 # CBSE [ Delhi ]_X_Mathematics_2006_Set I

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• Q1

Find the sum of all the two digit natural numbers divisible by 4.

Marks:3 • Q2

The 6th term of an Arithmetic Progression (AP) is -10 and the 10th term is -26. Determine the 15th term of the AP.

Marks:3 • Q3

A household article is available for Rs. 2,500 cash or Rs. 520 cash down payment followed by four equal monthly instalments. If the rate of interest charged under the instalment plan is 25% per annum, find the amount of each instalment.

Marks:3

Now out of Syllabus

• Q4

A man borrows Rs. 36,410 from a finance company and has to repay it in three equal annual installments. Find the amount of each installment if the rate of interest is 10% per annum compounded annually.

Marks:3

Now out of Syllabus

• Q5

Solve for x: 12abx2 - (9a2 - 8b2)x - 6ab = 0

Marks:3 • Q6

If (x - 2) (x + 3) is the HCF of the polynomials

P(x) = (x2 - 3x +2) (2x2 + 7x + a) and
Q(x) = (x2 + 4x + 3) (3x2 - 7x + b).
Find the values of a and b.

Marks:3

Now Out of syllabus

• Q7

Solve for x and y:
47x + 31y = 63
31x + 47y = 15

Marks:3 • Q8

In Figure 3, AB =AC ,Prove that BE = EC Marks:3

Since tangent from an external point to a circle are equal in length.

BD = BE

CE = CF

Now
AB = AC (given)

AB – AD = AC –AF

BD = CF

BE = CE

proved

• Q9

A two-digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the number.

Marks:3

Let the unit place digit = x

Tens Place digit = y

Number = 10y + x

On interchanging the digits, the new number = 10x + y

y = 35/x

According to the question

18 + x + 10y = 10x + y

18 = 9x-9y

x - y = 2

x – 35/x = 2 • Q10

In Figure 1, ACB = 90° , CD AB, prove that CD2 = BD.AD. Marks:3 In Triangle ACB and Triangle ADC

Angle A = angle A ( Same angle)

Angle C = angle D ( Both 90 degree)

By AA

Triangle ACB similar to triangle ADC

Similarly Triangle ACB is similar to BDC

So triangle ADC is similar to BDC