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

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. From the adjacent diagram n[P(AΔB)] is

(a)

8

(b)

16

(c)

32

(d)

64

2. 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%

3. Which one of the following is an irrational number ____________

(a)

$\sqrt { 25 }$

(b)

$\sqrt { \frac { 9 }{ 4 } }$

(c)

$\frac { 7 }{ 11 }$

(d)

$\pi$

4. Which of the following is not an irrational number?

(a)

$\sqrt { 2 }$

(b)

$\sqrt { 5 }$

(c)

$\sqrt { 3 }$

(d)

$\sqrt { 25 }$

5. The type of the polynomial 4–3x3 is

(a)

constant polynomial

(b)

linear polynomial

(c)

(d)

cubic polynomial.

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

(a)

0

(b)

1

(c)

2

(d)

3

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

(a)

Square

(b)

Equilateral triangle

(c)

Regular hexagon

(d)

Regular octagon

8. Point (0, –7) lies ________

(a)

on the x-axis

(b)

(c)

on the y-axis

(d)

9. A point on the y-axis is ________________

(a)

(1, 1)

(b)

(6,0)

(c)

(0,6)

(d)

(-1, -1)

10. The mean of the first 10 prime numbers is ___________

(a)

12.6

(b)

12.7

(c)

12.8

(d)

12.9

11. 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

12. if sin 300 = x and cos 600 = y, then x2  + y2 is

(a)

$\frac { 1 }{ 2 }$

(b)

0

(c)

sin90°

(d)

cos90°

13. The lateral surface area of a cube of side 12 cm is

(a)

144 cm2

(b)

196 cm2

(c)

576 cm2

(d)

664 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 II

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

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. Express the following in the form 2n:
$\frac{1}{4}$

18. Use a fractional index to write $\sqrt [ 3 ]{ 7 }$

19. Find any 3 irrational numbers between 0.12 and 0.13.

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

21. 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.

22. Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure?
(0, –4) (0, –2) (0, 4) (0, 5)

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

24. 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.

25. 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

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

27. Find the value of $\frac{\tan 25^{\circ}}{\cot 65^{\circ}}+\frac{\sin 40^{\circ}}{\cos 50^{\circ}}$

28. Find the TSA and LSA of a cuboid whose length, breadth and height are 10 cm, 12 cm and 14 cm respectively.

29. In a survey of 400 youngsters aged 16-20 years, it was found that 191 have their voter ID card. If a youngster is selected at random, find the probability that the youngster does not have their voter ID card.

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
(ii) BΔA

32. In the adjacent diagram, if n(U) = 125, y is two times of x and z is 10 more than x, then find the value of x,y and z.

33. Express the following decimal expression into rational numbers $3.1\overline { 7 }$

34. Can you reduce the following numbers to surds of same order :
(i) $\sqrt{3}$
(ii) $\sqrt [ 4 ]{ 3 }$
(iii) $\sqrt [ 3 ]{ 3 }$

35. Write in scientific notation ;(60000000)3

36. Write the following polynomials in standard form.

S.No Polynomial Standard form
1 5m4 -3m + 7m2 + 8
2 $\frac { 2 }{ 3 } y+{ 8y }^{ 3 }-12+\sqrt { 5 } { y }^{ 2 }$
3 12p2 -8p5 -10p4 -7
37. Expland the following using identities (4a + 3b) (4a - 3b)

38. In the given figure, ㄥCAB = 25°, find ㄥBDC, ㄥDBA and ㄥCOB

39. Find the distance between the points (–4, 3), (2, –3).

40. Show that the following points taken in order form an equilateral triangle in each case $A\left( 2,2 \right) ,B\left( -2,-2 \right) ,C\left( -2\sqrt { 3 } ,2\sqrt { 3 } \right)$

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. Find the value of cos19059'

43. The sides of a triangular park are in the ratio 9:10:11 and its perimeter is 300 m. Find the area of the triangular park.

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. Verify x3+y3+z3-3xyz = $\frac{1}{2}$[x+y+z][(x-y)2+(y-z)2+(z-x)2]

47. Prove that x -1 is a factor x5 - 45x4 + 36x3 + 45x2 - 36x-1

48. In the given Fig, ∠A = 64° , ∠ABC = 58°. If BO and CO are the bisectors of ∠ABC and ∠ACB respectively of ΔABC, find x° and y°.

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