C- XMPCB
















2011


1) Find the value of k if (x -2) is a factor of x³+ 2x²- Kx +10
Hence, determine whether x + 5 is also factor.

2) If A= 3   5 & B= 2
              4  -2          4  is the product AB possible ?  give reason.  If yes find AB

3) From a  pack of 52 playing cards all cards whose numbers are multiples of 3 are removed. A card is now drawn at random.
 What is the probability that card drawn is:
a) a face card (king, Jack , queen)
b) an even numbered red card.

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

5) 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

6) Abhi has a recurring deposit account in a bank. He deposits Rs 2500 per month for 2 years. If he gets RS 66250 at the time of maturity, find;
a) The intrest paid by the bank.
b) the rate of interest.

7) 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.

8) Solve the following inequation and represent the solution set on the number line 2x - 5 ≤ 5x + 4< 11, where x belongs to I, I is a set of integers .

9) 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.

10) A manufacturer sells a washing machine to a wholesaler for Rs 15000. The wholesaler sells it to a trader at a profit of Rs 1200 and the trader in turn sells it to a consumer at a profit of Rs 1800. If the rate of GST is 8% find,
a) The amount of GST received by the State Government on the sale of this machine from the manufacturer and the wholesaler.
b) The amount that consumer pays for the machine.

11) 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.

12) ABCD is a parallelogram where A(x,y), B(5,8), C(4,7) and D(2,-4). Find 
a) coordinates of A.
b) equation of diagonals BD.

13) 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.

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

15) If A= 2    5 & B= 4    -2
                1    3         -1     3 and I is the identity matrix of the same order and A' is the transpose of matrix A, find A'B + BI.

16) 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.

17) 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

18) 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.

19) Mr parik invested Rs 52000 on Rs 100 shares at a discount of Rs 20 playing 8% dividend . At the end of 1 year he sells the shares at a premium of Rs 20. Find 
a) the annual dividend.
b) the profit earned including his dividend.

20) 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.

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

22) 6 is the mean proportion between two numbers x and y and 48 is a third proportional of x and y. Find the numbers.

23) 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.

24) 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 .

25) 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

26) Given equation of line L₁ is y= 4.
a) Write the slope of line L₂ if L₂ is the bisector of angle O.
b) Write the coordinates of point P.
c) Find the equation of L



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