Q. 1. Solve any five of the following sub  questions: [5]
(i) △ ABC ~ △ PQR. If m ㄥA = 500, then what is the measure of ㄥP?
(ii) If the radius of a circle is 4 cm, then find the diameter of the circle.
(iii) Find the class mark of the class 21  25.
(iv) In the adjoining figure, find the value of sin Θ.
(v) How many tangents can be drawn to a circle from a point outside a circle?
(vi) Find the lower limit and upper limit of the class 30  34.
Q. 2. Solve any four of the following sub  questions: [8]
(i) In the △ ABC, line PQ  side BC. With the help of the given figure, find the value of x.
(ii) Two circles with radii 7 cm and 9 cm touch externally. Find the distance between the centres.
(iii) The base of a right  angled triangle is 12cm and its height is 5cm. Then find the length of the hypotenuse.
(iv) The side of a cube is 5 cm, find the volume of the cube.
(v) Convert the following classes into exclusive form:
11  15, 16  20, 21  25, 26  30.
(vi) Find the volume of a cuboid having its length, breadth and height 4 cm, 3 cm and 6 cm respectively.
Q. 3. Solve any three of the following sub  questions: [9]
(i) In a right  angled △RPA, ㄥP = 900, seg PD ⟂ RS. If RD = 4 and DS = 9, then find PD.
(ii) Find the value of : sin290  tan245.
(iii) Construct a circumcircle of an equilateral △PQR having side 5 cm.
(iv) The capacity of a cylindrical pickle jar is 1000 cm3 and the area of its base is 100 cm3. Find its height.
(v) The expenditure of people in a locality is shown below. Draw a histogram.
Expenditure (in Rs.)

200  300

300  400

400  500

500  600

600  700

No. of People

25

40

30

20

10

Q. 4. Solve any two of the following sub questions: [8]
(i) In △ABC seg AP is median. If AB2 + AC2 = 260 and BC = 18, then find the value of AP.
(ii) In the given figure, Q is the centre of the circle and seg PN and seg PM are tangent segments to the circle at points N and M respectively. If ㄥMPN = 500, find ㄥMQN.
(iii) Draw a circle with centre P and radius 3 cm. Draw tangents from a point A such that d(P,A) = 7 cm.
Q. 5. Solve any two of the following sub  questions. [10]
(i) In the given figure, an observer at point A looking a ship at point C from the top of a light  house makes an angle of depression 600. IF the height of the light  house is 90 metres, then find how far is that ship from the light  house.
(ii) How many lead balls each of radius 1 cm can be made from a sphere of radius 8 cm?
(iii) The marks obtained by a student in an examination in various subjects are given below:
Subjects

Marathi

English

Science

Mathematics

Social Science

Total

Marks

65

55

80

90

70

360

Represent the above data using a pie diagram.