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MATHEMATICS PAPER 2004.
Time allowed: 3 hours; Maximum Marks: 100
| General Instructions: | |
| 1) | All questions are compulsory. |
| 2) | The question paper consists of 25 questions divided into three parts. Questions (1-10) 10 questions of 3 marks each. Questions (11-20)10 questions of 4 marks each. Questions (21-25) 5 questions of 6 marks each. |
| 3) | There is no overall choice. However, an internal choice has been provided in each section. |
| 4) | In question on construction, the drawing should be neat and exactly as per the given measurements. |
| 5) | Use of calculator is not permitted. However, you may ask for Mathematical tables. |
| 6) | Please give the explanation for the answer where applicable. |
11.Solve the following system of linear equations graphically
5x – 6y + 30 = 0, 5x + 4y – 20 = 0. Also find the vertices of the triangle formed by the above two lines and X-axis.
12.Solve
for x: 
13.A hemispherical bowl of internal diameter 30cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5cm and height 6cm. Find the number of bottles necessary to empty the bowl.
14.Prove that 
16.Show that the points A(2, -2), B(14, 10), C(11,13) and D(-1,1) are the vertices of a rectangle.
17.Prove that the coordinates of the centroid of a DABC, with vertices
A(x1, y1) B(x2, y2),
C(x3, y3) and are given by 
18.The mean of the following frequency distribution is 57.6 and the sum of the observations is 50. Find the missing frequencies f1 and f2.
19.A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (i) white (ii) red (iii) not black (iv) red or white.
20.The following data shows the expenditure of an individual over various items:
Items |
Education |
Food |
Rent |
Clothing |
Others |
Expenditure |
1600 |
3200 |
4000 |
2400 |
3200 |
Represent the above data with the help of a pie-chart.
| Section A | Section B | Section C |
