 # CBSE [ All India]_X_Mathematics_2005_Set I

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• Q1

Solve for x: Marks:3 • Q2

The cash price of a machine is Rs 9,000. It is also available at Rs. 2,200 cash down payment followed by five equal monthly installments of Rs 1,400 each. Find the rate of interest under the installment plan.

Marks:3

Out of syllabus

• Q3

Add the difference of Marks:3

Out of syllabus

• Q4

Find the sum of all two digit odd positive numbers.

Marks:3

Two digit odd positive numbers are

11, 13, 15, 17, ..., 99

a = 11, d = 13 - 11 = 2

l = 99

a + (n - 1)d = 99

11 + (n - 1) 2 = 99

(n - 1) 2 = 88

n - 1 = 44

n = 45

Sn = (n/2)(2a + (n - 1) d)

= (45/2)(22 + 44 2)

= (45/2)(2 55)

= 45 55 = 2475

• Q5

Solve for x and y: Marks:3 • Q6

A two digit number is four times the sum of its digits and twice the product of the digits. Find the number.

Marks:3

Let the unit place digit be x and tens place digit be y

Sum of the digits = x + y

Number = x + 10y

According to the question

x + 10y = 4(x + y) -----(1)

and

x + 10y = 2xy -----(2)

On solving equation (1)

x + 10y = 4(x + y) 3x = 6y x = 2y

Putting the value of x in equation (2)

x + 10y = 2xy 2y + 10y = 4y2 12y = 4y2 y = 3 x = 2y = 6 Number = x + 10y = 6 + 30 = 36

• Q7

Find a and b so that the polynomials:

P(x) = (x² + 3x + 2)(x² + 2x + a) and

Q(x) = (x² + 7x + 12)(x² + 7x + b)

Marks:3

Out of syllabus.

• Q8

Solve for x: Marks:3 • Q9

The 8th term of an Arithmetic progression is zero. Prove that its 38th term is triple its 18th term.

Marks:3

Let the first term of an A.P be a and the common difference be d

8th term of A.P. = a + 7d

According to the question

a + 7d = 0 a = -7d

18th term of A.P. = a + 17d = -7d + 17d = 10d

38th term of A.P. = a + 37d = -7d + 37d = 30d

3 x 18th term = 38 term

Proved