Q. 1. Solve any five of the following sub - questions: [5]
(i) △ ABC ~ △ PQR. If AB/PQ = 1/2, then find the value of BC/QR.
(ii) If the diameter of circle is 10 cm, then find the radius of the circle.
(iii) What is the midpoint of class 16 - 20?
(iv) In the adjoining figure, find the value of cos Θ.
(v) How many tangents can be drawn to a circle from a point on the circle?
(vi) If a coin is tossed, what is its sample space?
Q. 2. Solve any four of the following sub - questions: [8]
(i) The lengths of sides of a triangle are 6 cm, 8 cm and 10 cm. Is this triangle right - angled? Give reason.
(ii) Radii of two internally touching circles are 10 units and 4 units.Find the distance between centres of the circles.
(iii) In the adjoining figure, 口PQRS is a trapezium. Seg PQ || Seg MN || seg SR. If PM = 6, MS = 8, NR = 4, then find QN.
(iv) Radius of a sphere is 7 cm. Find its curved surface area.
(v) A card is drawn from a well - shuffled pack of 52 cards. What is the probability that a card will be an ace?
(vi) Radius and slant height of a cone are 21 cm and 30 cm respectively. Find its curved surface area. (ㄫ = 22/7 )
Q. 3. Solve any three of the following sub - questions: [9]
(i) △ ABC ~ △ PQR and A( △ABC) = 144 cm2, A(△PQR) = 64 cm2. If BC = 12 cm, then find the value of QR.
(ii) Find the value of : tan245 + cot245.
(iii) Construct a regular hexagon with side 4 cm.
(iv) Volume of a cylindrical toy is 1570 cm2. Radius of its base is 10 cm. Find the height of the toy. (ㄫ = 3.14)
(v) Draw a histogram for the following data:
Marks
|
10 - 20
|
20 - 30
|
30 - 40
|
40 - 50
|
50 - 60
|
No. of Students
|
30
|
50
|
40
|
20
|
15
|
Q. 4. Solve any two of the following sub questions: [8]
(i) In △ABC seg AD is median. If AB = 11, AC = 17, BC = 12, then find the value of AD.
(ii) In the given figure, 口 ABCD is a cyclic quadrilateral. Chord AB ≌ Chord BC, Chord AD ≌ Chord CD, If ㄥADC = 3x0 and ㄥABC = 2x0, then find the measures of ㄥB and ㄥD.
(iii) Draw a circle with centre O and radius 4 cm. Take point A such that d(O,A) = 9 cm. Draw tangents from point A.
Q. 5. Solve any two of the following sub - questions. [10]
(i) In the given figure a player is sitting on a top of a tower 20 m high. It is observed that an angle of depression of a ball lying on the ground is 900. Find the distance between the foot of the tower and the ball.
(ii) The volume of a cone is the same as that of volume of a cylinder whose height is 9 cm and diameter 40 cm. Find the radius of the base of the cone if its height is 108 cm.
(iii) The following data indicate the number of students using different modes of transport.
Mode of Transport
|
Bicycle
|
Bus
|
Walk
|
Train
|
Car
|
Total
|
Number of students
|
140
|
100
|
70
|
40
|
10
|
360
|
Represent the above data using a pie diagram.
