Answer the following questions
Section-A
1. Find the value of the polynomial 2x + 5 at x = – 3.
2. Find the volume of a sphere whose surface area is 616 sq. cm.
3. A joker’s cap is in the shape of a right circular cone with base radius 7 cm and height
24 cm. Find the area of sheet required for 10 such caps.
4. Prove that “A diagonal of a parallelogram divides it into two congruent triangles”
5. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°,
∠BAC = 30°. Find ∠BCD.
6. If a sphere and a solid cube have the same surface area then find the ratio of their
volumes.
Section-B
7.
8. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and
DA respectively. Show that the quadrilateral PQRS is a rhombus.
9. A cylindrical roller 1.5 m long has a diameter of 70 cm. How many revolutions will it
make to level a playground measuring 50 m X 33 m?
10.
SECTION – C
11.
12. Construct a triangle PQR in which QR = 6 cm, ∠Q = 600 and PR – PQ = 2 cm.
13. Three girls Reshma, Salma and Mandeep are playing with each other standing at
points R, S and M respectively on the boundary of a circle of radius 5 m as shown in
the figure. Reshma throws a ball to Salma, Salma to Mandeep and Mandeep to
Reshma. If the distance between Reshma and Salma and between Salma and
Mandeep is 6 meters each and O is the center of the circle, then answer the following
questions:
(i) Find the distance between Reshma and Mandeep.
(ii) Find the value of length OE.
14.
Insurance is a means of protection from financial loss. It is a form of risk management,
primarily used to hedge against the risk of a contingent on uncertain loss. For
insurance awareness, an insurance company selected 2000 drivers at random in a
particular city, find a relationship between age and accidents. The data obtained is
given in the following table:
Answer the following questions:
(i) Find the probability for a driver chosen at random from the city being 18 – 29 years of age and having exactly 3 accidents in one year.
(ii) Find the probability for a driver chosen at random from the city having no
accidents in one year.
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