General Maths Geometry July 2016 Board Paper
Q. 1. Solve any five of the following sub - questions: [5]
(i) In figure, △ PQR and △QRT are right angled triangle. If PQ = 4 and RT = 2, then find A(△PQR) / A(△QRT).
(ii) In the given figure A is the centre of the circle. Write the name of inscribed angle.
(iii) Draw seg AB of length 5 cm and bisect it.
(iv) Write the upper class limit of class 40 - 60.
(v) Using the information given in figure, find XY. 
(vi) In figure, point C is the centre of circle. Write the name of the diameter. 
Q. 2. Solve any four of the following sub - questions: [8]
(i) The circles with radii 7 cm and 3 cm touch internally, then find the distance between centres.
(ii) In figure, △PQR is a right angled triangle, ㄥQ = 900, ㄥR = 400, Write the ratios of sin 400 and cos 400.
(iii) Draw ㄥXYZ of measure 1200 and bisect it.
(iv) Ray BP is the bisector of ㄥABC. Find the value of x from the information given in the figure.
(v) Two coins are tossed. Write a sample space (S) and n(S). If A be the event of getting exactly one head, then write event A and find n(A).
(vi) Draw a tangent at any point P on the circle of radius 2 cm with centre O.
Q. 3. Solve any three of the following sub - questions: [9]
(i) Find the height of right - angled triangle whose base is 4 and hypotenuse is 3.
(ii) The radius of a sphere is 14cm. Find its surface area. (ㄫ = 22/7 )
(iii) Find the value of cos2 300 - sin2 600.
(iv) In the figure, m(arc APC) = 500. Find ㄥABC.
(v) Construct the incircle of an equilateral △ ABC having side 5 cm.
Q. 4. Solve any two of the following sub questions: [8]
(i) An observer is at a distance of 80 metres from a tower, makes an angle of elevation of 600 with the top of the tower. What is the height of the tower?
(ii) The marks obtained by a student in an examination in various subjects are given below.
Subjects
|
Marathi
|
English
|
Science
|
Mathematics
|
Social Science
|
Total
|
Marks
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65
|
55
|
80
|
90
|
70
|
360
|
Represent the above data using a pie diagram.
(iii) Total volume of 21 steel balls in a bearing is 88 cm2. Find the diameter of each ball.
Q. 5. Solve any two of the following sub - questions. [10]
(i) In △ABC, AP is a median. If AP = 7, AB2 + AC2 = 260, then find BC.
(ii) The dimensions of a rectangular parallelepiped are in the ratio 4: 3: 2. If the surface area of vertical faces is 448 sq. cm. Find its length, breadth and height.
(iii) Represent the following data with a frequency polygon.
Class interval
|
18 - 20
|
21 - 23
|
24 - 26
|
27 - 29
|
30 - 32
|
Frequency
|
5
|
4
|
8
|
6
|
2
|