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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 linear equations graphically:
9.Simplify 
10.The first term, common difference and last term of an A.P are 12, 6 and 252 respectively. Find the sum of all terms of this A.P
11.Prove that any four vertices of a regular pentagon are cyclic.
(Out of syllabus.)
(OR)
BC is a chord of a circle with centre O. A is a point on arc BAC as shown in Figure 2. Prove that ∠BAC + ∠OBC = 900
12.Draw a circle of radius 4.5 cm. At a point A on it, draw a tangent to the circle without using the centre.
13.A toy in the
form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical
portion is 7 cm and the total height of the toy is 14.5 cm. Find the volume of the toy. (use π = 
)
14.The expenditure on different heads of a household ( in hundreds of rupees) is as follows:
Head |
Education |
Games |
Entertainment |
Gardening |
Decoration |
Expenditure |
20 |
10 |
15 |
10 |
17 |
Draw a pie diagram to represent the above data.
15.All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting (a) a black face card, (b) a queen, (c) a black card.
16.Prove
that 
17. Three consecutive vertices of a parallelogram are (2, 1); (1, 0) and (4, 3). Find the coordinates of the fourth vertex.
18. If the point C (1, 2) divides internally the line segment AB in the ratio 3 : 4, where the coordinates of A are (2, 5), find the coordinates of B.
19. A loan of Rs. 2550 is to be paid back in two equal half-yearly instalments. How much is each instalment if interest is compounded half-yearly at 8% per annum
| Section A | Section B | Section C |
