#### Important Questions Part-III

9th Standard

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Maths

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

Part - A

14 x 1 = 14
1. If A = {x, y, z} then the number of non - empty subsets of A is

(a)

8

(b)

5

(c)

6

(d)

7

2. 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%

3. 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

4. $\frac { \sqrt [ 3 ]{ 18 } }{ \sqrt [ 3 ]{ 2 } }$ is same as

(a)

3

(b)

$\sqrt [ 3 ]{ 9 }$

(c)

9

(d)

$\sqrt [ 6 ]{ 3 }$

5. The GCD of ak, ak+1, ak+5 where, kN

(a)

ak

(b)

ak+1

(c)

ak+5

(d)

1

6. Zero of (7+4x) is_______

(a)

$\cfrac { 4 }{ 7 }$

(b)

$\cfrac { -7 }{ 4 }$

(c)

7

(d)

4

7. The distance between the longest chord of a circle and the centre is________

(a)

1

(b)

0

(c)

2

(d)

5

8. 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)

$\sqrt{17}$

9. In what ratio does the point Q(1,6) divide the line segment joining the points P(2,7) and R(−2,3)

(a)

1:2

(b)

2:1

(c)

1:3

(d)

3:1

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

(a)

Frequency

(b)

range

(c)

mode

(d)

Median.

11. 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

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

(a)

0

(b)

2

(c)

1

(d)

-1

13. 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

14. The probability of an event cannot be

(a)

Equal to zero

(b)

Greater than zero

(c)

Equal to one

(d)

Less than zero

15. Part - B

14 x 2 = 28
16. Identify the following sets as null set or singleton set.
B = The set of all even natural numbers which are not divisible by 2

17. Write the following in the form of 4n:
8

18. Show that $\sqrt [ 3 ]{ 7 } >\sqrt [ 4 ]{ 5 }$ .

19. Evaluate : 10 -4

20. Which of the following expressions are polynomials. If not give reason: $\sqrt { 5 } x^{ 2 }+\sqrt { 3 } x+\sqrt { 2 }$

21. In figure ㄥABC = 1200, where A, B and C are points on the circle with centre O. Find ㄥOAC?

22. Find the length of median through A of a triangle whose vertices are A(−1,3), B(1,−1) and C(5,1).

23. If A (10, 11) and B (2 ,3) are the coordinates of end points of diameter of circle. Then find the centre of the circle.

24. Find the centroid of the triangle whose vertices are (2, -5), (5, 11) and (9,9)

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

26. If sin$\theta$ = $\cfrac { a }{ \sqrt { \left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }+2bc \right) } }$ ,then show that (b + c) sin $\theta$ = (a) cos $\theta$

27. Find the value of sin 3x. sin 6x. sin 9x when x = 10°

28. Find the area of a quadrilateral whose sides are PQ = 15 cm, QR = 8 cm, RS = 25 m.

29. In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

30. Part - C

14 x 3 = 42
31. From the venn-diagram, list the following:

(i) A
(ii) B
(iii) A ∩ B
(iv) AU B
(v) A-B
(vi) B-A
(vii) (A - B) ∩ (B - A)

32. In a mathematics class,20 children forgot to bring their rulers,17 children forgot to bring their pencil and 5 children forgot to bring both ruler and pencil. Then find the number of children
(i) who forgot to bring only pencil .
(ii) who forgot to bring only ruler .
(iii) in the class

33. Express the following decimal expression into rational numbers. $0.\overline { 24 }$

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

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

36. Find the quotient and remainder of the following. (4x3 + 6x2 – 23x +18)÷(x+3)

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

38. Let m || n and l is a transversal Such that ∠1 : ∠2 = 11 : 7. Determine all the eight angles.

39. 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)

40. Observe the given graph and complete the following table:

 Points Quadrant Ordered Pair A IV B (3,3) C (-2,3) D III
41. Find the median of the given data:36,44,86,31,37,44,86,35,60,51

42. Find the value of (i) sin38036' + tan12012' (ii) tan60025' - cos 49020'

43. The length, breadth and height of a cuboid is 120 mm, 10 cm and 8 cm respectively. Find the volume of 10 such cuboids.

44. 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?

45. Part - D

4 x 5 = 20
46. Find the quotient and remainder for the following using synthetic division:
(i) (x3+x2-7x-3) ÷ (x-3)
(ii) (x3+2x2-x-4) ÷ (x+2)
(iii) (x3+4x2+16x+61) ÷ (x-4)
(iv) (3x3-2x2+7x-5) ÷ (x+3)
(v) (3x3-4x2-10x+8) ÷ (3x-2)
(vi) (8x4-2x2+6x+5) ÷ (4x+1)

47. Find the quotient and remainder when 5x3 + 7x2 + 3x + 2 is divided by 3x + 2

48. Which type of quadrilateral satisfies the following properties?
(i) Both pairs of opposite angles are equal in size.
(ii) Both pairs of opposite sides are equal in length.
(iii) Each diagonal is an angle bisector.
(iv) The diagonals bisect each other.
(v) Each pair of consecutive angles is supplementary.
(vi) The diagonals are equal.
(vii) Can be divided into two congruent triangles.

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