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

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

(a)

(A∪B)′

(b)

(A∩B)′

(c)

A′∩B′

(d)

A∩B

2. Sets having the same number of elements are called ___________

(a)

overlapping sets

(b)

disjoints sets

(c)

equivalent sets

(d)

equal sets

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. 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 Auto fare is found as minimum rs 25 for 3 kilometer and thereafter rs12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

(a)

c = 25 + n

(b)

c = 25 + 12n

(c)

c = 25 + (n–3)12

(d)

c = (n–3)12

6. Divide x3-4x2+6x by "x" the result is _____________________

(a)

$x^{ 2 }+4x-6$

(b)

$x^{ 2 }-4x-6$

(c)

$x^{ 2 }-4x+6$

(d)

$x^{ 2 }+4x+6$

7. Orthocentre of a triangle is the point of concurrency of _______

(a)

medians

(b)

altitudes

(c)

angle bisectors

(d)

perpendicular bisectors of side

8. The distance between the points (-1, 2) and (3, 2) is____________

(a)

$\sqrt{14}$

(b)

$\sqrt{15}$

(c)

4

(d)

0

9. If (1,−2), (3,6), (x,10) and (3,2) are the vertices of the parallelogram taken in order, then the value of x is

(a)

6

(b)

5

(c)

4

(d)

3

10. Find the mean of the prime factors of 165.

(a)

5

(b)

11

(c)

13

(d)

55

11. Let be the mid point and b be the upper limit of a class in a continuous frequency distribution.The lower limit of the class is

(a)

2m-b

(b)

2m+b

(c)

m-b

(d)

m-2b

12. If cos A = $\frac { 3 }{ 5 }$, them the value of tan A is

(a)

$\frac { 4 }{ 5 }$

(b)

$\frac { 3 }{ 4 }$

(c)

$\frac { 5 }{ 3 }$

(d)

$\frac { 4 }{ 3 }$

13. The total surface area of a cuboid is

(a)

4a2 sq. units

(b)

6a2 sq. units

(c)

2(l + b)h sq. units

(d)

2(lb + bh + lh) sq. units

14. If A is any event in S then its complement P(A′) is equal to

(a)

1

(b)

0

(c)

1-A

(d)

1-P(A)

15. Part II

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

14 x 2 = 28
16. If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

17. Write the following in the form of 5n:
$\frac{1}{5}$

18. Multiply $\sqrt [ 3 ]{ 40 }$ and $\sqrt [ 3 ]{ 16 }$ .

19. Can you reduce the following to surds of same order $\sqrt [ 4 ]{ 5 }$

20. If f(x) = x2 - 4x + 3, find the values of f(1), f(-1), f(2), f(3). Also find the zeros of the polynomial f(x).

21. Find the supplement of the following angles.
Right angle

22. A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2,−3) and (2,1) respectively, then find the coordinates of C.

23. A, Band C are vertices of $\Delta$ABC. D, E and F are mid points of sides AB, BC and AC respectively. If the coordinates of A, D and Fare (-3, 5), (5, 1) and (-5, -1) respectively. Find the coordinates of B, C and E.

24. Using section formula, show that the points A (7, -5), B (9, -3) and C (13, 1), are collinear.

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 cot$\theta$ =, then find the value of  $\cfrac { 3cos\theta -4sin\theta }{ 5sin\theta +4cos\theta }$

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

28. Find the area of an equilateral triangle whose perimeter is 150 m.

29. In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

30. Part III

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

14 x 3 = 42
31. If A = {b,c,e,g,h} , B = {a,c,d,g,i} and C = {a,d,e,g,h} , then show that $A-(B\cap C)=(A-B)\cup (A-c)$.

32. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : intersection of sets

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

34. Rationalise the denominator and simplify $\frac { \sqrt { 5 } }{ \sqrt { 6 } +2 } -\frac { \sqrt { 5 } }{ \sqrt { 6 } -2 }$

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

36. Show that (x-3) is a factor of x+ 9x- x - 105

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

39. Show that the point (11,2) is the centre of the circle passing through the points (1,2), (3,–4) and (5, -6)

40. the mid-point formula to show that the mid-point of the hypotenuse of a right angled triangle is equidistant from the vertices (with suitable points).

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. cube has the total surface area of 486 cm2. Find its lateral surface area.

44. In an office, where 42 staff members work, 7 staff members use cars, 20 staff members use two-wheelers and the remaining 15 staff members use cycles. Find the relative frequencies.

45. Part IV

4 x 5 = 20
46. If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

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

48. In the given Fig. if AB = 2, BC = 6, AE = 6, BF = 8, CE = 7, and CF = 7, compute the ratio of the area of quadrilateral ABDE to the area of ΔCDF

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