)

1

(c)

2

(d)

3

3. If n(A $\cup$ B $\cup$ C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A$\cap$B) = 12, n(B$\cap$C) = 18 and n(A$\cap$C) = 15 , then n(A$\cap$B$\cap$C) is ___________

(a)

5

(b)

10

(c)

15

(d)

20

4. Which of the following is true?

(a)

$\left( A\cup B \right) =B\cup A$

(b)

${ \left( A\cup B \right) }^{ ' }{ A }^{ ' }{ -B }^{ ' }$

(c)

${ \left( A\cap B \right) }^{ ' }={ A }^{ ' }\cap { B }^{ ' }$

(d)

$A-\left( B\cap C \right) =\left( A-B \right) \cap \left( A-C \right)$

5. $n(A\cup B\cup C)$=________

(a)

n(A) + n(B) + n(C)

(b)

n(A) + n(b) + n(C) -$n\left( A\cap B\cap C \right)$

(c)

$n\left( A\cap B\cap C \right)$

(d)

n(A) + n(B) + n(C) -$n\left( A\cap B \right)$-$n\left( B\cap A \right) -n\left( A\cap C \right) +n\left( A\cap B\cap C \right)$

6. The number $0.\bar { 3 }$ in the form $\frac { p }{ q }$ where p and q are integers and $q\neq 0$

(a)

$\frac { 33 }{ 100 }$

(b)

$\frac { 3 }{ 10 }$

(c)

$\frac { 1 }{ 3 }$

(d)

$\frac { 3 }{ 100 }$

7. Which one of the following has terminating decimal expansion?

(a)

$\frac { 7 }{ 9 }$

(b)

$\frac { 8 }{ 15 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 5 }{ 32 }$

8. $\left( 0.000729 \right) ^{ \frac { -3 }{ 4 } }\times \left( 0.09 \right) ^{ \frac { -3 }{ 4 } }$ = ______.

(a)

$\frac { { 10 }^{ 3 } }{ { 3 }^{ 3 } }$

(b)

$\frac { { 10 }^{ 5 } }{ { 3 }^{ 5 } }$

(c)

$\frac { { 10 }^{ 2 } }{ { 3 }^{ 2 } }$

(d)

$\frac { { 10 }^{ 6 } }{ { 3 }^{ 6 } }$

9. In simple form,$\sqrt [ 3 ]{ 54 }$ is ?

(a)

$3\sqrt [ 3 ]{ 2 }$

(b)

$3\sqrt { 27 }$

(c)

$3\sqrt { 2 }$

(d)

$\sqrt { 3 }$

10. The length of a square is 1.2$\times$103 m. Its area is_______

(a)

14.4 $\times$ 106

(b)

1.44 $\times$ 106

(c)

0.144 $\times$ 10

(d)

1440

11. Which of the following is a monomial?

(a)

${ 4x }^{ 2 }$

(b)

$a+b$

(c)

$a+b+c$

(d)

$a+b+c+d$

12. The area of a rectangle with length $2l^{ 2 }m$ and breadth $3l^{ 2 }m$ is_______________________

(a)

$6l^{ 3 }m^{ 3 }$

(b)

$l^{ 3 }m^{ 3 }$

(c)

$2l^{ 3 }m$

(d)

$4l^{ 3 }m^{ 3 }$

13. The degree of the polynomial $\sqrt { 2 } { x }^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5x^{ 3 }$ is _______________

(a)

2

(b)

3

(c)

4

(d)

5

14. (a+b−c)2 is equal to ______.

(a)

(a−b+c)2

(b)

(−a−b+c)2

(c)

(a+b+c)2

(d)

(a-b-c)2

15. If one of the factor of x2-9x+18 is (x-3) then the other factor is_________

(a)

x-9

(b)

x+6

(c)

(x-6)

(d)

x-18

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. The angle sum of a convex polygon with number of sides 7 is ________

(a)

900°

(b)

1080°

(c)

1444°

(d)

720°

18. The point of concurrency of the medians of a triangle is known as __________

(a)

circumcentre

(b)

incentre

(c)

orthocentre

(d)

centroid

19. ABCD is a parallelogram as shown. Find x and y.

(a)

1, 7

(b)

2, 6

(c)

3, 5

(d)

4, 4

20. In the figure, O is the centre of the circle and ㄥACB = 40° then ㄥAOB = ________.

(a)

80°

(b)

85°

(c)

70°

(d)

65°

21. In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ㄥQRS = 100°, then ㄥTVS = ______.

(a)

80°

(b)

100°

(c)

70°

(d)

90°

22. 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

23. Point (0, –7) lies ________

(a)

on the x-axis

(b)

(c)

on the y-axis

(d)

24. On which quadrant does the point (- 4, 3) lie?

(a)

I

(b)

II

(c)

III

(d)

IV

25. 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)

26. A point which lies in the III quadrant is__________________

(a)

(5, 4)

(b)

(5, - 4)

(c)

(-5, - 4)

(d)

(-5,4)

27. The point (0, -3) lies on _______________

(a)

+ ve x-axis

(b)

+ ve y-axis

(c)

- ve x-axis

(d)

- ve y-axis

28. In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.

(a)

1 :3

(b)

2 :5

(c)

3 :1

(d)

5 :2

29. The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value of discarded number is _______.

(a)

101

(b)

100

(c)

99

(d)

98

30. For which set of numbers do the mean, median and mode all have the same values?

(a)

2, 2, 2, 4

(b)

1, 3, 3, 3, 5

(c)

1, 1, 2, 5, 6

(d)

1, 1, 2, 1, 5

31. 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

32. Which one of the following is not a measure of central tendency?

(a)

Mean

(b)

Range

(c)

Median

(d)

Mode

33. The mean of the first 10 whole number is

(a)

4

(b)

4.5

(c)

5

(d)

5.5

34. Find the mean of the prime factors of 165 _____________

(a)

5

(b)

11

(c)

13

(d)

55

35. The value of $\frac { 1-{ tan }^{ 2 }{ 45 }^{ 0 } }{ 1+{ tan }^{ 2 }{ 45 }^{ 0 } }$ is ________.

(a)

2

(b)

1

(c)

0

(d)

$\frac { 1 }{ 2 }$

36. The value of tan 1° tan 2° tan 3°...tan 89° is ________.

(a)

0

(b)

1

(c)

2

(d)

$\frac { \sqrt { 3 } }{ 2 }$

37. 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

38. If the ratio of the sides of two cubes are 2:3, then ratio of their surface areas will be _______.

(a)

4 : 6

(b)

4 : 9

(c)

6 : 9

(d)

16 : 36

39. If A is any event in S and its complement is A' then, P(A′) is equal to _______.

(a)

1

(b)

0

(c)

1-A

(d)

1-P(A)

40. A collection of one or more outcomes of an experiment is called _______.

(a)

Event

(b)

Outcome

(c)

Sample point

(d)

None of the above

41. Part - B

25 x 2 = 50
42. Are A = {x : x ∈ N, 4 ≤ x ≤ 8} and B = { 4, 5, 6, 7, 8} equal sets?

43. If U = {a, b, c, d, e, f, g, h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets. (B′)′

44. Write the following in "Roster" form?
(a) A = set of the months having 31 days.
(b) B = {x : x is a natural number of 2 digits divisible by 13}
(c) C = {set of vowels in the word "father"}
(d) D = {x : 5 < x < 10 ; x ∈ N}
(e) E = {x: x is a square natural number less than 16}

45. State Associative property of sets.

46. Express the following in the form ${p\over q},$ where p and q are integers and q $\ne$ 0.
$0.\overline {47}$

47. Write the following in the form of 5n?
625

48. Write the following in scientific notation: (50000000)4

49. Find the value of ${ 729 }^{ \frac { -5 }{ 6 } }$

50. Factorise the following: a3+b3-3ab+1

51. ABCD is a cyclic quadrilateral such that $\angle$A = (4y + 20) ° , $\angle$B = (3y –5) ° , $\angle$C =(4x) ° and $\angle$D = (7x + 5) ° . Find the four angles.

52. Solve $\cfrac { 17(2-x)-5(x+12) }{ 1-7x } =8$

53. Objective: To find the mid-point of a line segment using paper folding
Procedure: Make a line segment on a paper by folding it and name it PQ. Fold the line segment PQ in such a way that P falls on Q and mark the point of intersection of the line segment and the crease formed by folding the paper as M. M is the midpoint of PQ.

54. A chord is 12 cm away from the centre of the circle of radius 15 cm. Find the length of the chord

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

56. Find the value of Xo

57. The centre of a circle is (−4, 2). If one end of the diameter of the circle is (−3, 7) then find the other end.

58. Find the coordinates of the point which divides the line segment joining the points (3, 1) and (5, 13) internally in the ratio 3 : 5.

59. In a rice mill, seven labours are receiving the daily wages of Rs. 500, Rs. 600, Rs. 600, Rs. 800, Rs. 800, Rs. 800 and Rs. 1000, find the modal wage

60. In a week, temperature of a certain place is measured during winter are as follows 26oC, 24oC, 28oC, 31oC, 30oC, 26oC, 24oC. Find the mean temperature of the week.

61. If cos A = $\frac { 2x }{ 1+{ x }^{ 2 } }$ then find the values of sinA and tan A in terms of x.

62. Find the six trigo'nometric ratios of the angle 0 using the diagram

63. The volume of a container is 1440 m3. The length and breadth of the container are 15 m and 8 m respectively. Find its height.

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

65. The probability of guessing the correct answer to a certain question is $\frac { x }{ 3 }$. If the probability of not guessing the correct answer is $\frac { x }{ 5 }$, then find the value of x.

66. Two dice are thrown simultaneously. Find the probability of getting
(i) an even number as the sum.
(ii) atotal of at least 10
(iii) a doublet of even number.

67. Part - C

15 x 3 = 45
68. In a college, 240 students play cricket, 180 students play football, 164 students play hockey, 42 play both cricket and football, 38 play both football and hockey, 40 play both cricket and hockey and 16 play all the three games. If each student participate in atleast one game, then find
(i) the number of students in the college
(ii) the number of students who play only one game.

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

70. If $\sqrt{2}$ =1.414, $\sqrt{3}$ = 1.732, $\sqrt{5}$ = 2.236, $\sqrt{10}$ = 3.162 then find the values of the following correct to 3 places of decimals.
(i) $\sqrt { 40 } -\sqrt { 20 }$
(ii) $\sqrt { 300 } -\sqrt { 90 } -\sqrt { 8 }$

71. Write in scientific notation: (500000)5$\times$(3000)3

72. Find the quotient and remainder of the following.
(8x3 – 1)÷(2x–1)

73. In (4x + 3) a factor of 4x+ 15x- 31 x -30

74. ABCD is a rectangle and P, Q, Rand S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

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

76. Show that the following points taken in order form an equilateral triangle in each case
$A\left( \sqrt { 3 } ,2 \right) ,B\left( 0,1 \right) ,C\left( 0,3 \right)$

77. Read the coordinates of the vertices of the triangle ABC with the following figure.

78. Find the mean, median and mode of the following distribution:

 Weight(in kgs) Number of students 25-34 35-44 45-54 55-64 65-74 75-84 4 8 10 14 8 6
79. Find the six trigonometric ratios of the angle $\theta$ using the given diagram.

80. 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 Rs. 80 per m2.

81. The probability that it will rain tomorrow is $\\ \frac { 91 }{ 100 }$. What is the probability that it will not rain tomorrow?

82. Part - D

10 x 5 = 50
83. 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.

84. Find any three rational numbers between $\frac { 1 }{ 2 }$ and $\frac { 1 }{ 5 }$

85. Represent $-\frac { 2 }{ 11 } ,-\frac { 5 }{ 11 } and-\frac { 9 }{ 11 }$on the number line.

86. Find the quotient and remainder when 4x3 + 6x2 + 7x + 2 is divided by x - 2

87. Diagonal AC of a parallelogram ABCD bisects ㄥA. Show that
(i) it bisects ㄥC also
(ii) ABCD is a rhombus.

88. Construct  $\triangle$ABC in which AB = BC = 8cm and $\angle$B =70o. Locate its in centre and draw the incircle

89. Find the type of triangle formed by (-1, -1), (1, 1) and ($-\sqrt{13},\sqrt{13}$)

90. Calculate the mean of the following distribution using Assumed Mean Method

 Class Interval 0-10 10-20 20-30 30-40 40-50 Frequency 5 7 15 28 8
91. Find the area of a quadrilateral ABCD whose sides are AB = 8cm, BC = 15 cm, CD = 12 cm, AD = 25 cm and = 90°.