ANSWER ALL QUESTIONS IN THIS SECTION.

1. A certain sum amount to Rs.1323 in 2 years and to Rs.1389.15 in 3 years. Find the rate
   and the sum.[6]
2. Find the compound interest on Rs. 400 for 2 years at 5% p.a. [6]
3. In the figure below ABCD is a 11gm. E is a point on CD, AE intersects BD at O. EF || CB.
    Find the following area ratios if DF : FB = 3 : 1. (i) DFE : DDBC (ii) DOFE : DODA     [6]

                        
4. (i) Solve without using tables : (sin49°/cos41°)² + (cos41°/sin49°)²       [3]
   (ii) In the DABC, ÐBAC = 90°, AD ^ BC, AB = 15cm and     BD = 9cm. Find the length of DC.    [3]

                                 
5. Construct an equilateral triangle in and about a circle. [8]
6. (i) Solve 2/x+1 - 4/2x-7 = 3/2-x   [4]
   (ii) Solve 4x⁴ - 25x² + 36 = 0      [4]

SECTION - B

ANSWER ANY 4 QUESTIONS FROM THIS SECTION.
ALL QUESTIONS CARRY EQUAL MARKS [10]

7. (i) If R = {9x,y) xSw, ySw L 2x+y = 4}
then write :-
(a) the range of R
(b) the domain of R
(c) R as a set of ordered pairs.

(ii) The upper part of a tree broken over by the wind makes an angle of 38° with the ground
    and the horizontal distance from the root of the tree to the point where the top of the tree
    meets the ground is 20mts. Find the height  of the tree before it was broken.
8. (a) If é -1 0 ù éa bù = é1 0ù then find a, b., c and d.
              ë 0 1 û    ëc dû   ë0-1û
(b) Let Mx é1 1ù = [ 1,2] where M is a matrix. State the order of M and find M.
                ë1 2 û
(c) Find the arithmetic mean of the numbers 5,3,8,7,6,1. What is the new mean if 3 is
    added to each number?
9. (a) Draw x = 3, y = 4, and y = x. Write down the co-ordinates of the vertices of the triangle
    enclosed between the above lines.
(b) If y - 2x = 3 and 2y = px + 8 are parallel find the value of p.
10. (a) Find the mean of the following table by direct method

(b) In the figure below D ABC ~ D DEF AB = 12 BC = 16, AC = 14, DE = 6 and ÐB = 60°.
Find the sides EF, DF and measure of ÐE.


11. (a)Construct the cyclic quadrilateral ABCD in which AB = 7cm. BC = 9cm.
ÐABC = 75° and D is equidistant from B and C. Measure CD.
(b) Construct a histogram to represent the following data :

12. (a)
As shown in diagram below if ÐAPC = 70° then find mÐABC
(b) Show that in any circle the length of a chord not passing through the
centre, is less than that of a diameter.

13. (a) The dimensions of a rectangular parallelopiped are in ratio 4:3:2.
If the surface area of vertical faces is 448 sqcm. Find its length , breadth
and height.
(b) The following figure shows four tangents of a circle touching it in points
A, B, C and D respectively. These four tangents form a parallelogram PQRS.
If PB = 5 and BQ = 3 find PS.