#### Important Questions

9th Standard

Reg.No. :
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Maths

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

Part - A

40 x 1 = 40
1. Let A = {∅} and B = P(A), then A∩B is

(a)

{ ∅, {∅} }

(b)

{∅}

(c)

(d)

{0}

2. A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

(a)

equal set

(b)

equivalent sets

(c)

overlapping sets

(d)

disjoint sets

3. The set (A - B) U(B - A) is ___________

(a)

AΔB

(b)

AUB

(c)

A∩B

(d)

A'UB'

4. The shade region with adjoint diagram represents ___________

(a)

A - B

(b)

B - A

(c)

A'

(d)

B'

5. 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)

6. $0.\overline { 34 } +0.3\bar { 4 }$ =

(a)

$0.6\overline { 87 }$

(b)

$0.\overline { 68 }$

(c)

$0.6\bar { 8 }$

(d)

$0.68\bar { 7 }$

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

(a)

- 0.75

(b)

- 0.50

(c)

-0.25

(d)

- 0.125

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

(a)

$\frac { 7 }{ 9 }$

(b)

$\frac { 8 }{ 15 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 5 }{ 32 }$

9. When (2$\sqrt{5}$-$\sqrt{2}$)2 is simplified, we get

(a)

4$\sqrt{5}$+2$\sqrt{2}$

(b)

22-4$\sqrt{10}$

(c)

8-4$\sqrt{10}$

(d)

2$\sqrt{10}$-2

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

(a)

5

(b)

4

(c)

2

(d)

3

11. The product of the polynomials p(x) = 4x –3 q(x) = 4x + 3

(a)

1 – x – 8

(b)

16x2 – 9

(c)

18x3 + 12x2 – 12x – 8

(d)

18x3 – 12x2 + 12x + 8

12. The sum of ${ 5x }^{ 2 };-7x^{ 2 };8x^{ 2 };11x^{ 2 }\quad and\quad -9x^{ 2 }$ is _________________________

(a)

$2{ x }^{ 2 }$

(b)

$4{ x }^{ 2 }$

(c)

$6{ x }^{ 2 }$

(d)

$8{ x }^{ 2 }$

13. 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

14. The value of the polynomial f(x)=6x-3x2+9 when x=-1 is _____________________

(a)

0

(b)

1

(c)

2

(d)

3

15. Zero of (7+4x) is_______

(a)

$\cfrac { 4 }{ 7 }$

(b)

$\cfrac { -7 }{ 4 }$

(c)

7

(d)

4

16. Which condition does not satisfy the linear equation ax + by + c = 0

(a)

a $\neq$ 0 , b = 0

(b)

a = 0 , b $\neq$ 0

(c)

a = 0 , b = 0 , c $\neq$ 0

(d)

a $\neq$0, b $\neq$ 0

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

(a)

circumcentre

(b)

incentre

(c)

orthocentre

(d)

centroid

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

(a)

80°

(b)

85°

(c)

70°

(d)

65°

19. In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ㄥQR = 80°, then ㄥTVS=

(a)

80°

(b)

100°

(c)

70°

(d)

90°

20. If the length of a chord decreases, then its distance from the centre__________

(a)

Increases

(b)

decreases

(c)

same

(d)

cannot say

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

(a)

60o

(b)

90°

(c)

1200

(d)

180o

22. The angle subtend by a semicircle at the remaining part of the circumference is___________

(a)

60o

(b)

90o

(c)

120o

(d)

180°

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

(a)

$\sqrt{14}$

(b)

$\sqrt{15}$

(c)

4

(d)

0

24. 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)

$\sqrt{17}$

25. The point which is on y-axis with ordinate - 5 is _____________

(a)

(0, - 5)

(b)

(-5,0)

(c)

(5,0)

(d)

(0,5)

26. The diagonal of a square formed by the points (1, 0), (0, 1), (-1, 0) and (0, - 1) is_______________

(a)

2

(b)

4

(c)

$\sqrt{2}$

(d)

8

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 centroid of the triangle with vertices (−1,−6), (−2,12) and (9,3) is

(a)

(3,2)

(b)

(2,3)

(c)

(4,3)

(d)

(3,4)

29. Data available in an unorganized form is called ------------- data

(a)

Grouped data

(b)

class interval

(c)

mode

(d)

raw data

30. A particular observation which occurs maximum number of times in a given data is called its

(a)

Frequency

(b)

range

(c)

mode

(d)

Median.

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

(a)

Mean

(b)

Range

(c)

Median

(d)

Mode

32. 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

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 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)

$\bar{X}$

35. If 2sin 2$\theta$ = $\sqrt { 3 }$ , them the value of $\theta$ is

(a)

900

(b)

300

(c)

450

(d)

600

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

(a)

2

(b)

1

(c)

0

(d)

$\frac { 1 }{ 2 }$

37. If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is

(a)

3 cm2

(b)

6 cm2

(c)

9 cm2

(d)

12 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. A particular result of an experiment is called

(a)

Trial

(b)

Simple event

(c)

Compound event

(d)

Outcome

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. Find the cardinal number of the following sets.
R = {x : x is an integers, x∈Z and –5 ≤ x <5}

43. Represent U= {1,2,3,4,5,6,7,8,9,10} A = {1,2,4,6,8,10} and B = {3,6,1,10} in venn-diagram, then find (i) (A UB)' (ii) (A ∩ B)'

44. 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)'

45. If A={ x : x = 2n, n $\in$ W and n<4}, B = {x : x = n, n  2 $\in$ N and n ≤ 4} and C = {0, 1, 2, 5, 6} , then verify the associative property of intersection of sets.

46. If x=$\sqrt{5}$+2, then find the value of ${ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } }$

47. Simplify the following: $2\sqrt [ 3 ]{ 40 } +3\sqrt [ 3 ]{ 625 } -4\sqrt [ 3 ]{ 320 }$

48. Can you reduce the following numbers to surds of same of same order $\sqrt { 5 }$

49. Express the surds in the simple form $\sqrt { 27 }$

50. Find the number of zeros of the following polynomials represented by their graphs.

51. Factorise the following: 25a2-10a+1

52. Find the value of s for the following system of equa~on has infinitely many
solutions. 2x - 3y = 7; (s +2) x - (2s + l)y = 3(2s -1)

53. Find the complement of the following angles (1°= 60′ minutes, 1′ = 60′′ seconds)
45°

54. Procedure:
(I) Make a parallelogram on a chart/graph paper and cut it.
(ii) Draw diagonal of the parallelogram.
(iii) Cut along the diagonal and obtain two triangles.
(iv) Superimpose one triangle onto the other.
What do you conclude?

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

56. Find the value of Xo

57. Find the coordinates of the point which divides the line segment joining A(−5,11) and B(4,−7) in the ratio 7:2.

58. If the centroid of a triangle is at (10, -1) and two vertices are (3,2) and (5, -11). Find the third vertex of a triangle.

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

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

61. If 3cot A = 2 , then find the value of = $\frac { 4sinA-3cosA }{ 2sinA+3cosA }$

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

63. The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of white washing the walls and ceiling at the rate of Rs.8.50 per m2.

64. Using Heron's formula, find the area of a triangle whose sides are 41 m, 15 m, 25 m.

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
(i) two heads
(ii) one head
(iii) at least one head
(iv) at most one head

67. Part - C

15 x 3 = 45
68. If A={b,e,f,g} and B={c,e,g,h}, then verify the commutative property of (i) union of sets (ii) intersection of sets.

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

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

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

72. Study the following pattern and write the algebraic expression
(i)

 Shape Number Number of matchsticks 1 2 3 4 5 4 7 10 13 16

(ii)

 Shape Number Number of Square Boxes 1 2 3 4 5 1 4 7 10 13
73. Identify monomials, binomials and trinomial from the following expression.
(i) -8 abc
(ii) 3a2bc+8-9a2
(iii) -9
(iv) a2+b2+c2-k2
(v) a+b
(vi) 7ab3
(vii) -z+$\sqrt{3}$z3

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. The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?

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

78. Find the sum of the deviations from the arithmetic mean for the following observations:
21, 30, 22, 16, 24, 28, 18, 17

79. 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
80. Find the value of cos19059'

81. 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

82. Team I and Team II play 10 cricket matches each of 20 overs. Their total scores in each match are tabulated in the table as follows:

 Match numbers 1 2 3 4 5 6 7 8 9 10 Team I 200 122 111 88 156 184 99 199 121 156 Team II 143 123 156 92 164 72 100 201 98 157

What is the relative frequency of Team I winning?

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  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. Prove that x -1 is a factor x5 - 45x4 + 36x3 + 45x2 - 36x-1

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

91. 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
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. 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.