SECTION A

40 Marks

ANSWER ALL QUESTIONS IN THIS SECTION

1) A sum of money is lent at compound interest payable annually. 
   If the interestfor the second and third years are Rs.330 and Rs.363, find the rate and the 
   sum. [6]
2) The value of a machine reduces by 5% every year. If its present value 
   is Rs.4000. what would be its value 2 years later? [6]
3) In a trapezium ABCD side AB ôôside DC, diagonals AC and BD cut each other
   at O. If AB=6, DC=20,OD=15. Find OB [6]
   
4) I) Prove 1/cosec q +1 = Sin q/1+Sin q [3]
  ii) 
      In the above figure, prove that [3]
      AB2+CD2 =AD2+BC2
5)    Inscribe a circle in a regular pentagon using ruler and compass. [8]

6) i) Solve Ö2x2-17 = 9 [4]
  ii) Solve 4x2-12+a if its roots are equal to 3/2 then find the value 
      of `a'. [4]


                                               SECTION (B)                                       40 Marks

   ANSWER ONLY 4 QUESTION IN THIS SECTION
   ALL QUESTIONS CARRY EQUAL MARKS [10]

7) i) If A = { 1,2,3} and B = {4,5} Find: -
   a) AxB
   b) BxA 
   c) n(AxB)
  ii) Two boys are on opposite sides of a tower. They measure the angles of 
      elevation of the top of the tower as 33° and 24° respectively. If 
      the height of the tower is 100 m. Find the distance between the two boys.

8) a) Given A = é1 2ù and B = é5 6ù
                      ë 3 4û             ë7 8û
      Find A+B and ¼(A+B).
   b) Let A = é4 -2ù B = é0 2ù C = é-2 0ù
                   ë6 -3û       ë1-1û       ë1-3 û
      Find A2-A+BC
   c) Find the median and mode of the following
   i) 5,7,9,13,11,5,5,5,5,3,3
  ii) 25,36,45,17,9,43,25,25,45

9) a) Draw the graph of y = 2x+4. Use your graph to find:-
   i) the slope
  ii) the intercept on the y axis
 iii) the area between the line and axes.
   b) If A(2,a), B (3,-1) and C(4,-5) are collinear, find a.

10)a) Villagers age 10-20 20-30 30-40
      Literate       10     5     15
      Illiterate     20     10    15
      Find the mean of literates and illiterates.
   b) In the figure below DADC ~ DBEC, AD = 35 AC = 42, BE = 30 AND EC = 21. 
      Find BC and DC.


11)a) Draw circles of diameters 5 cm and 3cm respectively with their centres 
      5cm apart. Draw a transverse common tangent to the two circles and measure 
      its length.
   b) Draw a 'less than' cumulative frequency curve for following:
   

 
      
12)a) Vertices of a rectangle ABCD are on a circle. Show that arc ABC~ arcADC, 
      with refernce to the given figure below.

   b) P is the centre of circle. Points A,B,C lie on the circle. P is between 
      A and B. BC = 10 and AC = 24. Determine the radius.

  
13)a) A barrel (drum) is to be painted from inside and outside. It has no 
      lid. The radius of its base and height are 1.5m and 2m respectively. Find 
      the expenditure of painting at the rate of Rs.8 per sq. meter. [p = 3.14]
   b) A is the centre of a circle. The radius of the circle is 11. B is a point 
      at a distance 61 from A. Determine the length of a tangent segment BR drawn 
      to the circle from B. If seg BS is the other tangent segment drawn to the 
      circle from B, determine perimeter of ARBS.



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