#### Annual Exam Model Question Paper 2019 - 2020 Part-V

9th Standard

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Maths

Time : 02:45:00 Hrs
Total Marks : 100

Part I

Choose the most suitable answer from the given four alternatives and write the option code with the corresponding answer.

14 x 1 = 14
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. The set (A - B) U(B - A) is ___________

(a)

AΔB

(b)

AUB

(c)

A∩B

(d)

A'UB'

3. The length and breadth of a rectangular plot are 5 x 105 and 4 x 104 metres respectively. Its area is ______

(a)

9 x 101 m2

(b)

9 x 109 m2

(c)

2 x 1010 m2

(d)

20 x 1020 m2

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

(a)

3

(b)

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

(c)

$\sqrt { 3 }$

(d)

$\sqrt [ 3 ]{ 3 }$

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

(a)

0

(b)

1

(c)

2

(d)

3

6. The linear equation in one variable is

(a)

2x + 2 = y

(b)

5x − 7 = 6 − 2x

(c)

2t(5 − t) = 0

(d)

7p − q = 0

7. The perpendicular line from the centre of the circle to the chord divided the chord in the ratio________

(a)

1: 1

(b)

1: 2

(c)

2: 1

(d)

1: 3

8. The distance between the points (4, -1) and the origin is___________

(a)

$\sqrt{24}$

(b)

$\sqrt{37}$

(c)

$\sqrt{26}$

(d)

$\sqrt{17}$

9. 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

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. The mean of 5,9,x,17,and 21 is 13,then find the value of x

(a)

9

(b)

13

(c)

17

(d)

21

12. The value of 2tan30° tan60° is

(a)

1

(b)

2

(c)

$2\sqrt { 3 }$

(d)

6

13. The perimeter of an equilateral triangle is 30 cm. The area is

(a)

$10\sqrt { 3 }$ cm2

(b)

$12\sqrt { 3 }$ cm2

(c)

$15\sqrt { 3 }$ cm2

(d)

$25\sqrt { 3 }$ cm 2

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

(a)

Random variable

(b)

Trial

(c)

Simple event

(d)

Probability

15. Part II

Answer any 10 questions. Question no. 28 is compulsory.

14 x 2 = 28
16. 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′$\cup$B′

17. Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
$7\over 16$

18. Write the following in the form of 5n
$\sqrt{5}$

19. The mass of the Earth is 5.97 x 1024 kg and that of the Moon is 0.073 x 1024 kg. What is their total mass?

20. Factorise the following expressions: pr+qr+pq+p2

21. Which ones are not quadrilaterals?

22. Find the distance between the following pairs of points. (3,4) and (– 7, 2)

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 coordinates of the point which divides, the line segment joining the point A (3,7) and B (-11, -2) in the ratio 5 : 1.

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

26. Find the six trigo'nometric ratios of the angle 0 using the diagram

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

28. Find the volume of a cube whose surface are is a 96 cm2.

29. A manufacturer tested 7000 LED lights at random and found that 25 of them were defective. If a LED light is selected at random, what is the probability that the selected LED light is a defective one.

30. Part III

Answer any 10 questions. Question no. 42 is compulsory.

14 x 3 = 42
31. Given that A = {1,3,5,7} B = {1,2,4,6,8}. Find (i) AΔB and (it) BΔA

32. If K = {a,b,d e f }  L = {b,c,d,g} and M = {a,b,c,d,h}, then find the following:
(i) K $\cup$(L $\cap$ M)
(ii) K $\cap$(L $\cup$ M)
(iii) (K$\cup$L)$\cap$(K$\cup$M)
(iv)
(K$\cap$L)$\cup$(K$\cap$M)

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

34. (i) Add 3$\sqrt{7}$ and 5$\sqrt{7}$ . Check whether the sum is rational or irrational. (ii) Subtract 4$\sqrt{5}$ from  7$\sqrt{5}$ . Is the answer rational or irrational?

35. Write in scientific notation ;(60000000)3

36. If x4 –3x3 + 5x2 –7 is divided by x2 + x + 1 then find the quotient and the remainder.

37. Show that x+4 is a factor of x+ 6x- 7x - 60

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

39. Determine whether the given set of points in each case are collinear or not (a,–2), (a,3), (a,0)

40. If (x,3), (6,y), (8,2) and (9,4) are the vertices of a parallelogram taken in order, then find the value of x and y.

41. The median of observation 11,12,14,18,x+12,x+4,30,32,35,41 arrenged in ascending order is 24.Find the values of x.

42. For the measures in the figure, compute sine, cosine and tangent ratios of the angle $\theta$

43. The total surface area of a cube is 864 cm2. Find its volume

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 IV

4 x 5 = 20
46. Factorise the following:
(i) (p-q2)-6(p-q)-16
(ii) 9(2xy)2-4(2x-y)-13
(iii) m2+2mm-24n2
(iv) $\sqrt{5}a^2+2a-3\sqrt5$
(v) a4-2a2+2
(vi) 8m3-2m2n-15mn2
(vii) $4\sqrt{3}x^2+5x-2\sqrt{3}$
(viii) a4-7a2+1
(ix) $a^2+{1\over a^2}-18$
(x) ${1\over x^2}+{1\over y^2}+{2\over xy}$
(xi) ${3\over x^2}+{8\over xy}+{4\over y^2}$

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

48. Draw ΔPQR with sides PQ = 7 cm, QR = 8 cm and PR = 5 cm and construct its Orthocentre.

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