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MATHEMATICS PAPER 2006.
Time allowed: 3 hours; Maximum Marks: 100
| 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 contain 10 (1- 10) questions of 3 marks each. Section B contains 10 questions 10 (11-20) questions of 4 marks each. Section C contains 5 (21-25) questions of 6 marks each. |
| 3) | There is no overall choice. However, an internal choice has been provided in each section. |
| 4) | In question on construction, the drawing should be neat and exactly as per the given measurements. |
| 5) | Use of calculator is not permitted. However, you may ask for Mathematical tables. |
| 6) | Please give the explanation for the answer where applicable. |
21. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides.
Making use of the above, prove the following:
In the figure below,
ABCD is a rhombus. Prove that 
22. Prove that if a chord drawn through the point of contact of a tangent to a circle, then the angles which this chord makes with the given tangent are equal respectively to the angles formed in the corresponding alternate segments.
Using the above, do the following:
AB is a diameter
and AC is the chord of the circle such that 
The tangent at C intersects AB produced in D.
Prove that 
23. A bucket made up of a metal sheet is in the form of a frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of the metal sheet used, if it costs Rs. 10 per 100 cm2.
24. A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 300. Calculate the distance of the hill from the ship and the height of the hill.
25. Mrs. Ruchi’s salary is Rs. 32,250 per month exclusive of HRA. She donates Rs. 12,000 to Prime Minister’s Relief Fund (100% exemption). She also donates Rs. 6,000 to a school and gets a relief of 50% on this donation. She contributes Rs. 5,000 per month towards her Provident Fund. She pays a quarterly premium of Rs. 2,500 towards her LIC policy and invests Rs. 25,000 in NSCs. If Rs. 2,700 is the tax deducted each month from her salary for 11 months, find the tax deducted from her salary in the last month of the year.
Use the following for calculating income tax:
| Section A | Section B | Section C |
