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SET - I
MATHEMATICS PAPER 2009.
Time allowed: 3 hours; Maximum Marks: 80
| General Instructions: | |
| 1) | All questions are compulsory. |
| 2) | The question paper consists of thirty questions divided into 4 sections A, B, C and D. Section A comprises of ten questions of 01 mark each, Section B comprises of five questions of 02 marks each, Section C comprises ten questions of 03 marks each and Section D comprises of five questions of 06 marks each. |
| 3) | All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question. |
| 4) | There is no overall choice. However, internal choice has been provided in one question of 02 marks each, three questions of 03 marks each and two questions of 06 marks each. You have to attempt only one of the alternatives in all such questions. |
| 5) | In question on construction, drawing should be near and exactly as per the given measurements. |
| 6) | Use of calculators is not permitted. |
26. Solve the following equation for x.
9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0
27. Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Using the above theorem, prove that:
If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC
28. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.
29. A juice seller serves his customers using a glass as shown in figure. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use p = 3.14)
30. During the medical checkup of 35 students of a class, their weights were recorded as follows:
Weight (in kg) Number of students
38 – 40 3
40 – 42 2
42 – 44 4
44 – 46 5
46 – 48 14
48 – 50 4
50 – 52 3
Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph.
| Section A | Section B | Section C | Section D |
