# CBSE [ All India]_X_Mathematics_2004_Set I

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• Q1

Solve the following system of linear equations:

Marks:3

• Q2

The sum of the digits of a two digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number.

Marks:3

Let the unit digit of the number be x and tens digit of number be y

Original number = 10y + x

According to the question

x + y = 15       ---------(1)

On interchanging the digits, number is 10x + y

According to the question

10x + y – 10y - x = 9

9x - 9y = 9

x - y = 1       ---------(2)

2x = 16

x = 8

putting the value of x in (2)

8 - y = 1

-y = 1 - 8 = -7

y = 7

number = 78

• Q3

p2x2 + (p2 - q2)x - q2 = 0

Marks:3

• Q4

Marks:3

Out of Syllabus

• Q5

Marks:3

Not in Syllabus

• Q6

The 8th term of an Arithmetic Progression (A.P.) is 37 and its 12th term is 57. Find the A.P.

Marks:3

8th term = a + 7d = 37      ...(1)

12th term = a + 11d = 57   ...(2)

Subtract (1) from (2)

4d = 20

d = 5

Put the value of d in (1)

a + 35 = 37

a = 2

A.P. is 2, 7, 12, 17, …

• Q7

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

Marks:3

• Q8

Which term of the Arithmetic Progression 3, 10, 17, ... will be 84 more than its 13 th term?

Marks:3

First term of the series a = 3

Common difference of series d = 7

Required number = T13+84

a + 12 d + 84=?

3 + 12 (7) + 84 =?

3+84+84 = 171

let nth term be 171

tn = a+(n-1)d

171 = 3+(n-1)7

168 = (n-1)7

24 = n-1

n = 24+1

n = 25

• Q9

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.

Marks:3

Not in syllabus