### 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, ã„¥Q = 900, ã„¥R = 400, Write the ratios of sin 400 and cos 400.

(iii) Draw ã„¥XYZ of measure 1200 and bisect it.

(iv) Ray BP is the bisector of ã„¥ABC. 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. (ã„« = 22/7 )

(iii) Find the value of cos2 300 - sin2 600.

(iv) In the figure, m(arc APC) = 500. Find ã„¥ABC.

(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 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