#### Annual Exam Model Question - 2019 - 2020 Paper-II

9th Standard

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Maths

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

Part I

Answer all the questions.

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 n(A $\cup$ B $\cup$ C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A$\cap$B) = 12, n(B$\cap$C) = 18 and n(A$\cap$C) = 15 , then n(A$\cap$B$\cap$C) is

(a)

5

(b)

10

(c)

15

(d)

20

2. $\left[ n\left( A\cup B\cup C \right) ^{ ' } \right]$=_______

(a)

$n\left( A\cap B\cap C \right)$

(b)

$n\left( U \right) -n\left( A\cup B\cup C \right)$

(c)

n(U)

(d)

$\Phi$

3. if $\frac { 1 }{ 7 }$ = $0.\bar { 142857 }$ then the value of $\frac { 5 }{ 7 }$

(a)

$0.\overline { 142857 }$

(b)

$0.\overline { 714285 }$

(c)

$0.\overline { 571428 }$

(d)

0.714285

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

(a)

5

(b)

4

(c)

2

(d)

3

5. If x51 + 51 is divided by x + 1, then the remainder is

(a)

0

(b)

1

(c)

49

(d)

50

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

(a)

q(-2)

(b)

x - 2

(c)

0

(d)

-2

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

(a)

900°

(b)

1080°

(c)

1444°

(d)

720°

8. Signs of the abscissa and ordinate of a point in the fourth quadrant are respectively

(a)

(+,+)

(b)

( –, –)

(c)

(–, +)

(d)

( +, –)

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

(a)

(0, - 5)

(b)

(-5,0)

(c)

(5,0)

(d)

(0,5)

10. The mean of the first 10 prime numbers is

(a)

12.6

(b)

12.7

(c)

12.8

(d)

12.9

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 $\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' }$ is

(a)

0

(b)

2

(c)

1

(d)

-1

13. 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

14. A random experiment contains

(a)

Atleast one outcome

(b)

At least two outcomes

(c)

Atmost one outcome

(d)

Atmost two outcomes

15. Part II

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

10 x 2 = 20
16. Write the set of letters of the following words in Roster form
ASSESSMENT

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

18. Find the value of $\left( \frac { 1 }{ 27 } \right) ^{ \frac { -2 }{ 3 } }$

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

20. Factorise the following: m3+$\frac{1}{m^2}$-23

21. This is a copy of the tangram puzzle. The tangram puzzle consists of 7 geometric pieces which are normally boxed in the shape·of a square. The pieces, called 'tans', are used to create different patterns including animals, people, numbers, geometric shapes and many more.
You can make several polygons using the pieces in different ways.

22. Show that the line segment joining the mid-points of two sides of a triangle is half of the third side
(Hint: Place triangle ABC in a clever way such that A is (0,0), B is (2a,0) and C to be (2b,2c). Now consider the line segment joining the mid-points of AC and BC. This will make calculations simpler).

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. A car travels, at an uniform speed. At 2pm it is at a distance of 5 km at 6pm it is at a distance of 120 km. Using section formula, find at what distance it will reach 2 midnight.

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. If 3 (tan $\theta$) + 4 (sec $\theta$ x sin 6) = 24. Then find all the trigonometric ratios of the angle $\theta$

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

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

29. 1500 families were surveyed and following data was recorded about their maids at homes

 Type of maids Only part time Only full time Both Number of families 860 370 250

A family is selected at random. Find the probability that the family selected has
(i) Both types of maids
(ii) Part time maids
(iii) No maids

30. Part III

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

10 x 5 = 50
31. Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B cars. Is this data correct?

32. 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.

33. Express the following decimal expression into rational numbers $0.\overline { 0001 }$

34. Find the value of a and b if $\frac { \sqrt { 7 } -2 }{ \sqrt { 7 } +2 }$=a$\sqrt{7}$+b

35. Arrange in ascending order:$\sqrt [ 3 ]{ 5 } ,\sqrt [ 4 ]{ 7 } ,\sqrt [ 2 ]{ 6 }$

36. Find the GCD of (x - 7)2,(x + 7)2,(x - 4)3

37. Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) $\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0$

38. Construct the ΔPQR such that PQ = 5cm, PR= 6cm and ㄥQP = ° R 60 and locate its centroid

39. 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?

40. The point (3,−4) is the centre of a circle. If AB is a diameter of the circle and B is (5,−6), find the coordinates of A.

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

43. Two identical cubes of side 7 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid.

44. When a dice is rolled, find the probability to get the number greater than 4?

45. Part IV

Answer all the questions

2 x 8 = 16
1. Solve 3x − 4y = 10 and 4x + 3y = 5 by the method of cross multiplication.

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

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

2. Construct an isosceles triangle PQR where PQ= PR and ㄥQ = 500, QR = 7cm. Also draw its circumcircle.