i)
 
All sides are equal.
Type: Equilateral triangle.
ii) 

Three sidesare different lengths,
Type: Scalene triangle .
iii)

Two sides are equal,
Type : Isoceles triangle.
iv)
 
Three sides are different lengths.
Type: Scalene triangle.

c.p T.V. = Rs. 12,000
He spent = Rs. 1,000
= Rs. 13,000
m.p = Rs. 15,000
Discount = Rs. 1,000
c.p Fridge = Rs. 11,000
Painting Charges = Rs. 1,500
= Rs. 12,500
m.p = 15,500
Discount = Rs. 1,000
c.p of tv and fridge
= 13,000 + 12,500
c.p = Rs. 25,500
m.p = Rs. 15,000 + 15,500 = Rs. 30,500
Discount = Rs. 1,000 + Rs. 1,000 =
= Rs. 2000
Therefore s.p = m.p - Discount
= 30,500 - 2,000 = Rs. 28,500
s.p = Rs. 28,500
Here, s.p > c.p
Therefore profit = s.p - c.p
= 28,500 - 25,500
Therefore Profit = Rs. 3,000

Given
Profit = Rs. 50
1 dozen Pens Rs. 216
Therefore 12 pens = 216
He paid = 48
c.p = Rs. 274
s.p = c.p + profit
= Rs. 274 + Rs. 50
s.p = Rs. 324
Discount = Rs. 2
1 dozen = 2 \(\times\)12 = Rs. 24
m.p = s.p + discount
= Rs. 324 + Rs. 24
12 pens = Rs. 348
Therefore 1 pen = 348 / 12 = 29
Therefore the m.p of each pen = Rs. 29

Length of the line segments are
AB = 2 cm, BC = 2.5 cm, CD = 2.5 cm DE = 2 cm.
1^st way distance = AB + BC + CD + DE = [2 + 2.5 + 2.5 + 2]cm = 9 cm
2^nd way distance = AG = 2.5 cm, GF = 1.7 cm, F to E = 1.7 + 2.8 = 4.5 cm
= (2.5 + 1.7 + 4.5) cm = 8.7 cm
3^rd way distance = AH = 3 cm, HI = 2.3 cm, IJ = 1 cm, JE = 3.2cm
= [3 + 2.3 + 1 + 3.2] cm = 9.5cm
Therefore the shortest way to reach the grains = 2^nd way (middle way 8.7 cm distance)

Malarvizhi comes to her home once in 5 days. Similarly, Karthiga and Anjalicome to their homes once in 6 days and 10 days respectively.
Therefore 5 days, 6 days, 10 days.

LCM = \(5 \times 2 \times 3\) = 30
Therefore all the three will meet again once in 30 days on 31^st of October.

Yes, given number is 173,
factors are 173 = 1, 173
173 have only two factors.
Therefore is a prime number.

8461 > 7535 > 6214 > 2943

102

\(\angle COD\ and\ \angle AOB\) have the point 'O' in common

\(\angle AOB,\angle BOZ,\angle AOZ\)

9 -1 = 8
98 - 21 = 77
987 - 321 = 666
9876 - 4321 = 5555
98765 - 54321 = 44444
Next will be
987654 - 654321 = 333333

Price of cool drinks per kg =P Rs.
Three times = 3P
5 Rs. more = 3P +5
\(\therefore \) Price of oil per kg = 3P +5

2n shows double the number of students who like icecream.

Let x^o be an angle
Given,
Two complementary angles are in ratio \(7: 2=\frac{7}{2}\)
It is equivalent to \(\frac{7 \times x}{2 \times x}=\frac{7 x}{2 x}\)
7x and 2x are two complementary angles
\(\therefore\) 7x + 2x = 90^o
9x^o = 90^o 
x^o = 10
\(\therefore\) 7x^o = 70 and 2x^o = 20 
Two angles are 70˚ and 20˚

supplementary angle of 90º = 180º - 90º = 90º

The single portions  A, B, C, D, E, F, G and H are 8 triangles. 
Taking the combination of 2 E & F, F & G, & H and E & H are 4 triangles.
There are 8 + 4 = 12 triangles.

5:4
\(\frac{5}{4}\times\frac{2}{2}=\frac{10}{8}=10:8\)
\(\frac{5}{4}\times\frac{3}{3}=\frac{15}{12}=15:12\)
Equivalent ratios of 5 : 4 are 10 : 8 and 15 : 12

9y - 4

We know that the place value increases from right to left
[ \(\therefore\) Arranging the digits in ascending order from right to left we get the largest number]
Largest number is 75320
Smallest number is  20357
[ \(\therefore\) Reverse order of 75320 is 02357. It becomes four digit number 2357]

(i) Given
1^st month = 1210
2^nd month = 2100
3^rd month = 2550
4^th month = 3160
5^th month = 3310
Tree diagram

Total = 1210 + 2100 + 2550 + 3160 + 3310.
ii) Given
Ram had a bank deposit = Rs. 7,55,250
He had withdrawn = Rs. 5,34,500
Therefore the amount left in his amount
= Rs. 7,55,250 - Rs. 5,34,500
Tree diagram

iii) Given
No. of bicycles produced in 1 day = 1,600
No. of bicycles produced in 20 days
= 1600 \(\times\) 20
Tree Diagram

iv) Given
Total amount = Rs. 90,000
No. of employees = 30
= 90,000 / 30
Tree Diagram

The pictograph is given by

(a) 9 Full pictures and a half picture represent the number of students in the year2000
(b) 5 symbols

The odd numbers between 1 to 17 are 1, 3, 5, 7, 9, 11, 13, 15, 17.
Step 1: Place the smaller numbers 1, 3 : 5 on the comers.

Step 2: Arrange another set of smaller numbers 7, 9 and 11 on each side.

Step 3: Arrange the remaining numbers 13, 15, 17 to give the total 30.

Magic sum = 30.

(a) green balls = 4, Yellow balls = 3, black balls =  5.
so, Black balls
(b) 5 parts of Black balls = 40 balls
\(\therefore \) 1 part of Black balls = \(\frac{40}{5}=8 \text { balls }\)
4part of Green balls = 4 \(\times\) 8 = 32
3 part of yellow balls = 3 \(\times\) 8 = 24
If there are 40 black balls, then total number of balls = 32 + 24 + 40 = 96 balls
(c) Number of green balls = 32
Number of Yellow balls = 24

Step 1: Number of digits in the two given numbers are equal.
Step 2: Compare the place values using the place value chart.

Compare the digits of the two numbers from the highest place value as noted below.

Here only the digits in the ones place are not equal and 6 < 8.
Hence, 59283746 < 59283748.

                   Tree diagram

 (a + b) + c                            a + (b+c)
( a + b) + c = a + (b+c)
Yes, they are equal.

 
Construction: 
1. Draw a line segment XY = 7.8 cm. Mark a point A on the line.
2. Place the set square on XY. Mark a point B above XY such that AB = 5 cm.
3. Using a scale and set square draw a line BC through B.
4. The line BC is parallel to XY. That is BC || XY.

Somu bought a bike =Rs. 28,000
He spent = 2,000
c.p = Rs. 30,000
s.p = Rs. 30,000
Therefore s.p = c.p
Therefore No profit / No loss

Given 1l = 1000 ml
2 litre = 2 \(\times\)1000 = 2000 ml
(i) 100 ml = 2000 ml / 100 ml = 20 glasses
(ii) 50 ml = 2000 ml / 50 ml = 40 glasses
(iii) 500 ml = 2000 ml / 500 ml = 4 glasses
(iv) 1 I = 2000 mll 1000 ml = 2 glasses
(v) 250 ml = 2000 ml /250 ml = 8 glasses

Given statement
The ropes of length 1 m 20 cm, 3 m 60 cm and 4 m.
1 m 20 cm = 120 cm, 3 m 60 cm = 360 cm and 4 m = 400 cm
To find the length of the longest rope.

HCF = \(5 \times 2 \times 2 \times 2\) = 40
Therefore the length of the longest rope = 40 cm.

We know that
Total matches played: Matches wont  Matches lost
\(\therefore \) 5+k=8    7=6+m    4+6=n
\(\therefore \)k=3         \(\therefore \) m=1    \(\therefore \)n=10
  7+2=a     6+3=9     6+c=10
\(\therefore \)a=9        \(\therefore \)b=6        \(\therefore \)c=4
k=3  m=1   n=10   a=9   b=6   c=4   x=4   y=9   x=4
x+4=8      3+6=y
\(\therefore \)a=9       \(\therefore \) y=9

Construction:
(i) Placed the centre of the protractor at the Vertex A. Lined up the \(\overline { EG } \) ray with the 0° line. Then draw and labelled a point F at the 135° mark on the (a) inner scale (anti clockwise) and (b) outer scale (clockwise)
(ii) Removed the protractor and draw \(\overline { EF } \) to complete the angle.
Now LE= LFEG = LGEF = 135°.

The number of dots given are 1, 3, 6, 10, 15, ...

1^st number = 1
2^nd number = 1 + 2 = 3
3^rd number = 3 + 3 = 6
4^th number = 6 + 4 = 10
5^th number = 10 + 5 = 15
6^th number will be 15 + 6 = 21
7^th number will be 21 + 7 = 28
8^th number will be 28 + 8 = 36
9^th number will be 36 + 9 = 45
10^th number will be 45 + 10 = 55
Number of dots in the 10^th figure = 55.

A, B, C, D, & E are five triangles.
No combination of these triangles taken 2 at a time, form any triangle.
Only the combinations of A, F & C; A, F & D; B, F & E; B, F & D and C, F & E form triangles when taken 3 triangles at a time.
Hence, the total number of triangles = 5 + 5 = 10.

By unitary method, we can solve this as follows :
Cost of a dozen balls = Rs.180
\(\Rightarrow\)Cost of 12 balls = Rs.180
Cost of 1 ball =\(180\over 12\) = Rs.15
Cost of 5 balls = 5 \(\times\) 15 = Rs. 75
Hence, Pari has to pay Rs. 75 for 5 balls.

Number of mobiles sold in 1 month = 1250
1 year = 12 months
2 years = 2 \(\times\) 12
= 24 months
Number of mobiles sold in 24 months = 1250 \(\times\) 24 = 30,000
Number of mobiles sold in 2 years = 30,000

\(1:2=\frac{1}{2}\)
\(2:1=\frac{2}{1}\times\frac{2}{2}=\frac{4}{2}\)
Here \(\frac{4}{2}\) larger than \(\frac{1}{2}\)
\(\therefore\) 2 : 1 larger than 1: 2

12 less to 5 times n