General Maths Geometry March 2015 Board Paper

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.

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