#### Important Questions Part-V

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. From the adjacent diagram n[P(AΔB)] is

(a)

8

(b)

16

(c)

32

(d)

64

3. The set does not have a proper subset is __________

(a)

Finite set

(b)

Infinite set

(c)

Null set

(d)

Singleton set

4. $\left[ n\left( A\cup B\cup C \right) ^{ ' } \right]$=_______

(a)

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

(b)

$n\left( U \right) -n\left( A\cup B\cup C \right)$

(c)

n(U)

(d)

$\Phi$

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. 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. An irrational number between 2 and 2.5 is

(a)

$\sqrt { 11 }$

(b)

$\sqrt { 5 }$

(c)

$\sqrt { 2.5 }$

(d)

$\sqrt { 8 }$

8. The rational number lying between $\frac { 1 }{ 5 }$ and $\frac { 1 }{ 2 }$ is___________.

(a)

$\frac { 7 }{ 20 }$

(b)

$\frac { 2 }{ 10 }$

(c)

$\frac { 2 }{ 7 }$

(d)

$\frac { 3 }{ 10 }$

9. $\sqrt [ 4 ]{ 405 } =h\sqrt [ 4 ]{ 5 }$, then h=

(a)

5

(b)

4

(c)

2

(d)

3

10. Rationalising the denominator  $\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } }$

(a)

3

(b)

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

(c)

$\sqrt { 3 }$

(d)

$\sqrt [ 3 ]{ 3 }$

11. The root of the polynomial equation 2x + 3 = 0 is

(a)

$\frac{1}{3}$

(b)

$-\frac{1}{3}$

(c)

$-\frac{3}{2}$

(d)

$-\frac{2}{3}$

12. The roots of the polynominal equation ${ x }^{ 2 }+2x=0$are_______________

(a)

x=0, 2

(b)

x=1, 2

(c)

x=1, -2

(d)

x=0, -2

13. If x - 2 is a factor of q(x), then the remainder is___________

(a)

q(-2)

(b)

x - 2

(c)

0

(d)

-2

14. The polynomial whose factors are (x+2)(x+3)is_____

(a)

x+ 5x + 6

(b)

x- 4

(c)

x- 9

(d)

x+ 6x + 5

15. Degree of the .linear polynimial is ________

(a)

1

(b)

2

(c)

3

(d)

4

16. Which of the following is a linear equation

(a)

$x+\frac { 1 }{ x } =2$

(b)

x(x −1) = 2

(c)

3x+5=$\frac { 2 }{ 3 }$

(d)

x3 - x =5

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

(a)

Square

(b)

Equilateral triangle

(c)

Regular hexagon

(d)

Regular octagon

18. In a parallelogram $\angle{A}:\angle{B}=1:2$ Then ㄥA ............

(a)

30°

(b)

60°

(c)

45°

(d)

90°

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, ABCD is a cyclic quadrilateral in which DC produced to E and CF is drawn parallel to AB such that ㄥADC=80° and ㄥECF=20°, then ㄥBAD=?

(a)

100°

(b)

20°

(c)

120°

(d)

110°

21. In the given figure, If OP=17cm PQ=30, cm and OS is perpendicular to PQ, then RS is

(a)

10cm

(b)

6cm

(c)

7cm

(d)

9cm.

22. The angle subtend by equal chords of a circle at the centre is________

(a)

Complementary

(b)

Supplementary

(c)

equal

(d)

unequal

23. The distance between the point ( 5, –1 ) and the origin is _________

(a)

$\sqrt { 24 }$

(b)

$\sqrt { 37 }$

(c)

$\sqrt { 26 }$

(d)

$\sqrt { 17 }$

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

(a)

I

(b)

II

(c)

III

(d)

IV

25. A point which lies in the III quadrant is__________________

(a)

(5, 4)

(b)

(5, - 4)

(c)

(-5, - 4)

(d)

(-5,4)

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

(a)

$\sqrt{14}$

(b)

$\sqrt{15}$

(c)

4

(d)

0

27. The centre of a circle is (0, 0). One end point of a diameter is (5, -1), then ______________

(a)

$\sqrt{24}$

(b)

$\sqrt{37}$

(c)

$\sqrt{26}$

(d)

$\sqrt{17}$

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 median of the first 10 whole numbers is

(a)

4

(b)

4.5

(c)

5

(d)

5.5

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

(a)

5

(b)

11

(c)

13

(d)

55

31. The mean of set of seven number is 81.If one of the nimbers is discarded,the mean of remaining number is 78.The value of discarded number is

(a)

101

(b)

100

(c)

99

(d)

98

32. 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

33. 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

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

(a)

26

(b)

46

(c)

48

(d)

52

35. The value of tan72°.tan18° is

(a)

0

(b)

1

(c)

180

(d)

720

36. The value of $\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' }$ is

(a)

0

(b)

2

(c)

1

(d)

-1

37. 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

38. The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is

(a)

280 cm2

(b)

300 cm2

(c)

360 cm2

(d)

600 cm2

39. The probability of an event cannot be

(a)

Equal to zero

(b)

Greater than zero

(c)

Equal to one

(d)

Less than zero

40. 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)

41. Part - B

25 x 2 = 50
42. If S = {square, rectangle, circle, rhombus, triangle}, list the elements of the following subset of S.
The set of shapes in which the sum of all interior angles is 1800.

43. Using the given Venn diagram, write the elements of
A∪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. Let U= {x : -3 : << 4} A = {-1,2,3} B = {0,1,2,3} C = {-3;-2,-1,0,1,2}. Find (i) A' UB' (ii) (A ∩ B)' (iii) (A ⋂ C)'

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:
$\sqrt{8}$

48. Express the following in the form 3n$\sqrt { 27 }$

49. Find any 3 irrational numbers between 0.12 and 0.13.

50. Write the coefficient of xand x in each of the following polynomials $6-{ 2x }^{ 2 }+3x^{ 3 }-\sqrt { 7 } x$

51. Expand the following: (2x+3y+4z)2

52. Solve using the method of substitution.
5x - y = 5 , 3x +y = 11

53. In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ㄥDBC=40° and ㄥBAC=60°

54. In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8cm and CD = 6cm. If OM⊥AB and OL⊥CD distance between LM is 7cm. Find the radius of the circle?

55. 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.

56. Find the value of Xo

57. Find the coordinates of the point which divides the line segment joining the points A(4,−3) and B(9,7) in the ratio 3:2.

58. 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.

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

60. In a week, temperature of a certain place is measured during winter are as follows 260C,240C,280C,310C,260C.Find the mean temperatureof the week.

61. Find the value of the following:
$\left( \frac { cos47° }{ sin43° } \right) +\left( \frac { sin72° }{ cos18° } \right) =2cos^{ 2 }45°$

62. From the given figure, find all the trigonometric ratios of angle $\theta$.

63. The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes.

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

65. Frame two problems in calculating probability, based on the spinner shown here.

66. Two unbiased coins are tossed simultaneously find the probability of getting

67. Part - C

15 x 3 = 45
68. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : union sets

69. Verify A -(BUC) = (A-B)∩(A-C) using Venn diagrams.

70. Express in scientific notation:
(i) 9768854
(ii) 0.04567891
(iii) 72006865.48

71. Express the following surds in its simple form $\sqrt [ 4 ]{ 324 }$

72. Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial
p(x)=7x2+6x-1 q(x)=6x-9

73. In (5x+4) a factor of 5x+ 14x- 32x -32

74. Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

75. In the figure find x0 and y0.

76. Show that the following points taken in order form the vertices of a parallelogram. A(–3, 1), B(–6, –7), C (3, –9) and D(6, –1)

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

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

 Age No. of persons 15-19 20-24 25-29 30-34 35-39 40-44 4 20 38 24 10 9
79. Find the Median of the given data: 36, 44, 86, 31, 37, 44, 86, 35, 60, 51

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

81. The sides of a triangular park are in the ratio 9:10:11 and its perimeter is 300 m. Find the area of the triangular park.

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

83. Part - D

10 x 5 = 50
84. In a school,80 students like Maths,90 students like Science 82 students like History, 21 like both Maths and Science 19 like both science and History 20 like both Maths and History and 8 liked all the three subjects. If each student  like atleast one subject, then find (i) the number of students in the school (ii)the number of students who like only one subject.

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

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

89. Construct the centroid of $\triangle$PQR such that PQ = 9 cm, PQ = 7cm, RP = 8 cm.

90. Show that the point A (3,7) B (6, 5) and C (15, -1) are collinear.

91. In the class, weight of students is measured for the class records. Caculate mean weight of the students using direct method.

 Weight in kg 15-25 25-35 35-45 45-55 55-65 56-75 No.of students 4 11 19 14 0 2
92. The following are the scored by the students in the Summative Assessment exam

 Class 0-10 10-20 20-30 30-40 40-50 50-60 No.of students 2 7 15 10 11 5

93. A farmer has a field in the shape of a rhombus. The perimeter of the field is 400 m and one of its diagonal is 120 m. He wants to divide the field into two equal parts to grow two different types of vegetables. Find the area of the field.