C & W
















2011


1)  Solve the following equation:
x - 18/x = 6. Give your answer correct to two significant figures.

2) In the figure O is the centre of the circle.
Tangents at A and B meet at C
If angle ACO= 30°, find the angle BCO, AOB, APB

3) Mr Kumar borrowed Rs 15000 for two years. The rate of interest for the two successive years are 8% and 10% respectively. If he repays Rs 6200 at the end of the first year, find the outstanding amount at the end of the second year ?

4) ABC is a triangle and G(4,3) is the centroid of the triangle. If A(1,3), B(4,b) and C(a,1l, find a and b.

5) A mathematical aptitude test of 50 students was recorded as follows :
Marks    no of students 
50-60        4 
60-70        8
70-80       14
80-90       19
9-100        5
Draw a histogram for the above data using a graph paper and locate the mode.

6) A solid cone of radius 5cm and height 8cm is melted and made into small spheres of radius 0.5cm. Find the number of spheres is formed.

7) use a graph paper to answer the following questions. (Take 1cm= 1 unit on both axes)
a) plot A(4,4), B(4,-6) and C(8,0),  the vertices of a triangle ABC .
b) Reflect ABC on the y-axis and and name it as A'B'C'.
c) Write the co-ordinate of the image A', B' and C'.
d) Give a geometrical name for the figure AA'C'B'BC.
e) identify the line of symmetry of AA'C'B'BC.

8) Solve for x: {√(3x+4) + √(3x -5)}/{√(3x+4) - √(3x -5)} = 9.

9) In the following figure ABC is a right angled triangle with angle BAC= 90°,
and AD perpendicular BC.
a) prove ∆ ADB ~ ∆ CDA
b) if BD= 18cm, CD = 8cm find AD.
c) find the ratio of the area of ∆ ADB to area of ∆ CDA.

10) a) Using step deviation method, calculate the mean marks of the following distribution. 
b) State the model class .
Class interval   frequency 
50-55                   5
55-60                  20
60-65                  10
65-70                  10
70-75                    9
75-80                    6
80-85                   12
85-90                    8

11) Marks obtained by 200 students in an examination are given below:
Marks    frequency 
00-10        5
10-20        11
20-30        10
30-40       20
40-50       37
60-70       40
70-80       29
80-90       14
90-100      6
Draw an ogive for the given distribution taking 2 cm= 10 marks on one axis and 2cm = 20 students in the other axis. Using the graph, determine:
a) The median marks
b) The number of students who failed if minimum marks required to pass is 40.
c) If scoring 85 and more marks is considered as grade one. find the number of students who secured grade one in the examination.

12) Calculate the area of the shaded region, if the diameter of the semicircle is equal to 14 cm
13) Evaluate: 2(tan35/cot 55)² + (cot 55/tan35)² - 3(sec 40/cosec50)

14) Draw a circle of radius 3.5cm. Mark a point P outside the circle at a distance of 6cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of tangent.

15) Show: (cosecA - sinA)(secA - cosA) sec²A= tanA.

16) In what period of time will Rs12000 yield Rs3972 as compound at 10% per annum, if compounded on an yearly basis ?

17) 6 is the mean proportion between two numbers x and y and 48 is a third proportional of x and y. Find the numbers.

18) A man observes the angle of elevation of the top of a building to be 30°.  He walks towards it in a horizontal line through its base. On covering 60m the angle of elevation changes to 60°. Find the height of the building correct to the nearest metre.

19) ABC is a triangle with AB= 10cm, BC= 8cm and AC= 6cm (not drawn to scale).
Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles .

20) Rs 480 is divided equally among x children. if the number of children were 20 more than each would have Rs 12 less.  Find x






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