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CBSE X (All India)
MATHEMATICS PAPER 2005.

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 2

2.Find the sum of all two digit odd positive numbers.

### Question 3

3. Solve for x and y:  and

### Question 4

4. Find a  and b so that the polynomials:

q(x)=(

have (as common factor.

5.Solve for x:

### Question 6

6.The 8 th term of an Arithmetic progression is zero. Prove that its  term is triple its th term.

### Question 7

7.The cash price of a machine is Rs  It is also available at

Rs.  cash down payment followed by five equal monthly installments
of Rs
each. Find the rate of interest under the installment plan.

### Question 8

8.Deepak borrowed a sum of money and returned it in three equal quarterly installments of Rs 1,40,608. If the rate of interest charged is 16% per annum compounded quarterly, find the sum borrowed. Also find the total interest charged.

### Question 9

9.The perpendicular from vertex A on the side BC of triangle ABC intersects BC at Point D such that  Prove that

### Question 10

10.In the given figure, find the length of DE if AE=15cm, DB = 4 cm and CD = 9 cm.

 Section A Section B Section C