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.
