$$\eqalign{ & \frac{{489.1375 \times 0.0483 \times 1.956}}{{0.0873 \times 92.581 \times 99.749}} \approx \frac{{489 \times 0.05 \times 2}}{{0.09 \times 93 \times 100}} \cr & = \frac{{489}}{{9 \times 93 \times 10}} \cr & = \frac{{163}}{{279}} \times \frac{1}{{10}} \cr & = \frac{{0.58}}{{10}} \cr & = 0.058 \approx 0.06 \cr} $$

Given expression = (11.98)² + (0.02)² + 11.98 × X
For the given expression to be a perfect square,
(a + b)² = a² + b² + 2ab
we must have
11.98 × X = 2 × 11.98 × 0.02
∴ X = 0.04

$$\eqalign{ & {\text{Given}}\,{\text{expression}} \cr & = \frac{{ {0.3333} }}{{ {0.2222} }} \times \frac{{\left( {0.1667} \right)\left( {0.8333} \right)}}{{\left( {0.6667} \right)\left( {0.1250} \right)}} \cr & = \frac{{3333}}{{2222}} \times \frac{{\frac{1}{6} \times \frac{5}{6}}}{{\frac{2}{3} \times \frac{{125}}{{1000}}}} \cr & = {\frac{3}{2} \times \frac{1}{6} \times \frac{5}{6} \times \frac{3}{2} \times 8} \cr & = \frac{5}{2} \cr & = 2.50 \cr} $$

$$\eqalign{ & \text{Let } a = 2.39 \text{ and } b = 1.61 \cr & {\text{Given Expression}} \cr & = \frac{{{a^2} - {b^2}}}{{a - b}} \cr & = \frac{{\left( {a + b} \right)\left( {a - b} \right)}}{{ {a - b} }} \cr & = {a + b} \cr & = {2.39 + 1.61} \cr & = 4 \cr} $$

$$\eqalign{ & {\text{Required decimal}} \cr & = \frac{1}{{60 \times 60}} \cr & = \frac{1}{{3600}} \cr & = .00027 \cr} $$

$$\eqalign{ & {\text{Given}}\,{\text{expression}} \cr & = \frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + \left( {0.96 \times 0.1} \right) + {{\left( {0.1} \right)}^2}}} \cr & = {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \cr & = \frac{\left(a-b\right) \left(a^2 + ab + b^2 \right)}{\left(a^2 + ab + b^2 \right)} \cr & = {a - b} \cr & = {0.96 - 0.1} \cr & = 0.86 \cr} $$

$$\eqalign{ & {\text{Give}}\,{\text{expression}} \cr & = \frac{{{{\left( {0.1} \right)}^3} + {{\left( {0.02} \right)}^3}}}{{{2^3}\left[ {{{\left( {0.1} \right)}^3} + {{\left( {0.02} \right)}^3}} \right]}} \cr & = \frac{1}{8} \cr & = 0.125 \cr} $$

$$\eqalign{ & \frac{{29.94}}{{1.45}} \cr & = \frac{{299.4}}{{14.5}} \cr} $$
  $$ = {\frac{{2994}}{{14.5}} \times \frac{1}{{10}}} $$    [Here, Substitute 172 in the place of $${\frac{{2994}}{{14.5}}}$$ ]
$$\eqalign{ & = \frac{{172}}{{10}} \cr & = 17.2 \cr} $$

Suppose commodity X will cost 40 paise more than Y after z years
Then,(4.20 + 0.40z) − (6.30 + 0.15z) = 0.40
⇒ 0.25z = 0.40 + 2.10
$$\eqalign{ & \Rightarrow z = \frac{{2.50}}{{0.25}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{250}}{{25}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 10 \cr} $$
∴ X will cost 40 paise more than Y 10 years
After 2001 i.e., 2011

Converting each of the given fractions in to decimal form, we get
$$\eqalign{ & \frac{1}{3} = 0.33 \cr & \frac{2}{5} = 0.4 \cr & \frac{3}{7} = 0.42 \cr & \frac{4}{5} = 0.8 \cr & \frac{5}{6} = 0.83 \cr & \frac{6}{7} = 0.85 \cr} $$
Clearly, 0.85 > 0.83 > 0.8 > 0.42 > 0.4 > 0.33
So, $$\frac{6}{7}$$ > $$\frac{5}{6}$$ > $$\frac{4}{5}$$ > $$\frac{3}{7}$$ > $$\frac{2}{5}$$ > $$\frac{1}{3}$$

Given expression :
= (100 - 0.25)² - 2250.0625
= (100)² + (0.25)² - 2 × 100 × 0.25 - 2250.0625
= 10000.0625 - 50 - 2250.0625
= 10000.0625 - 2300.0625
= 7700

given expression :
= $$\frac{0.05 × 6.25}{2.5}$$
= $$\frac{0.3125}{2.5}$$
= $$\frac{3.125}{25}$$
= 0.125

= $$\frac{29.94}{1.45}$$
= $$\frac{299.4}{14.5}$$
= $$\frac{2994}{14.5}$$ × $$\frac{1}{10}$$
= $$\frac{172}{10}$$
= 17.2

$$\frac{241.6 × 0.3814 × 6.842}{0.4618 × 38.25 × 73.65}$$
≈ $$\frac{240 × 0.38 × 6.9}{0.46 × 38 × 75}$$
= $$\frac{240 × 38 × 69}{46 × 38 × 75}$$ &nbsp × $$\frac{1}{10}$$
= $$\frac{24}{5}$$ × $$\frac{1}{10}$$
= $$\frac{4.8}{10}$$
= 0.48
So, the value is close to 0.4

Given expression :
= $$\frac{0.2 (0.2 + 0.02)}{0.044}$$
= $$\frac{0.2 ×0.22}{0.044}$$
= $$\frac{0.044}{0.044}$$
= 1

$$\eqalign{ & 2\frac{{1.5}}{5} + 2\frac{1}{6} - 1\frac{{3.5}}{{15}} = \frac{{{x^{\frac{1}{3}}}}}{4} + 1\frac{7}{{30}} \cr & \Rightarrow \frac{{11.5}}{5} + \frac{{13}}{6} - \frac{{18.5}}{{15}} = \frac{{{x^{\frac{1}{3}}}}}{4} + \frac{{37}}{{30}} \cr} $$
⇒ L.C.M. of 5, 6 and 15 is 30
$$\eqalign{ & \Rightarrow \frac{{69 + 65 - 37}}{{30}} = \frac{{{x^{\frac{1}{3}}}}}{4} + \frac{{37}}{{30}} \cr & \Rightarrow \frac{{97}}{{30}} = \frac{{{x^{\frac{1}{3}}}}}{4} + \frac{{37}}{{30}} \cr & \Rightarrow \frac{{{x^{\frac{1}{3}}}}}{4} = \frac{{97}}{{30}} - \frac{{37}}{{30}} \cr & \Rightarrow {x^{\frac{1}{3}}} = \frac{{60}}{{30}} \times 4 \cr & \Rightarrow {x^{\frac{1}{3}}} = 8 \cr & \Rightarrow x = {\left( 8 \right)^3} \cr & \Rightarrow x = 512 \cr} $$
Hence, the number is 512

Given expression :
= $$\frac{441 × 16}{21 × 16 × 21}$$
= $$\frac{{7056}}{{7056}}$$
= 1

Given expression :
[(0.98)³ + (0.02)³ + 3 × 0.98 × 0.02 (0.98 + 0.02)] - 1
= (0.98 + 0.02)³ - 1
= (1)³ - 1
= 0

{(41.99)² - (18.04)²} ÷ ? = (13.11)² - 138.99
⇒ {(42)² - (18)²} ÷ ? = (13)² - 139 {∵ a² - b² = (a + b) (a - b)}
⇒ {(42 + 18) (42 - 18)} ÷ ? = 169 - 139
⇒ 60 × 24 ÷ ? = 30
⇒ ? = $$\frac{60 × 24}{30}$$
⇒ ? = 48

Given expression :
= $$\frac{3.20 (3.25 - 3.05)}{0.064}$$
= $$\frac{3.20 × 0.2}{0.064}$$
= $$\frac{0.64}{0.064}$$
= $$\frac{64}{6.4}$$
= 10

= $$\frac{17292}{33}$$ × $$\frac{1}{8}$$
= $$\frac{17292}{33 × 8}$$
= 65.5

= 3899 ÷ 11.99 - 2379 ÷ 13.97
= 3899 ÷ 12 - 2380 ÷ 14
≈ 325 - 170
= 155

Let the missing number be x
Given, $$1\frac{1}{2}$$ + $$2\frac{2}{7}$$ = $$3\frac{1}{2}$$ + x
x = $$1\frac{1}{2}$$ + $$2\frac{2}{7}$$ - $$3\frac{1}{2}$$
x = $$\frac{3}{2}$$ + $$\frac{16}{7}$$ - $$\frac{7}{2}$$
x = $$\frac{21 + 32 - 49}{14}$$
x = $$\frac{4}{14}$$
x = $$\frac{2}{7}$$
Hence, the number is $$\frac{2}{7}$$

Given expression :
= $$\frac{16 × 32}{8}$$
= 16 × 4
= 64

Given $$\frac{3}{5}$$ of $$\frac{4}{7}$$ of $$\frac{5}{12}$$ of 1015
⇒ x = $$\frac{3}{5}$$ × $$\frac{4}{7}$$ × $$\frac{5}{12}$$ × 1015
⇒ x = 145

= $$\frac{0.0203 × 2.92}{0.0073 × 14.5 × 0.7}$$
= $$\frac{203 × 292}{73 × 145 × 7}$$
= $$\frac{4}{5}$$
= 0.8

$$\eqalign{ & = \frac{{{{\left( {2.3} \right)}^3} - 0.027}}{{{{\left( {2.3} \right)}^2} + 0.69 + 0.09}} \cr & = \frac{{{{\left( {2.3} \right)}^3} - {{\left( {0.03} \right)}^3}}}{{{{\left( {2.3} \right)}^2} + \left( {2.3 \times 0.3} \right) + {{\left( {0.3} \right)}^2}}} \cr & = \left[ {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \right] \cr & = \left( {a - b} \right) \cr & = \left( {2.3 - 0.3} \right) \cr & = 2 \cr} $$

$$\eqalign{ & = \frac{1}{4} + \frac{1}{{4 \times 5}} + \frac{1}{{4 \times 5 \times 6}} \cr & = \frac{1}{4}\left( {1 + \frac{1}{5} + \frac{1}{{30}}} \right) \cr & = \frac{1}{4}\left( {\frac{{30 + 6 + 1}}{{30}}} \right) \cr & = \frac{1}{4} \times \frac{{37}}{{30}} \cr & = \frac{{37}}{{120}} \cr & = 0.3083 \cr} $$

Given expression :
(833.25 - 384.45) ÷ 24
= 18.7

Given expression :
0.5 × 0.5 + $$\frac{0.5}{5}$$
= 0.25 + 0.1
= 0.35