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CBSE X (All India)
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.
SECTION A

### Question 1

1. Solve the system of equations

2.    Find

### Question 3

3.  If  is the HCF of the polynomials

and

Find the values of c and b.

### Question 4

4. Using the quadratic formula, solve the equation:

### Question 5

5. The 5th term of an Arithmetic Progression (A.P.) is 26 and the 10th term is 51. Determine the 15th term of the A.P.

### Question 6

6. Find the sum of all the natural numbers less than 100 which are divisible by 6.

### Question 7

7. A household article is available for Rs. 970 cash or Rs. 210 cash down payment followed by three equal monthly instalments. If the rate of interest charged under the instalment plan is 16% per annum, find the amount of instalment.

### Question 8

8. A man borrows Rs. 25,200 from a finance company and has to repay it in two equal annual instalments. If the interest is charged at the rate of 10% per annum compounded annually, calculate the amount of instalment.

### Question 9

9. In the below figure,  Prove that

### Question 10

10. In Figure 2, PT = 6 cm, AB = 5 cm. Find the length of PA.

 Section A Section B Section C