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MATHEMATICS PAPER 2008.
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. |
20. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Use the above for the following :
If the areas of two similar triangles are equal, prove that they are congruent.
21. If a line touches a circle and from the point of contact a chord is drawn, the angles which this chord makes with the given line are equal respectively to the angles formed in the corresponding alternate segments.
Use the above for the following: In Figure 3, ABCD is a cyclic quadrilateral and PQ is the tangent to the circle at C.
If BD is the diameter and DCQ = 40° and ABD = 60°, find
(i) ∠ ADB
(ii) ∠ BCP.
Fig. 3
22. The
numerator of a fraction is one less than its denominator. If three is added to
each of the numerator and denominator, the fraction is increased by 
. Find the fraction.
23. A hemispherical bowl of internal diameter 36 cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. Find the number of bottles needed to empty the bowl.
24. A
pole 5 m high is fixed on the top of a tower. The angle of elevation of the top
of the pole observed from a point A on the ground is 60° and the angle of
depression of point A from the top of the tower is 45°. Find the height of the
tower. (Take 
= 1.732)
25. The salary of Hukam Singh is Rs. 42,000 per month (exclusive of HRA). He donates Rs. 30,000 to Prime Minister’s Relief Fund (100% exemption). He contributes Rs. 6,500 per month towards Provident Fund and Rs. 5,000 quarterly towards LIC premium. He also purchases NSC worth Rs. 10,000. He pays income tax of Rs. 5,100 per month for 11 months. Calculate the income tax he has to pay in the 12th 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
lab Income tax
(i) Upto Rs. 1,00,000 No tax
(ii) From Rs. 1,00,001 to Rs. 1,50,000 10% of the taxable income exceeding Rs. 1,00,000
(iii) From Rs. 1,50,001 to Rs. 2,50,000 Rs. 5,000 + 20% of the amount
exceeding Rs. 1,50,000
(iv) Rs. 2,50,001 and above Rs. 25,000 + 30% of the amount
exceeding Rs. 2,50,000
(c) Education Cess 2% of Income tax :
| Section A | Section B | Section C |
