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SET - II
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. |
Question number 16 to 25 carry 3 mark each.
16. Show that the square of any positive odd integer is of the form 8m + 1, for some integer m.
OR
Prove that 
is not a rational number.
17.If the polynomial 6x4 + 8x3 - 5x2 + ax + b is exactly divisible by the polynomial 2x2 - 5, the find the values of a and b.
18.If 9th term of an A.P. is zero, prove that its 29th term is double of its 19th term.
19.Draw a circle of radius 3 cm. From a point P, 6 cm away from its centre, construct a pair of tangents to the circle. Measure the lengths of the tangents.
20.In figure 1, two triangles ABC and DBC lie on the same side of base BC. P is a point on BC such that PQ || BA and PR || BD. Prove that QR || AD.
21. In figure 2, a triangle ABC is right angled at B.
Side BC is trisected at points D and E. Prove that 8
OR
In figure 3, a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF.
22. Prove that
23.Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
24. In figure 4, the shape of the top of a table in a restaurant is that of a sector of a circle with centre O and ∠BOD = 90°. If BO = OD = 60 cm, find
(i) the area of the top of the table.
(ii) the perimeter of the table top.
(Take π = 3.14)
OR
In figure 5, ABCD is a square of side
14 cm and APD and BPC are semicircles. Find the area of shaded region.
(Take 
)
25. A box has cards numbered 14 to 99. Cards are mixed thoroughly and a card is drawn from the bag at random. Find the probability that the number on the card, drawn from the box is
(i) an odd number,
(ii) a perfect square number,
(iii) a number divisible by 7.
| Section A | Section B | Section C | Section D |
