Rangoli International School
Rangoli International School
Rangoli International School
SECTION-A
SECTION-B
SECTION -C
III. Solve the following:
1. Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x +2.
2. Factorise x3 – 23x2 + 142x – 120.
3. ABCD is a trapezium in which AB || DC and ∠ ∠ . Find angles C and D of the
trapezium.
4. In the given figure, ∠OAB = 300 and ∠OCB = 570. Find ∠BOC and ∠AOC.
5. Sides of a triangle are in ratio of 12: 17: 25 and it's perimeter is 540 cm. Find its area.
6.The height of a cone is 16 cm and its base radius is 12 cm. Find the curved surface area
and the total surface area of the cone (Use = 3.14).
7.The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find
the cost of white-washing its curved surface at the rate of Rs 210 per 100 m 2.
8. Find the capacity in litres of a conical vessel whose diameter is 14 cm and slant height is
25 cm.
SECTION-D
IV. Solve the following:
1. Factorise each of the following cubic expressions:
(i) 27q3 – 125p3 – 135q2p + 225qp2
(ii) 8x3 + 729 + 108x2 + 486x
2. ABCD is a parallelogram and ∠DAB = 600. If the bisectors AP and BP of angles A and B
respectively, meet at P on CD, prove that P is the midpoint of CD.
3. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
4. If two chords of a circle are equally inclined to the diameter through their point of
intersection, prove that the chords are equal.
5. If the non parallel sides of a trapezium are equal, prove that it is a cyclic.
6. Find
(i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m
in diameter and 4.5 m high.
(ii) how much steel was actually used, if of the steel actually used was wasted in making
the tank.