# Class 10-2005

**SECTION A**

### Question 1

Add the difference of (x-4/x-3) and (x+7/x+8) to x+8/x²+5x-24

### Question 2

Find the sum of all two digit odd positive numbers.

### Question 3

x y | |

a b |

and ax – by = a^{2} – b^{2}

Question 4

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)

** **

have (x^{2} + 4x + 3) as common factor.

### Question 5

Solve for x: a²b²x²+b²x-a²x-1=0

### Question 6

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

### Question 7

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

### Question 8

Deepak borrowed a sum of money and returned it in three equal quarterly installments of Rs 1,40,608. If the rate of interest charged is 16% per annum compounded quarterly, find the sum borrowed. Also find the total interest charged.

### Question 9

The perpendicular from vertex A on the side BC of triangle ABC intersects BC at Point D such that DB= 3CD Prove that

2 AB² = 2AC² + BC²

### Question 10

In the given figure, find the length of DE if AE=15cm, DB = 4 cm and CD = 9 cm.

**SECTION B**

### Question 11

Solve the following system of equations graphically:

2x – y = 4 ; 3y – x = 3 Find the points where the lines meet the Y-axis.

### Question 12

A two digit number is such that the product of its digits is 15. If 18 is added to the number, the digits interchange their places, find the number.

### Question 13

The base radius and height of a right circular solid cone are 2cm and 8cm respectively. It is melted and recast into spheres of diameter 2cm each. Find the number of spheres so formed.

### Question 14

1/sec x- tanx- 1/cos x = 1/cos x- 1/sec x + tan x

### Question 15

Prove that the points (0,0); (5,5) and (-5,5) are vertices of a right isosceles triangle.

### Question 17

The line joining the points(2,1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x – y + k = 0 , find the value of k.

### Question 18

If the mean of the following data is 18.75. find the value of **p** :

x_{i} |
10 |
15 |
P |
25 |
30 |

f_{i} |
5 |
10 |
7 |
8 |
2 |

### Question 20

A bag contains 8 red,6 white and 4 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is:

(i) Red or white (ii) Not black (ii) Neither white nor black.

**SECTION C**

### Question 21

Prove that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

### Question 22

Two pillars of equal height stand on either side of a roadway which is 150m wide. From a point on the roadway between the pillars, the elevations of the top of the pillars are 60^{0 }and 30^{0}. Find the height of the pillars and the position of the point.

### Question 23

A tent is in the form of a cylinder of diameter 4.2m and height 4m , surmounted by a cone of equal base and height 2. Find the capacity of the tent and the cost of canvas for making the tent at Rs100 per sq.m.

### Question 24

PAB is a secant to a circle intersecting it at A and B and PT is a tangent to the circle.

Prove that :

**PA x PB = PT ^{2}**