Annual Exam Model Question Paper 2019 - 2020 Part-IX

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 B ⊆ A then n(A∩B) is

(a)

n(A – B)

(b)

n(B)

(c)

n(B – A)

(d)

n(A)

2. If A is a proper subset ofB, then A ∩ B = __________

(a)

A

(b)

B

(c)

Ø

(d)

A U B

3. What is 5.92 x 10-3 written in decimal form?

(a)

0.000592

(b)

0.00592

(c)

0.0592

(d)

0.592

4. The length of a square is 1.2X103 m. Its area is_______

(a)

14.4 X 106

(b)

1.44 X 106

(c)

0.144 X 10

(d)

1440

5. The zero of the polynomial 2x+5 is

(a)

$\frac {5}{2}$

(b)

$-\frac {5}{2}$

(c)

$\frac {2}{5}$

(d)

$-\frac {2}{5}$

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 in a semi circle is_________

(a)

180°

(b)

90°

(c)

60°

(d)

45°

8. If Q1,Q2, Q3, Q4 are the quadrants in a Cartesian plane then ${ Q }_{ 2 }\cap { Q }_{ 3 }$

(a)

${ Q }_{ 1 }\cup { Q }_{ 2 }$

(b)

${ Q }_{ 2 }\cup { Q }_{ 3 }$

(c)

Null set

(d)

Negative x-axis

9. The point whose abscissa is 5 and lies on the x-axis is__________

(a)

(-5, 0)

(b)

(5,5)

(c)

(0,5)

(d)

(5,0)

10. The mean of a,b,c,d and e is 28. If the mean of a, c and e is 24, then mean of b and d is

(a)

24

(b)

36

(c)

26

(d)

34

11. The mean of the first 10 whole number is

(a)

4

(b)

4.5

(c)

5

(d)

5.5

12. The value of 3sin700sec200 + 2sin490sec510 is

(a)

2

(b)

3

(c)

5

(d)

6

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 letter is chosen at random from the word “STATISTICS”. The probability of getting a vowel is

(a)

$\frac { 1 }{ 10 }$

(b)

$\frac { 2 }{ 10 }$

(c)

$\frac { 3 }{ 10 }$

(d)

$\frac { 4 }{ 10 }$

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 3n$\sqrt { 27 }$

18. Find whether x and y are rational or irrational in the following
(i) a = 2 + $\sqrt { 3 }$ , B = 2 - $\sqrt { 3 }$ ; x = a + b,Y = a+ b
(ii) a = $\sqrt { 2 }$  + 7, B = $\sqrt { 2 }$ - 7 ; x = a + b, Y = a - b
(iii) a = $\sqrt { 75 }$, b = $\sqrt { 3 }$, x = ab, y = $\frac { a }{ b }$
(iv) a = $\sqrt { 18 }$, b = $\sqrt { 3 }$, x = ab, y = $\frac { a }{ b }$

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

20. Expand the following: (2a-3b+4c)2

21. Draw the circumcircle for, An isosceles right triangle having 6 cm as the length of the equal sides.

22. The points A(−5,4) , B(−1,−2) and C(5,2) are the vertices of an isosceles rightangled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square.

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. From the given figure, find all the trigonometric ratios of angle $\theta$.

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

28. Find the surface 'area of a cube whose edge is
(i) 27 cm
(ii) 3 cm
(iii) 6 cm
(iv) 2.1 cm

29. Two dice are rolled, find the probability that the sum is
(i) equal to 1
(ii) equal to 4
(iii) less than 13

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. Verify $\left( A\cup B \right) '$=$A'\cap B'$ using Venn diagrams

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

34. Locate an irrational number between two rational numbers$\frac { 23 }{ 10 }$ and$\frac { 12 }{ 5 }$

35. Add $\sqrt [ 5 ]{ 11 }$ and $\sqrt [ 7 ]{ 11 }$.Check whether the sum is rational or irrational

36. What must added to ${ x }^{ 4 }-3x^{ 2 }+2x+6\quad to\quad get\quad { x }^{ 4 }-2x^{ 3 }-x+8?$

37. Find the value of k for which the given system of equations kx + 2y = 3; 2x − 3y = 1 has a unique solution.

38. In the figure, AB is parallel to CD, find x

39. Find the perimeter of the triangle whose vertices are(3,2), (7,2) and (7, 5).

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. Find the median of the given values:47,53,62,71,83,21,43,47,41

42. Find the value of sin 64034'.

43. Find the TSA and LSA of a cuboid whose length, breadth and height are 7.5 m, 3 m and 5 m respectively.

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

45. Part IV

Answer all the questions

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

48. Construct an isosceles triangle ABC with AB = BC of sides 7 cm and ㄥB = 700 and locate its Orthocentre.

49. Draw an equilateral triangle of side 8 cm and locate its incentre .Also   draw the incircle