Another pair of such numbers is
13 x 62 = 31 x 26.

The required angle is 180^o.

(i) By paper folding
(ii) By using ruler and compasses.

4.7 cm.

Radius of the circles will be equal.

Here, given the radii of two circles are 5 cm and 5.4 cm.

Ratio of income to expenditure = 7 : 5
Let the income and expenditure per month be Rs 7x and 5x respectively.
Then, saving per month = Rs 7x - Rs 5x = Rs 2x
According to the question,
2x= 2000
⇒ x =\(\frac{2000}{2}\) =1000
⇒ 7x = 7 x 1000 = 7000
Hence, his income is Rs 7000 per month.

The conditions remaining the same, they will cross each other again after 45 + 45 = 90 minutes.

Construct a perpendicular to a line from a point on it.
                   
Here, \(\angle\)PAR = 90^o.

We know that, perpendicular bisector of a line segment is its axis of symmetry.
Step I Draw a line segment \(\bar{PQ}\) = 7 cm.
Step II With P and 0 as centres and radius more than half of \(\bar{PQ}\), draw two arcs which intersect each other at A and B.
                        
Step III Join A and B.
Thus, AB is the axis of symmetry of \(\bar{PQ}\).

Given, radius of circle is 3 cm.
Steps of construction are as follows:
Step I Draw a circle of radius 3 cm.
Step II Draw two perpendicular diameters AB and CD.
                  
Step III Join A and D, D and B, Band C and A and C.
Thus, quadrilateral ABCD is a square.

Longest chord is diameter. Yes, it will pass through the centre.

In order to construct a line segment of length 7.3 cm using a ruler, we use the following steps:
Step I Mark a point A on the paper and place the ruler so that zero mark of the ruler is at A.
Step II Mark with a pencil a point B against the mark on the ruler which indicates 7.3 cm.
Step III Join the points A and B by moving the tip of the pencil against the straight edge of the ruler.
                
The line segment AB, so obtained is the required line segment of length 7.3 cm.

Circles which have the same centre and different radii are called concentric circles.
        

A chord of a circle divides the circle into two parts, where each part is called a segment of the circle.
          

The unit's digit is 0 only in the numbers in front of Index Finger and Ring Finger. Moreover, the greater numbers with 0 as the unit's digit come in front of Index Finger before Ring Finger.
Hence, 1000 will come in front of Index Finger.

Let in the two digit number to be added,
Unit's digit = x and, ten's digit = y
Then, the number to be added = 10y + x
On reversing the digits,
Unit's digit = y and, ten's digit = x
∴ The number to be added = 10x + y
According to the question,
27 + (10y + x) = 10x + y
⇒ 9x- 9y = 27
⇒ x-y=3
⇒  x=y+3
When y = I, x = 4 ∴ Number = 14
When y = 2, x = 5 ∴ Number = 25
When y = 3, x = 6 ∴ Number=36
When y = 4, x = 7 ∴ Number = 47
When y = 5, x = 8 ∴ Number = 58
When y = 6, x = 9 ∴ Number = 69
Hence, the required two digit numbers are 14, 25, 36, 47, 58, 69.