Given: \(\cfrac { 3 }{ 5 } ,\cfrac { 9 }{ 10 } ,\cfrac { 11 }{ 15 } \)
LCM of 5; 10 and 15 is 30.
\(\cfrac { 3 }{ 5 } \cfrac { 6 }{ 6 } \times \cfrac { 18 }{ 30 } ,\cfrac { 9 }{ 10 } \times \cfrac { 3 }{ 3 } =\cfrac { 27 }{ 30 } ,\cfrac { 11 }{ 15 } \times \cfrac { 2 }{ 2 } =\cfrac { 22 }{ 30 } \)
\(\Rightarrow \cfrac { 18 }{ 30 } <\cfrac { 22 }{ 30 } <\cfrac { 27 }{ 30 } \)
\(\therefore\) Ascending order :\(\cfrac { 3 }{ 5 } ,\cfrac { 11 }{ 15 } ,\cfrac { 9 }{ 10 } \)

Fibonaxxi sequence 1,1,2,3,5,8,13,21,34,55

(i) 1 \(\times\) 1 = 1
11 \(\times\) 11 = 121
111 \(\times\) 111 = 12321
1111 \(\times\) 1111 = 1234321
11111 \(\times\) 11111 = 123454321
(ii)

The order of rotational symmetry of each face of a die are

(i) Hidden word isDECODE
(ii) Hidden word is KICK
(iii) Hidden word is BED
(iv) Hidden word WAY
(v) Hidden word MAT H
(vi) Hidden word TOM A T 0

Area of a rectangle = 820 sq. cm
Width (b) = 20 cm
Length (l) =?
Perimeter =?
\(I=\cfrac { A }{ b } \)
= \(\cfrac { 820 }{ 20 } =41\\ \)
= =2(41+20)
= 2 (61) = 122 cm
\(\therefore\) I = 41 cm , P = 122 cm

Length (l) = 6 m
breadth (b) = 4 m
Perimeter of the rectangle (P) = 2 (1+b) units
= 2 (6 + 4)
= 2(10) = 20m
Area(A) = l\(\times\)b = (6 \(\times\) 4)m²
= 24m
\(\therefore\) P = 20 m, A = 24 m²

(i) 44
Opposite number = - 44
(ii) -19 
Opposite number = +19 or 19
(iii) 0
Opposite number = 0  
(iv) - 312
Opposite number = + 312 or 312
(v) 789 
Opposite number = - 789

Total distance = \(5\cfrac { 3 }{ 4 } km=\cfrac { 23 }{ 4 } km\)
He had walked = \(2\cfrac { 1 }{ 2 } km=\cfrac { 5 }{ 2 } km\)
Difference = \(\left( \cfrac { 23 }{ 4 } -\cfrac { 5 }{ 2 } \right) km\)
= \(\cfrac { 23-\left( 5\times 2 \right) }{ 4 } =\cfrac { 23-10 }{ 4 } =\cfrac { 13 }{ 4 } km\)
\(\therefore 3\cfrac { 1 }{ 4 } km\) distance still he has to walk to reach his house

No, It is not possible with angles 90°, 90°, 0°.
Because there cannot be two right angles in a triangle

All angles are right angles two triangles formed.
Both are Isoceles right angled triangle.

Given
A man bought the 400 m cloth
c.p = Rs. 60,000
He sold it at the rate of Rs. 400 / metre.
Therefore 1 m = Rs. 400
Therefore 400 mm = Rs. 400 \(\times\) 400 m
s.p = Rs. 1,60,000
Here, s.p > c.p
Therefore profit = s.p - c.p
= Rs. 1,60,000 - Rs. 60,000
Therefore profit = Rs. 1,00,000

Given
Sugan bought a Jeans Pant = Rs. 750
c.p = Rs. 750
s.p = Rs. 710
Here, c.p > s.p
Loss = c.p - s.p = Rs.750 - 710
Therefore Loss = Rs. 40

i) (Rectangle Shape)
A door has 1m wide and 2 m 50 cm high.
Therefore l = 2 m 50 cm = 250 cm
b = 1 m = 100 cm
Area = I \(\times\) b = 250 \(\times\) 100 = 25000 cm²
ii) A bed have 2 m and 20 cm length and 90 cm wide.
Therefore I = 2 m 20 cm = 220 cm
b = 90 cm
Area = I \(\times\) b = 220 \(\times\) 90 = 19,800 cm²
Area of door > Area of a bed
Yes, we can take a bed into the room,

A clock gains = 3 minutes every hour.
Duratioa of time between 5 a.m. and 7 p.m. = 14 hrs
Minutes gained for 14 hrs = 14 \(\times\) 3 = 42 min
The time shown by clock at 7 p.m.
= 7 hours 42 mins.

Given LCM = 210, HCF = 14
Let the two numbers be x and y.
x * y = HCF(x,y) x LCM(x,y) = 210 \(\times\) 14
Product of 2 given numbers == 2940
Therefore two pairs possible,

The smallest 3 digit composite number = 100
The biggest three digit composite number = 999

562634 < 570000 < 572634

8461 > 7535 > 6214 > 2943

Supplementary angle is 120°
Complementary angle is 30°

\(\angle ZYX \)

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.

obtuse angle

straight angle

The pictograph for the mode of transport of students

The number of dots given are 1, 4, 9, 11, 16, 25, ...
The no. of dots are in the pattern 1 \(\times\) 1, 2 \(\times\) 2, 3 \(\times\) 3, 4 \(\times\) 4, 5 \(\times\) 5 .... 10 \(\times\) 10
\(\therefore \) The number of dots in the 10^th figure = 100.

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.

To round off 337598482 to ten crore
The digit is the ten crores place is 3
The digit to the right is 3 < 0
\(\therefore\) The digit in ten crore place remains the same 3.
Changing the digit to the right of 3 zeros we get 30,00,00,000
\(\therefore\) 337598482 \(\simeq \) 30,00,00,000

We have to round off 4065 to hundreds
The place value is hundred
The digit in hundreds place is 0
The digit to the right is 6 > 5
Adding 1 to 0 \(\Rightarrow\) 0 + 1 = 1
changing the digits to the right of 41 to zeros
4065 \(\simeq \) 4100 \(\Rightarrow\) 4100

The Tally marks table is given below.

g - 300
g - 1 = 300 -1 and g + 1 = 300 +1 
= 299 and 301

56 + 2x

Step 1: Express the quantity in the same unit. (Hint : 1 Hour = 60 minutes)
Step 2: Now, the ratio of 40 minutes to 60 minutes is 40:60 \(\Rightarrow {40\over 60}={40\div 20\over 60\div 20}={2\over 3}=2:3\)
This is the ratio in the simplest form.
20 \(\times\) 1 = 20
20 \(\times\) 2 = 40
20 \(\times\) 3 = 60
1 hour = 60 minutes

500 g to 250 g = 500 : 250 \(\Rightarrow\) \({500\over 250}={500 \div 250\over 250\div 250}={2\over1}=2:1\)
This is the ratio in the simplest form.