# CBSE [ All India]_X_Mathematics_2006_Set I

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• Q1

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

Marks:3

Now, out of Syllabus

• Q2

If (x + 2) (x - 3) is the HCF of the polynomials p(x) = (x2 + x - 2) (3x2 - 8x + c) and q(x) = (x2 + x - 12) (2x2 + x + b). Find the values of c and b.

Marks:3

Now out of syllabus

• Q3

The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.

Marks:3

• Q4

Solve the system of equations:
bx/a - ay/b + a + b = 0 and bx - ay + 2ab = 0

Marks:3

• Q5

Using the quadratic formula, solve the equation:
a2b2x2 – (4b4 – 3a4)x – 12a2b2 = 0

Marks:3

• Q6

Marks:3

Now out of syllabus

• Q7

The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.

Marks:3

let one umber be x, other will be 8 - x

• Q8

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.

Marks:3

Let Ist terms of A.P = a and common difference be d

5th term = a+4d = 26

10th term = a+9d = 51

a + 4d = 26

a + 9d = 51

on subtracting

5d = 25

d = 5

putting the value of d in Ist

a+4d = 26

a+20 = 26

a = 6

first term = 6

15th term = a+14d

6+14(5)

6+70

= 76

• Q9

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

Marks:3

Series of natural numbers which are divisible by 6

6, 12, 18…96

First term a = 6

Last term l = 96

Common difference d = 6

Number of terms = 96/6 = 16

Sn = n/2(a+l)

=16/2(6+96)

=8(102)

S16 =816