Important Questions Part-II

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 U ={x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is

(a)

{1, 6, 7, 8, 9}

(b)

{1, 2, 3, 4}

(c)

{2, 3, 4, 5}

(d)

{ }

2. If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is

(a)

W

(b)

X

(c)

Y

(d)

N

3. In a town 30% like only coffee,20% like only tea,10% like only like,15% like only any two of them,5% only like all the three. What is the percentage of people who like none them.

(a)

15%

(b)

20%

(c)

10%

(d)

5%

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

(a)

$\Phi$

(b)

A

(c)

U

(d)

$A\cap B\cap C$

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. 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. If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

(a)

a rational number

(b)

a natural number

(c)

an irrational number

(d)

an integer

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. Which is the best example of a number written in scientific notation?

(a)

0.5 x 105

(b)

0.1254

(c)

5.367 x 10-6

(d)

12.5 x 102

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 degree of the polynomial $\sqrt { 2 } { x }^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5x^{ 3 }\quad is$_____________________

(a)

2

(b)

3

(c)

4

(d)

5

12. The remainder when (x2-2x+7) is divided by (x + 4) is

(a)

28

(b)

31

(c)

30

(d)

20

13. If there are 36 students of class 9 and 48 students of class 10, what is the minimum number of rows to arrange them in which each row consists of same class with same number of students

(a)

12

(b)

144

(c)

7

(d)

72

14. Zero of (7+4x) is_______

(a)

$\cfrac { 4 }{ 7 }$

(b)

$\cfrac { -7 }{ 4 }$

(c)

7

(d)

4

15. (a-b) (a2+ab+b2)=_________

(a)

a+ b+ c- 3abc

(b)

a- b2

(c)

a+ b3

(d)

a3 - b3

16. 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

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 bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is

(a)

∠C + ∠D

(b)

$\frac { 1 }{ 2 } (\angle C+\angle D)$

(c)

$\frac { 1 }{ 2 } \angle C+\frac { 1 }{ 3 } \angle D$

(d)

$\frac { 1 }{ 3 } \angle C+\frac { 1 }{ 2 } \angle D$.

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

(a)

900°

(b)

1080°

(c)

1444°

(d)

720°

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

(a)

30°

(b)

60°

(c)

45°

(d)

90°

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

(a)

Complementary

(b)

Supplementary

(c)

equal

(d)

unequal

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

(a)

60o

(b)

90°

(c)

1200

(d)

180o

23. Point (–3,5) lie in the ________ quadrant

(a)

I

(b)

II

(c)

III

(d)

IV

24. 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)

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 (4, -1) and the origin is___________

(a)

$\sqrt{24}$

(b)

$\sqrt{37}$

(c)

$\sqrt{26}$

(d)

$\sqrt{17}$

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

(a)

$\sqrt{14}$

(b)

$\sqrt{15}$

(c)

4

(d)

0

28. If $P(\frac{a}{3},\frac{b}{2})$is the mid-point of the line segment joining A(−4,3) and B(−2,4) then (a,b) is

(a)

(-9, 7)

(b)

$(-3, \frac{7}{2})$

(c)

(9, -7)

(d)

$(3, -\frac{7}{2})$

29. The mean of the square of first 11 natural numbers is

(a)

26

(b)

46

(c)

48

(d)

52

30. The mean of the first 10 prime numbers is

(a)

12.6

(b)

12.7

(c)

12.8

(d)

12.9

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

(a)

Frequency

(b)

range

(c)

mode

(d)

median

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 3sin700sec200 + 2sin490sec510 is

(a)

2

(b)

3

(c)

5

(d)

6

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 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 number between 0 and 1 that is used to measure uncertainty is called

(a)

Random variable

(b)

Trial

(c)

Simple event

(d)

Probability

40. The probability of an event cannot be

(a)

Equal to zero

(b)

Greater than zero

(c)

Equal to one

(d)

Less than zero

41. Part - B

25 x 2 = 50
42. 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. (A$\cap$B)′

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. (A′)′

44. In a class there are 50 students who are offered either History, geography or both. 35 were offered History and 10 were offered History and Geography both. How many students were offered Geography?

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. Express the following in the form  ${p\over q},$  where p and q are integers and q $\ne$ 0.
$0.5\overline {7}$

47. Find the value of $\left( 49 \right) ^{ \frac { 1 }{ 2 } }$

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

49. We used to write $\pi$ as $\frac{22}{7}.$ Can we say $\pi$ is a rational number?

50. Verify whether the following are zeros of the polynomial indicated against them, or not.
p(x) = x3 - 1, x = 1

51. Twice the area of a right angled triangle 15x2 + 19x + 6 sq. units. If its altitude is 5x + 3 units, find its base in terms of x.

52. Expand the following using identities: (2x-3b)2

53. Find the value of x

54. Draw a right triangle whose hypotenuse is 10 cm and one of the legs is 8 cm. Locate its incentre and also draw the incircle

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

63. The dimensions of a cuboidal box are 6 m × 400 cm × 1.5 m. Find the cost of painting its entire outer surface at the rate of Rs.22 per cm2.

64. Find the area of a quadrilateral whose sides are PQ = 15 cm, QR = 8 cm, RS = 25 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. What is the probability that a number selected from the numbers 1, 2, 3, ..., 25 is prime number when each of the given numbers is equally likely to be selected?

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 : union sets

70. Express the following decimal expression into rational numbers. $2.\overline { 327 }$

71. Multiply $\sqrt [ 4 ]{ 400 }$ and $\sqrt [ 4 ]{ 567 }$

72. Show that (x-3) is a factor of x+ 9x- x - 105

73. Find the value of k, for the following system of equation has infinitely many solutions. 2x − 3y = 7;(k + 2)x − (2k +1)y = 3(2k −1)

74. In the figure find x0 and y0.

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

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. (i) (i) Where do the following points lie?
P (-2, 0), Q (2,0), and R(3,0). .
(ii) Find the distance between the following points using coordinates given in question
(i) (a) P and R (b) Q and R.

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. In a class test in mathematics, 10 students scored 75 marks, 12 students scored 60 marks, 8 students scored 40 marks and 3 students scored 30 marks. Find the mean of their score

80. If tan A  = $\frac { 2 }{ 3 }$ , then find all the other trigonometric ratios.

81. cube has the total surface area of 486 cm2. Find its lateral surface area.

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. If P = {x :x$\in$ N and 1$\in$ N and n<6} and R={4,6,8,9,1,12} then verify $P-\left( Q\cap R \right) =\left( P-Q \right) \cup \left( P-R \right)$

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

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

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

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

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

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

91. 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

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°.