#### Important Questions - Part-VIII

9th Standard

Reg.No. :
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Maths

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

Part - A

40 x 1 = 40
1. Which of the following is correct?

(a)

{7} ∈ {1,2,3,4,5,6,7,8,9,10}

(b)

7 ∈ {1,2,3,4,5,6,7,8,9,10}

(c)

7 ∉ {1,2,3,4,5,6,7,8,9,10}

(d)

{7} $\nsubseteq$ {1,2,3,4,5,6,7,8,9,10}

2. The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

(a)

A ∩ B

(b)

A U B

(c)

A - B

(d)

A Δ B

3. 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

4. If U={x:x$\in$W and x<20},A={2,4,,6,8},B={6,8,12,14} then $\left[ n\left( A\cup B^{ ' } \right) \right]$

(a)

15%

(b)

20%

(c)

10%

(d)

5%

5. For any three sets,P,Q,R$\left( P\cap Q \right) ^{ ' }$

(a)

${ P }^{ ' }\cup { Q }^{ ' }$

(b)

$P\cup Q$

(c)

${ P }^{ ' }$

(d)

${ Q }^{ ' }$

6. The value of $\bar { 0.03 }$ +$\bar { 0.03 }$  is ___________.

(a)

$\bar { 0.09 }$

(b)

$\bar { 0.09 }$

(c)

$\bar { 0.09 }$

(d)

0

7. $\sqrt{27}$+$\sqrt{12}$=

(a)

$\sqrt{39}$

(b)

5$\sqrt{6}$

(c)

5$\sqrt{3}$

(d)

3$\sqrt{5}$

8. When written with a rational denominator, the expression $\frac { 2\sqrt { 3 } }{ 3\sqrt { 2 } }$ can be simplified as

(a)

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

(b)

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

(c)

$\frac { \sqrt { 6 } }{ 3 }$

(d)

$\frac{2}{3}$

9. $\sqrt [ 5 ]{ 21 } \times 6\sqrt { 10 }$

(a)

$30\sqrt { 210 }$

(b)

30

(c)

$\sqrt { 210 }$

(d)

$210\sqrt { 30 }$

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. x3 – x2 is a …………..

(a)

monomial

(b)

binomial

(c)

trinomial

(d)

constant polynomial

12. The coefficient of ${ x }^{ 2 }\quad and\quad x\quad in\quad 2{ x }^{ 3 }-5{ x }^{ 2 }+6x-3\quad are\quad respectively$____________________

(a)

2, -5

(b)

2, 6

(c)

-5, 6

(d)

-5, -3

13. The GCD of x4-y4 and x2-y2 is

(a)

x4-y4

(b)

x2-y2

(c)

(x+y)2

(d)

(x+y)4

14. Which of the following has a factor?

(a)

x+ 2x

(b)

(x - 1)2

(c)

(x + 1)2

(d)

(x- 22)

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

(a)

q(-2)

(b)

x - 2

(c)

0

(d)

-2

16. (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

17. 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

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

(a)

Square

(b)

Equilateral triangle

(c)

Regular hexagon

(d)

Regular octagon

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

(a)

30°

(b)

60°

(c)

45°

(d)

90°

20. Which of the following is a formula to find the sum of interior angles of a quadrilateral of n-sides?

(a)

$\frac { n }{ 2 }$ x 180

(b)

$\left( \frac { n+1 }{ 2 } \right)$1800

(c)

$\left( \frac { n-1 }{ 2 } \right)$1800

(d)

(n-2)1800

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

(a)

80°

(b)

100°

(c)

70°

(d)

90°

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

(a)

45°

(b)

90°

(c)

180°

(d)

360°

23. If P( –1,1), Q( 3,–4), R( 1, –1), S(–2, –3) and T( –4, 4) are plotted on a graph paper, then the points in the fourth quadrant are

(a)

P and T

(b)

Q and R

(c)

only S

(d)

P and Q

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 (0, -3) lies on _______________

(a)

+ ve x-axis

(b)

+ ve y-axis

(c)

- ve x-axis

(d)

- ve y-axis

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

(a)

(0, - 5)

(b)

(-5,0)

(c)

(5,0)

(d)

(0,5)

27. 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

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

(a)

Frequency

(b)

range

(c)

mode

(d)

Median.

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. 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. If the mean of five observations x,x+2,x+4,x+6,x+8, is 11, then the mean of first three observations is

(a)

9

(b)

11

(c)

13

(d)

15

33. The mean of the first 10 prime number is

(a)

12.6

(b)

12.7

(c)

12.8

(d)

12.9

34. Find the mean of the prime factors of 165

(a)

5

(b)

11

(c)

13

(d)

55

35. The value of $\frac { tan15° }{ cot75° }$ is

(a)

cos900

(b)

sin300

(c)

tan450

(d)

cos300

36. The value of tan1°.tan2°.tan3°...tan89° is

(a)

0

(b)

1

(c)

2

(d)

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

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 number of bricks each measuring 50 cm × 30 cm × 20 cm that will be required to build a wall whose dimensions are 5 m × 3 m × 2 m is

(a)

1000

(b)

2000

(c)

3000

(d)

5000

39. The probability of all possible outcomes of a random experiment is always equal to

(a)

One

(b)

Zero

(c)

Infinity

(d)

All of the above

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. From the given Venn diagram, write the elements of

(i) A
(ii) B
(iii) A – B
(iv) B – A
(v) A′
(vi) B′
(vii) U

43. IfA= {1,2,3} B= {3,5,6} C={3,4,7}.Find(i)A-(BUC) (ii) BΔC (iii)AΔB

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=$\left\{ -\frac { 1 }{ 2 } ,0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2 \right\}$, B=$\left\{ 0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2,\frac { 5 }{ 2 } \right\}$ and C=$\left\{ -\frac { 1 }{ 2 } .\frac { 1 }{ 4 } ,1,2,\frac { 5 }{ 2 } \right\}$, then verify $A\cap (B\cap C)=(A\cap B)\cap C$ .

46. Use a fractional index to write: $\sqrt{5}$

47. Evaluate : $\left( \cfrac { 1 }{ 9 } \right) ^{ -3 }$

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

49. Represent the following as decimal form
(i) $\frac { -4 }{ 11 }$
(ii) $\frac { 11 }{ 75 }$

50. Verify whether the following are zeros of the polynomial indicated against them, or not.
p(x) = (x+3) (x-4), x=-3, x=4

51. Factorise the following : 64m+ 27n3

52. Akshaya has 2 rupee coins and 5 rupee coins in her purse. If in all she has 80 coins totalling Rs 220, how many coins of each kind does she have.

53. Identify which ones are trapeziums and which are not.

54. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord

55. The chord of length 32 em is drawn at the distance of 12 cm from the centre of the circle. Find the radius of the circle

56. In a circle, AB and CD are two parallel chords with centre 0 and radius 5 em such that AB = 8 cm and CD = 6 em determine the distance between the chords?

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

58. Find the coordinates of the point which divides the line segment joining the points (3,1) and (S, 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. The mean weight of 4 members of a family is 60 kg. Three of them have the weight 56kg,68kg and 72 kg respectively. Find the weight of the fourth member.

61. Evaluate:
(i)sin300 +cos 300
(ii) tan600.cot600
(iii) $\frac { tan45° }{ tan30°+tan60° }$
(iv)sin2450 +cos2450

62. Find the value of $\cfrac { cos{ 63 }^{ 0 }20' }{ sin{ 26 }^{ 0 }40' }$

63. The parallel sides of a trapezium are 15 m and 10 m long and its non-parallel sides are 8 m and 7 m long. Find the area of the trapezium.

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. A company manufactures 10000 Laptops in 6 months. In that 25 of them are found to be defective. When you choose one Laptop from the manufactured, what is the probability that selected Laptop is a good one.

66. One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is
(i) an ace,
(ii) either red card or king.

67. Part - C

15 x 3 = 45
68. In a class there are 40 students. 26 have opted for Mathematics and 24 have opted for Science. How many student have opted for Mathematics and Science.

69. U={x:x ∈Z, -2 ≤ x ≤ 10}, A={x : x =2p +1, p ∈Z, -1≤ p ≤ 4}, B = {x : x =3q + 1,q∈Z, -1 ≤ q< 4} verify De Morgan’s laws for complementation.

70. Express the following decimal expression into rational numbers $17.2\overline { 15 }$

71. Sho that $\sqrt [ 3 ]{ 2 } >\sqrt [ 5 ]{ 3 }$

72. What must be subtracted from ${ y }^{ 4 }+{ 2y }^{ 3 }-3y+8\quad to\quad get\quad { y }^{ 4 }-{ 2y }^{ 3 }+6?$

73. (i) Prove that (x -1) is a factor of x3-7x+13x-7
(ii) Prove that (x + 1) is a factor of x3+7x2+13x+7

74. ABCD is a parallelogram and AP and CQ are perpendic from vertex A and C on diagonal BD. Show that (i) ΔAPB ≅ ΔCQD (ii) AP=CQ

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

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. 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. The arithmetic mean of 6 values is 45 and if each value is increased by 4, then find the arithmetic mean of new set of values

79. The following are scores obtained by 11 players in a cricket match 7, 21, 45, 12, 56, 35, 25, 0, 58, 66, 29. Find the median score.

80. Evaluate: (i) $\frac { sin49° }{ cos41° }$ (ii) $\frac { sec63° }{ cosec27° }$

81. Find the Total Surface Area and Lateral Surface Area of the cube, whose side is 5 cm.

82. 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.

83. Part - D

10 x 5 = 50
84. Fill in the blanks with appropriate cardinal numbers

S.No n(A) n(B) n(AUB) n(A∩B) n(A-B) n(B-A)
1 30 45 65
2 20   55 10
3 50 65   25
4 30 43 70
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. Find the angle of the given cyclic quadrilateral ABCD in the figure.

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

90. Show that the given points (1, 1), (5, 4), (-2, 5) are the vertices of an isosceles right angled triangle.

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. 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
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.