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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. |
Question number 16 to 25 carry 3 marks each.
16. Prove that 
is
an irrational number.
17. Solve for x and y:
ax – by = 2ab
18. The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteenth terms of the A.P.
19. Evaluate:
20. Draw a right triangle in which sides (other
than hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle
whose sides are 
times
the corresponding sides of the first triangle.
21. In the figure below, AD ^ BC and 
Prove that 2 CA2 = 2 AB2 + BC2.
22. Find the ratio in which the point (2, y) divides the line segment joining the points (-2, 2) and (3, 7). Also find the value of y.
23. Find the area of the quadrilateral ABCD whose vertices are A(-4, -2), B(-3, -5), C(3, -2) and D(2, 3)
24. The area of an equilateral triangle is 
.
Taking each angular point as centre, circles are drawn with radius equal to half
the length of the side of the triangle.
Find the area of triangle not included
in the circles. [Take 
25. Two dice are thrown simultaneously. What is the probability that
(i) 5 will not come up on either of them?
(ii) 5 will come up on at least one?
(iii) 5 will come up at both dice?
| Section A | Section B | Section C | Section D |
