PAPER - III
SECTION - A
ANSWER ALL QUESTIONS IN THIS SECTION
1. Find the amount on Rs.2560 for 11/2 years at 61/4% p.a., the interest being compounded half yearly. [6]
2. A sum of Rs.1536 amounts to Rs.1632 after one year. How much would it amount to in the next year, at compound interest? [6]
3. Prove that the area of DABC and DDEF are in equal proportion with BC2 = AC2 = AC2. EF2 DE2 EF2 Given DABC ~ DDEF [6]
4. (i) 2sin67° + tan40° + cos0°. Evaluate without using tables. [3] cos23° cot50°
(ii) ABC is an isosceles triangle. AB=AC=41cm. BC=80cm. And AD is the altitude. Find AD and area of DABC. [3]
5. Using ruler and compasses, construct a square in and about a circle. [8]
6. (i ) Given that a+b = 6 and ab = 63/4. Find the value of a-b. [4] (ii) The roots of x2-6px+45 = 0 are p and 5p. Find the values of p. [4]
SECTION - B 40 MARKS
ANSWER ONLY 4 QUESTIONS IN THIS SECTION. ALL QUESTIONS CARRY EQUAL MARKS [10]
7. (I) If E = {5,6,7,8}, write the following relations as a set of ordered pairs from E to E. (i ) "is less than" (ii) "is 1 more than". (II)In DABC, ÐB = 90°, ÐA = 32°33¢ and AB = 4.8 find ÐC, BC and AB.
8. (a) Find x and y if é 1 -2 ù éxù = é-3ù ë 3 2 û ëyû = ë 7û (b) Show that é1 2ù is a solution of x2-2x = 3I where I = é1 0ù ë2 1û ë0 1û (c) Calculate the median and mode of 2,4,4,8,16,21,21,21,43.
9. (a) Solve graphically y = x and y = -x+2. (b) Given 2my-3x = 4 and 3my+8x = 10 are perpendicular to each other. Find m.
10. (a) The age distribution of the workers in a factory calculated to the nearest year, in a certain year was:
Calculate the mean age of a worker. (b) From the above diagram prove that DABM ~ DAMC ~ DABC.
11. (a) Using ruler and compass only draw in-circle to a triangle. (b) Construct a histogram to represent the following data:
12. (a) As shown in the figure m(arc PMQ) = 130°. Find mÐPQS and mÐPQR. (b) The length of a chord of a circle is 10. The distance of the chord from the centre is 8. Find the radius and the diameter of the circle.
13. (a) The radius of a cone is 5cm. And its perpendicular height is 12cm. Find the - (i ) curved surface area (ii ) Area of base (iii) Total surface area. (b) Angle between two radii of a circle is of 135°. Tangents to the circle are drawn at the out ends of these radii. Find the measure of the angle between the tangents.
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