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[Time: 3 hrs. to 3 hrs.] [M.M.: 90]General Instructions:1.All questions are compulsory.2. The question paper consists of 34 questions divided into four sections A, B, C and D. Section - A comprises of8 questions of1 mark each, Section - B comprises of6 questions of2 marks each, Section - C comprises of10 questions of 3 marks each andSection - D comprises of10questions of 4 marks each,3. Question numbers 1 to 8 in Section - A are multiple choice questions where you are to select one correct option out of the

given four.

4. There is no overall choice. However, internal choice has been provided in 1 question oftwo marks, 3 questions ofthreemarks each and 2 questions offour marks each. You have to attempt only one of the alternatives in all such questions.5. Use of calculator is not permitted.6.An additional 15 minutes time has been allotted to read this question paper only.

Section-AQuestion Numbers 1 to 8 carry 1 mark each. For each of the questions 1 to 8, four alternative choices have been provided of which onlyone is correct. You have to select the correct choice.1. In the given figure, AB is a diameter of circle. CD AB and DAB = 40 then BDC

is :

(A) 40 (B)90 (C) 130 (D) 1402. The point lying on the line 2x - y= 5 is:(A) (2, - 1) (B) (6, 1) (CM - 3, 1) (C) (3, 4)

3. In a cylinder, radius is doubled and height is halved. The curved surface area will be :(A) halved (B) doubled (C) same (D) four times

4. In a class, there are xgirls andyboys, a student is selected at random, then the probability ofselecting a boy is:

(A) x/y ( B ) x / ( x + y ) . (C)y/(x+y) (D)y/x5. A cuboid has dimensions 5 cm x 4 cm x 2 cm. Number of cubes of 2 cm side that can be cut from

cuboid is:

(A) 18 (B )5 (C )10 (D ) None of these

6. The mean of a, 6 is 8.5 and mean ofa, b, c is 7. The value ofc is:(A) 2 (B)4 (C)5 (D)9

7.

In the given figure, if ABCD is a parallelogram then length of BE is:(A) 24 cm (B)26cm (C) 6 cm (D) 8 cm

8. The ratio of the areas of two parallelograms on the same base and between the satt*l|j^mllelsis:

(A) 1 : 2 (B) 1 : 1 (C) 1 : 3 (D) 2 : 1Section-B

ABC is a triangle right angled at C. A line through the paid point M of hypotenuse AB andparallel to BC intersects AC at D. Show that ,(i) D is the mid point of AC

10. Find the mean of factors of 24.11. Curved surface area of a cone of radius 4 cm, is 20ncm2. Find total surface area of the samecone in terms of

\r OR ' 'The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Fihd the cost of white washing the walls of theroom and the ceiling at the rate of Rs 7.50 per m2,

12. Find the point at which, the equation 3x- 2y = 6 meets the x-axis.13. Find the co-ordinates of the points where the line 2x - y= 3 meets both the axes.14. In figure, E is any point on median AD of a AABC. Show that ar (ABE) = ar (ACE).^^^^^^^^^

B D C

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Section-C15. The taxi fare in a city is charged as per the rates stated below :Rate for the first kilometer of journey is Rs 5 and the rate for the subsequent distance covered is Rs 4 per km. takingdistance covered as xkm and total fare as Rsy.

Write the linear equation in variables xandyto express the above statement. Draw the graph for the linear equation.16. When three coins are tossed simultaneously, find the probability of getting at least two tails.17. The following is the distribution of weights (in kg) of 50 persons :

* ar (ABE) = ar (ACF)20. The radius of a spherical balloon increases from 7 cm to14 cm asair ispumped into it. Findthe ratio of surface areas of the balloon in two cases.

OR

The volume of a right circular cylinder is 3850 cubic cm. find its height if it's diameter is14 cm.21. A hemispherical bowl of internal and external diameters 6 cm and 10 cm ismelted and formedinto aright circular cylinder of radius 14 cm. Find the height of the cylinder.22. Diagonal AC and BD of a quadrilateral ABCD intersect at O insuch a way that ar (AOD) =ar(BOC). Prove that ABCD is a trapezium.23. Provethat equal chords of circle subtend equal angles at the centre.24. Construct a APQR inwhich PQ = 5.8 cm, QR + PR = 8.4 cm and Z Q = 60.

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Weight of the person Number of people

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Section-DV325. Prove that the area of an equilateral triangle is equal to ~-a2 where a,is th$ $ide of triangle.26. Prove that parallelograms on the same ba$e and between the same parallels are equal in area.27. 4 years before, age of a mother was 3 times the^a|1te of her daughter. Write a linear equation to - represent .this, situation anddraw its .graph. -A . B28. ABCD is a trapezium in which AB |f CD and AD = BC. / VShow that 2 J V( a)ZA = Z B / \(b)ZC = Z D ' / _________________ \D 1 C29. Prove that the diagonals of a parallelogram divide it into two congruent triangles.

OKIf X, Y and Z are the mid-points of sides BC, CA and AB of AABC respectively. Prove that AZXY is a parallelogram.

30. Solve for xy3s-5 4(3 + 2) = 254 + 7

3 + 5 15_ 40-4501__45-50_25_50-558_55-60__6 _60-65__ 4 _

65-706 _Draw a histogram for the above data..v. :ORThe height of50 students, measured to the nearest centimeters, have been found tobe as follows :135, 162,173,151, 176, 165,162, 145, 171, 172, 157, 161,172,158,163,175,148,173,163,159, 160,162,172,175, 176, 168, 167,170,172v173, 165, 151,149,169,173,138,156,148,159,166, 176,151,139,146,164,173,141,142,150,159Represent the data given above by a grouped frequency distribution table, taking class intervals as160 - 165,165 - 170 etc.18.Prove that quadrilateral formed by bisectors of the angles of a \ | gm isa rectangle.19.ABCDE isa pentagon. A line through B parallel to AC meets DC produced atF. Show that.(i)ar(ACB) = ar (ACF)(ii)ar (AEDF) = ar (ABCDE)ORXYis a line parallel toside BC of a triangle ABC passing through A. If BE || AC and CF11AB meet XYatE a&d Frespectively, show that

_ 40-4501__45-50_25_50-558_55-60__6 _60-65__ 4 _65-706 _Draw a histogram for the above data..v. :ORThe height of50 students, measured to the nearest centimeters, have been found tobe as follows :135, 162,173,151, 176, 165,162, 145, 171, 172, 157, 161,172,158,163,175,148,173,163,159, 160,162,172,175, 176, 168, 167,

170,172v173, 165, 151,149,169,173,138,156,148,159,166, 176,151,139,146,164,173,141,142,150,159Represent the data given above by a grouped frequency distribution table, taking class intervals as160 - 165,165 - 170 etc.18.Prove that quadrilateral formed by bisectors of the angles of a \ | gm isa rectangle.19.ABCDE isa pentagon. A line through B parallel to AC meets DC produced atF. Show that.(i)ar(ACB) = ar (ACF)(ii)ar (AEDF) = ar (ABCDE)ORXYis a line parallel toside BC of a triangle ABC passing through A. If BE || AC and CF11AB meet XYatE a&d Frespectively, show that

_ 40-4501__45-50_25_50-558_55-60__6 _60-65__ 4 _

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OR

A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's Father D is 8 years older than twice the age of B.If the present age of D is 48 years. Find the present ages of A, B and C.

31. A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical ball is droppedr 22into the tub raising the level of water by 6,75 cml What is the radius of the ball ? Use n = ~

32. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mma$4 the diameter of graphite T If the length of the pencil is 14 cm. Find the volume of wood and that of graphite. 33. A bag contains 12 balls out of which xare white. If one ball is taken out from the bag, find the probability of getting a white ball. If6 more white balls are added to the bag and the probability now for getting a white ball is double the previous one, find the value x. 34. Find mean, mode and median for the following data : ' 510, 15,18,10, 10, 20,10, 20,15, 21, 15 and 25.

65-706 _Draw a histogram for the above data..v. :ORThe height of50 students, measured to the nearest centimeters, have been found tobe as follows :135, 162,173,151, 176, 165,162, 145, 171, 172, 157, 161,172,158,163,175,148,173,163,159, 160,162,172,175, 176, 168, 167,170,172v173, 165, 151,149,169,173,138,156,148,159,166, 176,151,139,146,164,173,141,142,150,159Represent the data given above by a grouped frequency distribution table, taking class intervals as160 - 165,165 - 170 etc.18.Prove that quadrilateral formed by bisectors of the angles of a \ | gm isa rectangle.19.ABCDE isa pentagon. A line through B parallel to AC meets DC produced atF. Show that.(i)ar(ACB) = ar (ACF)(ii)ar (AEDF) = ar (ABCDE)ORXYis a line parallel toside BC of a triangle ABC passing through A. If BE || AC and CF11AB meet XYatE a&d Frespectively, show that

_ 40-4501__45-50_25_50-558_55-60__6 _60-65__ 4 _

65-706 _Draw a histogram for the above data..v. :ORThe height of50 students, measured to the nearest centimeters, have been found tobe as follows :135, 162,173,151, 176, 165,162, 145, 171, 172, 157, 161,172,158,163,175,148,173,163,159, 160,162,172,175, 176, 168, 167,170,172v173, 165, 151,149,169,173,138,156,148,159,166, 176,151,139,146,164,173,141,142,150,159Represent the data given above by a grouped frequency distribution table, taking class intervals as160 - 165,165 - 170 etc.18.Prove that quadrilateral formed by bisectors of the angles of a \ | gm isa rectangle.19.ABCDE isa pentagon. A line through B parallel to AC meets DC produced atF. Show that.(i)ar(ACB) = ar (ACF)(ii)ar (AEDF) = ar (ABCDE)ORXYis a line parallel toside BC of a triangle ABC passing through A. If BE || AC and CF11AB meet XYatE a&d Frespectively, show that