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MATHEMATICS PAPER 2007.
(FOREIGN)
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. |
20. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Using above, prove the following: In figure, O is the centre of the circle. If ∠BAO = 30 and ∠BCO = 40, find the value of ∠AOC.
21. State and prove Pythagoras theorem. Use the above to prove the following:
ABC is an isosceles right triangle, right angled at C. Prove that
.
22. The side of a square exceeds the side of another square by 4 cm and the sum of areas of two squares is 400 sq.cm. Find the dimensions of the squares.
23. A hollow copper sphere of external and internal diameter 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.
24. An observer in a lighthouse observes two ships on the same side of the lighthouse, and in the same straight line in with the base of the lighthouse. The angles of depression of the ships approaching it are 30 and 60. If the height of the lighthouse is 150 cm; find the distance between the ships.
25.Satish (aged 67 years) has monthly income of Rs. 30,000 (excluding HRA). He donates Rs. 80,000 to a charitable orphanage (50% exemption). He contributes Rs. 30,000 towards Public Provident Fund and purchases NSCs worth Rs. 20,000. He pays Rs. 1,500 as income tax per month for 11 months. Calculate the income tax to be paid by him in the12th month of the year
Use the following to calculate income tax:
(a) Savings 100% exemption for permissible savings
upto Rs. 1,00,000
(b) Rates of Income tax for Senior Citizens (over 65 years)
Slab Income tax
(i) Upto Rs. 1, 85,000 No tax
(ii) From Rs. 1, 85,001 to Rs. 2, 50,000 20% of the taxable income exceeding
Rs. 1, 85,000
(iii) From Rs. 2, 50, 001 and above Rs. 13,000 + 30% of the taxable
Exceeding Rs. 2, 50,000
(c) Education Cess 2% of Income tax payable
| Section A | Section B | Section C |
