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MATHEMATICS PAPER 2007.
Time allowed: 3 hours; Maximum Marks: 80
| General Instructions: | |
| 1) | All questions are compulsory. |
| 2) | The question paper consists of 25 questions divided into three sections- A, B and C. Section A contains 7 questions of 2 marks each, Section B is of 12 questions of 3 marks each and Section C is of 6 questions of 5 marks each. |
| 3) | There is no overall choice. However, an internal choice has been provided in two questions of two marks each, two questions of three marks each and two questions of five marks each. |
| 4) | In question on construction, the drawing should be neat and exactly as per the given measurements. |
| 5) | Use of calculators is not permitted. However, you may ask for Mathematical tables. |
8. Solve the following system of equations graphically.
9. Simplify the following rational expression in the lowest terms:
10. If the sum of first n terms of an A.P. is given by
11. In a cyclic quadrilateral ABCD, diagonal AC bisects ∠C. Prove that the tangent to the circle at A is parallel to the diagonal BD.
12. Construct a ∆ABC in which base BC = 6 cm,
13. The diameter of a solid copper sphere is 18 cm. It is melted and drawn into a wire of uniform cross-section. If the length of the wire is 108 m, find its diameter.
14 .The expenditure (in rupees) of a family for a month is as follows
Item |
Rent |
Food |
Education |
Electricity and water |
Others |
Expenditure |
800 |
3000 |
1200 |
400 |
1800 |
15. From a pack of 52 cards, red face cards are removed. After that a card is drawn at random at the pack. Find the probability that the card drawn is
a) a queen
b) a red card
c) a spade card
16. Prove that:
17. The coordinates of the mid-points of the sides of a triangle are (4, 3), (6, 0) and (7, −2). Find the coordinates of the centroid of the triangle.
18. If the distance of P(x, y) from two points with coordinates (5, 1) and (−1, 5) is equal, prove that 3x = 2y
19. A loan of Rs. 24,600 is to be paid back in two equal semi-annual instalments. If the interest is charged at 10% per annum, compounded semi annually, find the installment.
| Section A | Section B | Section C |
