The row sum of elements of a Pascal’s Triangle are shown below:

First row = 21 − 1 = 1
Second row = 22 − 1 = 2 x 1 = 2
Third row = 23 − 1 = 2 x 2 = 4
Fourth row = 24 − 1 = 2 x 2 x 2 = 8
Fifth row = 25 − 1 = 2 × 2 × 2 × 2 = 16
Sixth row = 26 − 1 = 2 × 2 × 2 × 2 × 2 = 32
Seventh row = 27 − 1 = 2 × 2 × 2 × 2 × 2 × 2 = 64
Eighth row = 28 − 1 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
Here x denotes the row and y denotes the corresponding row sum. The values of x and y can be tabulated as follows:

The relationship between x and y is y = 2^{x – 1.}

49¹⁷
Unit digit of base 49 is 9 and power is 17 (odd power).
Therefore, unit digit of 49¹⁷ is 9.

64¹⁰
Unit digit of base 64 is 4 and power is 10 (even power). Therefore, unit digit of 64¹⁰ is 6.

46³¹
Unit digit of base 46 is 6 and power is 31
Thus, the unit digit of 46³¹ is 6.

25²³
Unit digit of base 25 is 5 and power is 23
Thus, the unit digit of 25²³ is 5.

The perimeter of the rectangular garden
Perimeter include two lengths each of 16 m and two semi circular arcs of diameter 8 m.
Circumference of the semicircle = \(\frac { \pi d }{ 2 } \) units
= \(\frac { \pi \times 8 }{ 2 } \) = 4π
= 4 x 3.14
= 12.56 m
Therefore, circumference of two semicircles = 2 x 12.56
= 25.12 m
Total perimeter = length + length + circumference of two semicircles 
= 16 +16 + 25.12
= 32 + 25.12
= 57.12 m

The distance covered by the man is nothing but the circumference of the circle.
Given that the distance covered = 154 m
Therefore circumference of the circle = 154 m
That is, 2πr = 154
2 x \(\frac { 22 }{ 7 } \)x r = 154
r = 154 x \(\frac { 7 }{ 44 } \)
r = 3.5 x 7
= 24.5
Area of the park = πr² sq.units
= \(\frac { 22 }{ 7 } \)× 24.5 x 24.5
= 22 x 3.5 x 24.5
= 1886.5 m²
Cost of levelling the park per sq.m = Rs.25.
Cost of levelling the park of 1886.5 m² = 1886.5 x 25 = Rs.47,162.50

Given the diameter (d) = 28 cm
 Radius (r) = \(\frac { 28 }{ 2 } \) = 14 cm
Area of a circle = πr² sq.units
 = \(\frac { 22 }{ 7 } \) x 14 x 14
So, the area of the circle = 616 cm².

4.5 = 4 + \(\frac { 5 }{ 10 } \)
  = 4\(\frac { 5 }{ 10 } \) = 4\(\frac { 1 }{ 2 } \)
A juice container has 4\(\frac { 1 }{ 2 } \) litres of mango juice.

23 + \(\frac { 6 }{ 10 } \) + \(\frac { 8 }{ 1000 } \) = 23 + 6 x \(\frac { 1 }{ 10 } \) + 0 x  \(\frac { 1 }{ 100 } \) + 8 x \(\frac { 1 }{ 1000 } \)
  = 23.608 (since hundredths place is not there, it is taken as '0')

999 + 99 + 9 + \(\frac { 9 }{ 10 } \) + \(\frac { 9 }{ 100 } \) = 1107 + 9 x \(\frac { 1 }{ 10 } \) + 9 x \(\frac { 1 }{ 100 } \)
  = 1107.99

0.862 = \(\frac { 862 }{ 1000 } \)
 = \(\frac { 862\div 2 }{ 1000\div 2 } \) = \(\frac { 431 }{ 500 } \)

3.46 = 3 + \(\frac { 46 }{ 100 } \)
= 3 + \(\frac { 46\div 2 }{ 100\div 2 } \)
= 3 + \(\frac { 23 }{ 50 } \)
= 3 \(\frac { 23 }{ 50 } \)

In 3\(\frac { 1 }{ 5 } \), keep the whole number 3 as such, we can find a fraction equivalent to \(\frac { 1 }{ 5 } \)with denominator 10.
 3 + \(\frac { 1 }{ 5 } \) = 3 + \(\frac { 1\times 2 }{ 5\times 2 } =3+\frac { 2 }{ 10 }\) = 3.2

We have to find a fraction equivalent to \(\frac { 1 }{ 50 } \) whose denominator is 100.
 \(\frac { 1 }{ 50 } \) = \(\frac { 1\times 2 }{ 50\times 2 } =\frac { 2 }{ 100 }\) = 0.02

In \(\frac { 9 }{ 1000 } \), tenth and hundredth place is zero.
 Therefore, \(\frac { 9 }{ 1000 } \) = 0.009

We have to find a fraction equivalent to \(\frac { 3 }{ 4 } \) with denominator 100. Since there is no whole number that gives 10 when multiplied by 4, let us make the denominator as 100.
 so, \(\frac { 3 }{ 4 } \) = \(\frac { 3\times 25 }{ 4\times 25 } =\frac { 75 }{ 100 } \) = 0.75

 \(\frac { 5 }{ 100 } \) = 0.05

0.85 = 0 + \(\frac { 8 }{ 10 } \)+\(\frac { 5 }{ 100 } \)
  = \(\frac { 85 }{ 100 } \)=\(\frac { 17 }{ 20 } \)
 A capsule holds \(\frac { 17 }{ 20 } \) mg of medicine

Four hundred four and five hundredths.
  = 404 + \(\frac { 5 }{ 100 } \)
  = 404 + 0 x \(\frac { 1 }{ 10 } \) + 5 x \(\frac { 1 }{ 100 } \) = 404.05

153 + 96 + 7 + \(\frac { 5 }{ 10 } \) + \(\frac { 2 }{ 1000 } \) = 256 + 5 x \(\frac { 1 }{ 10 } \) + 0 x \(\frac { 1 }{ 100 } \) + 2 x \(\frac { 1 }{ 1000 } \)
  = 256.502 (since hundredths place is not there, it is taken as '0' )

0 04 = \(\frac { 4 }{ 100 } =\frac { 1 }{ 25 } \)

We have to find a fraction equivalent to \(\frac { 2 }{ 5 } \) whose denominator is 10.
 \(\frac { 2 }{ 5 } \) = \(\frac { 2\times 2 }{ 5\times 2 } =\frac { 4 }{ 10 } \) = 0.4

 \(\frac { 3 }{ 5 } \) = \(\frac { 6 }{ 10 } \) = 0.6