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

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

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

(a)

3

(b)

$\sqrt [ 3 ]{ 9 }$

(c)

9

(d)

$\sqrt [ 6 ]{ 3 }$

4. $\sqrt [ 3 ]{ 192 } +\sqrt [ 3 ]{ 24 }$

(a)

$3\sqrt [ 3 ]{ 6 }$

(b)

$6\sqrt [ 3 ]{ 3 }$

(c)

$\sqrt [ 3 ]{ 216 }$

(d)

$\sqrt [ 6 ]{ 216 }$

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

(a)

0

(b)

1

(c)

2

(d)

3

6. Which of the following statement is true for the equation 2x + 3y = 15

(a)

the equation has unique solution

(b)

the equation has two solution

(c)

the equation has no solution

(d)

the equation has infinite solutions

7. The point of concurrency of the medians of a triangle is known as __________

(a)

circumcentre

(b)

incentre

(c)

orthocentre

(d)

centroid

8. Point (0, –7) lies ________________________________

(a)

on the x-axis

(b)

(c)

on the y-axis

(d)

9. On which quadrant does the point (- 4, 3) lie?

(a)

I

(b)

II

(c)

III

(d)

IV

10. The mean of a set of numbers is $\bar X$. If each number is multiplied by z, the mean is

(a)

$\bar X + z$

(b)

$\bar X-z$

(c)

z$\bar X$

(d)

$\bar X$

11. The mean of the first 10 prime number is

(a)

12.6

(b)

12.7

(c)

12.8

(d)

12.9

12. The value of tan1°.tan2°.tan3°...tan89° is

(a)

0

(b)

1

(c)

2

(d)

$\frac { \sqrt { 3 } }{ 2 }$

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 all possible outcomes of a random experiment is always equal to

(a)

One

(b)

Zero

(c)

Infinity

(d)

All of the above

15. Part II

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

14 x 2 = 28
16. Which of the following sets are equivalent or unequal or equal sets?
G = {x : x is a prime number and 3 < x < 23}
H = {x : x is a divisor of 18}

17. Express the following in the form of $\frac { p }{ q }$  where p and q are integers and q $\neq$0.
(a)$\overline { 0.6 }$  (b) $\overline { 0.47 }$(c) $\overline { 0.001 }$

18. Convert the following rational numbers into decimal
(i) $3\over 4$
(ii) $5\over 8$
(iii) $9\over 25$

19. Give any two rational numbers lying between 0.5151151115…. and 0.5353353335…

20. If ${ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } }$=23, then find the value of $x+\frac { 1 }{ x }$ and ${ x }^{ 3 }+\frac { 1 }{ { x }^{ 3 } }$ .

21. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord

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. 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.

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

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 value of cos 19° 59' + tan 12° 12' + sin 49° 20'.

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

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

29. What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

30. Part III

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

14 x 3 = 42
31. 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.

32. If A={x:x ∈ Z, -2 < x ≤ 4}, B={x:x ∈ W, x ≤ 5}, C={-4,-1,0,2,3,4}, then verify A∪(B∩C)=(A∪B)∩(A∪C)A∪(B∩C)=(A∪B)∩(A∪C).

33. Express the following decimal expression into rational numbers $17.2\overline { 15 }$

34. Represent the following numbers in scientific notation:
(i) (300000)2 x (20000)4
(ii) (0.000001)11 ÷ (0.005)3
(iii) $\left\{ (0.00003 \right\} ^{ 6 }\times (0.00005)^{ 4 }\} \div \{ (0.009)^{ 3 }\times (0.05)^{ 2 }\}$

35. Simplify;$\sqrt { 44 } +\sqrt { 99 } -\sqrt { 275 }$

36. Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial
h(z)=z5-6z4+z f(z)=6z2+10z-7

37.  Expland : (x + 2 y + 3z)2

38. Construct the ΔLMN such that LM=7.5cm, MN=5cm and LN=8cm. Locate its centroid.

39. Calculate the distance between the points A (7, 3) and B which lies on the x-axis whose abscissa is 11.

40. Find the points which divide the line segment joining A(−11,4) and B(9,8) into four equal parts.

41. If the mean of the following data is 20.2, then find the value of p

 Marks 10 15 20 25 30 No.of students 6 8 p 10 6

42. i) If cosecA = sec340, find A (ii) If tanB = cot 470, find B.

43. Three different triangular plots are available for sale in a locality. Each plot has a perimeter of 120 m. The side lengths are also given:

 Shape of plot Perimeter Length of sides Right angled triangle 120m 30m, 40m, 50m Acute angled triangle 120 m 35 m, 40 m, 45 m Equilateral triangle 120 m 40 m, 40 m, 40 m

Help the buyer to decide which among these will be more spacious.

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

45. Part IV

4 x 5 = 20
46. Factorise the following:
(i) x2+10x+24
(ii) x2-2x-99
(iii) z2+4z-12
(iv) x2+14x-15
(v) p2-6p-16
(vi) t2+72-17t
(vii) x2-8x+15
(viii) y2-16-80
(ix) a2+10a-600

47. Factorise  2x3- x2 - 12x - 9 into linear factors

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. Diagonal AC of a parallelogram ABCD bisects ㄥA. Show that
(i) it bisects ㄥC also (ii) ABCD is a rhombus.