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__IX Maths mix SS2
Crash 2011__

__Section A__

1) In the
figure, O is the centre of the circle.Calculate the magnitudes of Ð

2)
Construct a triangle ABC in which ÐB=75^{0},
BC=5cm and AB =3cm

3) Find the value of a and b such that the following equations may have (3, -2) as a solution 5x + ay = 8; 7x+by = 4b

4) Find the value of k, if x=2,y=1 is a solution of the equation 2x+3y=k

5) Draw the graph of the equation 2x + y = 4. From the graph, find the value of y when x = 2

6) Find the median of 19, 25, 60, 49, 36, 31, 30, 32, and 56, if 25 is replaced by 52, what will be the new median

7) A die is thrown 100 times, and the number of times each number turned up is recorded in the following table.

No. on the die |
1 2 3 4 |

Frequency |
15 55 16 14 |

8) Find the probability that the number turned up is a prime number.

9) Find the volume of the sphere whose surface area is 154 sq. cm.

10) The
radius and height of a cone are in the ratio 4 : 3. The area of the base is 154
cm^{2}. Find the area of the curved surface.

__Section B__

11) Write the four solutions for the equation 2x+y = 7

12) A bag contains 4 red, 5 green and 3 blue marbles. A marble is selected at random from the bag. Calculate the probability of getting (a) a red ball (b) a blue ball (c) not a blue ball.

13) Construct a triangle with base of
length 5cm, sum of two sides 7.7cm and one of the angles of the base as 45^{0}.

14) In the figure, *l* is a line which intersects two concentric circles with centre P

at points A,C, D and B, Prove that AC = DB

15) In the
figure, PT touches the circle whose Centre is at R. Diameter SQ when produced
meets PT at P. Given Ð^{0}

16) In the following figure, AP||BQ||CR, Prove that ar(ΔAQC) = ar(ΔPBR)

17) Draw the graph of the equation 2x – 3y =5. From the graph,

find the value of y when (i) x = 4 and (ii) x = 3

18) In the figure, AD and BE are medians of a ΔABC and BE||DF. Prove that CF =(1/4) AC

19) Here is a linier equation that converts Fahrenheit

to Celsius: F= (9/5) C+32

20)

21) Draw the graph of the linier equation above using Celsius for x-axis and Fahrenheit for y-axis

22) If the
temperature is 30^{0} C, what is the temperature in Fahrenheit?

23) Find the missing frequency p for the following distribution whose mean is 7.68.

X |
3 |
5 |
7 |
9 |
11 |
13 |

F |
6 |
8 |
15 |
p |
8 |
4 |

24) The mean of 11 numbers is 35.If the mean of first 6 numbers is 32

and that of last 6 numbers is 37, find the sixth number

25) ABCD is a quadrilateral. A line through D parallel to AC meets BC produced in P.

Prove that ar (ΔABP) = ar (quad ABCD)

26) Prove that the figure formed by joining the mid points of the pairs of consecutive sides of a rectangle is a rhombus

__Section C__

27) The taxi fare in a city is as follows: For the first kilometer the fare is Rs 8 and for the subsequent distance.it is Rs 5 per km .Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information and draw its graph.

28) Construct a triangle ABC, in which ÐA=30^{0}, ÐB=90^{0} and AB+BC+AC=13 cm

29) 2000 families with 3 children were selected at random and the following data is recorded. Find

Girl child in family |
0 |
1 |
2 |
3 |

No.offamilies |
475 |
814 |
111 |
600 |

(a) probability of family having 0 girl (b )probability of family having 1 girl (c) probability of family having 2 girl (d) probability of family having more than 1 girl (e) probability of family at least 1 girl

30) Prove that the line segment joining the midpoint of the hypotenuse of a right angled triangle to the vertex of the right angle is half of the hypotenuse.

31) Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on remaining part of the circle. Using this prove that the angle subtended by a minor arc in the alternate segment is obtuse. .

32) A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder is 1.4 m. and its length is 5m. What will be the cost of painting it on the outside at the rate of Rs.10 per square metre?

33) A solid cube of side 24 cm is cut into 27 cubes of equal volume. What will be the side of the new cube?

Marks |
0-10 |
10-30 |
30-45 |
45-50 |
50-60 |

No. of students. |
8 |
20 |
18 |
10 |
6 |

34) Represent the following data by means of a frequency polygon and Histogram

__Section-
D__

35)
Any angle in the semicircle is 90^{0}
(b) 180^{0} (c) 270^{0} (d) 360^{0}

36)
Curved surface Area of cone is Лr^{2}
(b) 2Лrl (c) 2Лrh (d) Лrl

37)
CSA of
solid hemisphere is (a)2Лr^{2} (b) 4Лrl (c) 3Лr^{2} (d) Лrl

38) Median of 14, 15, 18,20,21,25 is (a)18(b)19 (c) 20 (d) 21

39)
Find angle ÐBCD *140 ^{0} (b) 110^{0} (c) 70^{0}
(d) 60^{0 }*

40) The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean. 14 (b) 12 (c) 10(d) 8

41)
1m^{3}=? Liter (a) 10 (b) 100 (c)
1000(d) 10000

42)
In a cyclic quadrilateral sum of opposite angles
are (a)90^{0} (b) 180^{0} (c) 360^{0}(d) None of these

43)
Slant height of cone is equal to (a) Лrl (b) r^{2}+h^{2
}(c) r^{2}-h^{2} (d) √ r^{2}+h^{2}

44)
Volume of cone = ...?.....Volume of cylinder (a)
/2 (b) 1/3^{ }(c) 1/4 (d) 1/5

45) Find the curved surface area of a cone having slant height 10 cm and circumference of base is 44 cm.

46) Find the total surface area of a sphere having diameter 14 cm.

**Section-E**

47) Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboids.

48) A rectangular sheet of paper 44 cm x 18 cm is rolled out along its length and a cylinder is formed. Find the radius of the cylinder formed.the inner diameter of the well is 3.5 m and 10 m deep find: Inner curved area

49) A hemispherical bowl made of brass has inner diameter 10.5 cm. find the cost of tin painting it on the inside at the rate of Rs 16 per 100 cm square.

50) The height of a cone is 16 cm and its base radius is 12 cms.find the curved and total surface area of the cone. Use, π = 3.14.

51) Find the lateral surface area of a closed cylindrical patrol storage tank that is 4.2 m in diameter and 4.5 m high.

52)
The radius and slant height of a cone are in the
ratio 4:7. If it’s curved surface area of this cone is 792 cm^{2}. Find
its radius. ( use = 22/7)

53) The diameter of the moon is one third of the earth. Find out the ratio of the surface area of the moon and earth.

54)
A wooden toy in the form of cone surmounted on a
hemisphere. The diameter of the base of the cone is 6 cm and height is 4 cm.
find the cost of painting the toy at the rate of Rs 5 per 1000 cm^{2}

55) A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

56) A
storage tank consists of circular cylinder with a hemisphere adjoined on either
end. If the external diameter of the cylinder is 1.4 m and its length be 8 m.
find the cost of painting it on the outside at the rate of Rs. 10 per m^{2}

57) If twice the son’s age in yrs. Is added to the age of his father, the sum is .Write its linear equation & draws its graph.

58) In a cyclic quadrilateral if one angle is thrice of its opposite angle. Write its linear equation & draw its graph.

59)
ABCD is a *||*gm. AB is produced to E so that BEAB. Prove that ED bisects BC.

60) In a Δ the line segment joining the mid-points of any two sides is parallel to the third side & is half of it.

61) Construct a ΔPQR in with its perimeter 10.4 cm and base angles of 45° & 60°.

62) The marks secured by 10 students are 68, 53, 93, 60, 80, 63, 58, 66, 73, 56, 62. Find the median marks.

63) If (-3,4)is a solution of the equation , find . 3x-4y=b,Find b.

64) A box contains 40 balls of the same shape & weight. Among the balls 10 balls are white, 16 are red & rest is black. What is the probability that a ball drawn from the box is not black ball?

65)
ABCD is a cyclic
quadrilateral in which D C BC is parallel to AD ∠ADC=110° & ∠BAC=50° **110° **then ∠DAC is: (a) 60° (b) 40° **50° **(c) 70°
(d) 110° A B

66) Choose the correct solution of equation x-y=12: (a) (4,3) (b) (0,-12) (c) (12,12) (d)

67) If BC is the diameter of the circle of centre O A D B and OD is the perpendicular to the chord AB of a circle, then (a) (b) 2CA=OD O (c) CA=OD (D) none of these C

68) If 2 is subtracted from the fraction we get –(5/4). Write its linear equation & draw its graph.

69)
In a
quadrilateral ABCD, the bisectors of *L*A
& *L*D meet at E. Prove that *L*B+*LC*=2*LA*ED

70) In a beauty contest the following girls participated: (1) Lara Dutta (4) Celina Jaitely (2) Priyanka Chopra (5) Aishwarya Rai (3) Diya Mirza (6) Sushmita Sen

What is the probability that (a) Lara Dutta (c) Aishwarya Rai or Sushmita Sen (b) Diya Mirza (d) not Celina Jaitely

71) A conical tent has the area of its base as 154m² & that of its curved surface area as 550m². Find the volume of the tent.

72)
Show that if the
two diagonals of a *||*gm are equal then it is a rectangle.

73) **. **If mode of the following data is 15, find k.

10, 15, 17, 15,(0.5k+6) , 17, 20.

74) **Solve for x -** (2x+1).

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