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CBSE X (All India)
MATHEMATICS PAPER 2004.

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 parts. Questions   (1-10) 10 questions of 3 marks each. Questions   (11-20)10 questions of 4 marks each. Questions (21-25)  5 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 following system of linear equations:

6(ax + by) = 3a + 2b, 6(bx – ay) = 3b – 2a

### Question 2

2.Using quadratic formula, solve the following quadratic equation for  x: p2x2 + (p2 – q2)x – q2 = 0

### Question 3

3.If (x – 3) (x + 2) is the GCD of the polynomials

P(x) = (x2 – 2x – 3) (2x2 + ax – 2) and Q(x) = (x2 + x – 2) (3x2 + bx – 3) find the value of a and b.

### Question 4

4.If

Express [P ´ Q ¸ R] as a rational expression in the lowest form.

### Question 5

5.The 8th term of an arithmetic progression (A.P.) is 37 and its 12th term is  57. Find the A.P.

### Question 6

6.Find the sum of the first 25 terms of an A.P. whose nth term is given by tn = 7 – 5n.

### Question 7

7.An electric fan is available for Rs. 600 cash or for Rs. 250 cash down payment followed by 3 monthly installments of Rs. 125 each. Find the rate of interest charged under the installment plan.

### Question 8

8.A loan of Rs. 4,200 is to be returned in two equal annual installments.  If the rate of interest is 10% per annum, compounded annually, calculate the amount of each installment.

### Question 9

9.In figure 1, ABCD is a trapezium in which AB ||DC. The diagonals AC and BD intersect at O. Prove  that

Fig.1

### Question 10

10.In figure 2, AB is a diameter of a circle, with centre O. If ÐABC = 70°, ÐCAD = 30° and ÐBAE = 60°. Find ÐBAC, ÐACD and ÐABE.

Fig.2

 Section A Section B Section C