Q21) Show that 2sec² - sec⁴ - 2cosec² + cosec⁴ = cot⁴ - tan⁴   (Marks 4)

Q22) In fig. AB is a diameter of circle with centre O, OA = 7 cm. Find the area of the shaded region ( use = 22/7). (Marks 4)

Q23) In fig. AB and CD are two parallel tangents to a circle with centre O. ST is tangent segment between two parallel tangents touching the circle at Q. Show that SOT = 90^o. (Marks 4)

Q24) Construct a quad. ABCD in which AB = 2.5 cm BC = 3.5 cm, AC = 4.2 cm, CD = 3.5 cm and AD = 2.5 cm. Construct another quad. AB'C'D' with diagonal AC' = 6.3 cm such that it is similar to quad ABCD.  (Marks 4)

Q25) Find the cost of living index number for the year 1995 assuming 1990 as the base year.  (Marks 4)

Section - C

Q26) Solve for x : 9^{x + 2} - 6 x 3^{x + 1} + 1 = 0  (Marks 6)

Q27) If a radius of the circular and of a conical bucket, which is 45 cm high are 28 cm, 7 cm, find the capacity of the bucket.  (Marks 6)

Q28) Prove that ratio of area of two similar triangles is equal to the ratio of squares of corresponding sides. Using the above do the following :-
In fig ABC and PQR are isosceles in which A = P
If ar(ABC)/ar(PQR) = 9/16, find AD/PS (Marks 6)
 

Q29) Prove that sum of either pair of opposite angles of a cyclic quadrilateral is 180^o. Using the above solve the following:

In fig POQ is a diameter and PQRS is a cyclic quadrilateral. If PSR = 150^o, find RPQ.  (Marks 6)

Q30) A man on the roof of a home, which is 10 m high, observes the angle of elevation of the top of a building as 42^o and angle of depression of the base of the building as 40^o. Find the height of the building and its distance from the home.  (Marks 6)

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