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$\frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y}$ $\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$ On simplifying the given equations, which of the following equations will be obtained ?

1xy = b
2bx = y
3ab = x
4yb = x

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Answer:- 4

Explanation:-

Solution:

\begin{aligned} \frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{(a^{2} + b^{2} - 2 a b) - (a^{2} + b^{2} + 2 a b)}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{- 4 a b}{- 4 a} = \frac{x}{y} \\ \Rightarrow b = \frac{x}{y} \\ \Rightarrow x = y b . \end{aligned}

$\eqalign{ & \frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} \cr & \Rightarrow \frac{{\left( {{a^2} + {b^2} - 2ab} \right) - \left( {{a^2} + {b^2} + 2ab} \right)}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow \frac{{ - 4ab}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow b = \frac{x}{y} \cr & \Rightarrow x = yb. \cr}$

$\frac{{(0.73)}^{3} + {(0.27)}^{3}}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} = ?$ $\frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} = ?$

10.27
20.4087
30.73
41

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given, \\ \frac{{(0.73)}^{3} + {(0.27)}^{3}}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} \\ let a = 0.73 and b = 0.27 \\ = \frac{(0.73 + 0.27) [{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27]}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} \\ [∵ a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)] \\ = 0.73 + 0.27 \\ = 1 \end{aligned}

$\eqalign{ & {\text{Given,}} \cr & \frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} \cr & {\text{let }}a = 0.73{\text{ and }}b = 0.27 \cr & = \frac{{\left( {0.73 + 0.27} \right)\left[ {{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27} \right]}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} \cr & \left[ {\because {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)} \right] \cr & = 0.73 + 0.27 \cr & = 1 \cr}$

03. 67 × 119 + 17 - 27 ÷ 259 = ?

1-13
2-3
34
47

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Answer:- 1

Explanation:-

Solution:

67 × 119 + 17 - 27 ÷ 259
⇒ 67 + 119 ÷ 17 × 27 -259
⇒ 67 + 7 × 27 - 259
⇒ 67 + 189 - 259
⇒ 256 - 259
⇒ -3

04. If x + y + z = 0, then x³ + y³ + z³ + 3xyz is equal to = ?

10
26xyz
312xyz
4xyz

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Answer:- 1

Explanation:-

Solution:

As we know
a³ + b³ + c³ + 3abc2 + b² + c² - ab - bc - ca)(a + b + c)
When, a + b + c = 0
Then a³ + b³ + c³ + 3abc = 0
When, x + y + z = 0
x³ + y³ + z³ = 3xyz
x³ + y³ + z³ + 3xyz
= 3xyz + 3xyz
= 6xyz

05. Solve 14 × 627 ÷ √(1089) = (?)³ + 141

15√5
2(125)²
325
45

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Answer:- 1

Explanation:-

Solution:

Let the missing number is a
Given,

\begin{aligned} 14 \times 627 \div \sqrt{(1089)} = {(a)}^{3} + 141 \\ \frac{14 \times 627}{\sqrt{1089}} = {(a)}^{3} + 141 \\ \frac{14 \times 627}{33} = a^{3} + 141 \\ 266 = a^{3} + 141 \\ a^{3} = 125 \\ a = \sqrt[3]{125} \\ a = 5 \end{aligned}

$\eqalign{ & 14 \times 627 \div \sqrt {\left( {1089} \right)} = {\left( a \right)^3} + 141 \cr & \frac{{14 \times 627}}{{\sqrt {1089} }} = {\left( a \right)^3} + 141 \cr & \frac{{14 \times 627}}{{33}} = {a^3} + 141 \cr & 266 = {a^3} + 141 \cr & {a^3} = 125 \cr & a = \root 3 \of {125} \cr & a = 5 \cr}$

06. Solve 4376 + 3209 - 1784 + 97 = 3125 + ?

12713
22743
32773
42793

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Answer:- 1

Explanation:-

Solution:

4376 + 3209 - 1784 + 97 = 3125 + x
⇒ 7682 - 1784 = 3125 + x
or, x = 7682 - 1784 - 3125
⇒ x = 2773
Hence,
the number is 2773

07. Solve : 128.43 + 30.21 + ? = 173

135.66
229.66
343.66
414.36

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Answer:- 1

Explanation:-

Solution:

Given Expression
128.43 + 30.21 + ? = 173
⇒ ? = 173 - 128.43 - 30.21
⇒ ? = 173 - 158.64
⇒ ? = 14.36

Simplify : $\sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} = ?$ $\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?$

1 $\frac{492}{7}$ $\frac{{492}}{7}$
2 $\frac{520}{3}$ $\frac{{520}}{3}$
3 $\frac{554}{7}$ $\frac{{554}}{7}$
4 $\frac{571}{5}$ $\frac{{571}}{5}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} \sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} \\ = \sqrt[3]{13 \times 13 \times 13 \times - 1} \times \sqrt{5 \times 5 \times 5 \times - 1} \div \sqrt[3]{\frac{27}{512}} \\ = (13 \times 5 \sqrt[3]{- 1 \times - 1}) \div \frac{3}{8} \\ = 13 \times 5 \times \frac{8}{3} \\ = \frac{520}{3} \end{aligned}

$\eqalign{ & \,\,\,\,\,\,\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, \cr & = \root 3 \of {13 \times 13 \times 13 \times - 1} \times \sqrt {5 \times 5 \times 5 \times - 1} \div \root 3 \of {\frac{{27}}{{512}}} \cr & = \left( {13 \times 5\root 3 \of { - 1 \times - 1} } \right) \div \frac{3}{8} \cr & = 13 \times 5 \times \frac{8}{3} \cr & = \frac{{520}}{3} \cr}$

If x + y = 2a, then the value of $\frac{a}{x - a} + \frac{a}{y - a} is = ?$ $\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$

12
20
3-1
41

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given, \\ x + y = 2 a \\ ∴ \frac{a}{x - a} + \frac{a}{y - a} \\ = \frac{a (y - a) + a (x - a)}{(x - a) (y - a)} \\ = \frac{a y - a^{2} + a x - a^{2}}{(x - a) (y - a)} \\ = \frac{a (x + y) - 2 a^{2}}{(x - a) (y - a)} \\ = \frac{a .2 a - 2 a^{2}}{(x - a) (y - a)} \\ = \frac{2 a^{2} - 2 a^{2}}{(x - a) (y - a)} \\ = 0 \end{aligned}

$\eqalign{ & {\text{Given, }} \cr & x + y = 2a \cr & \therefore \frac{a}{{x - a}} + \frac{a}{{y - a}} \cr & = \frac{{a\left( {y - a} \right) + a\left( {x - a} \right)}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{ay - {a^2} + ax - {a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{a\left( {x + y} \right) - 2{a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{a.2a - 2{a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = \frac{{2{a^2} - 2{a^2}}}{{\left( {x - a} \right)\left( {y - a} \right)}} \cr & = 0 \cr}$

${(64 - 38) \times 4} \div 3 = ?$ $\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 3 = ?$

14
21
38
42

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given, \\ {(64 - 38) \times 4} \div 3 \\ = \frac{26 \times 4}{13} \\ = 8 \end{aligned}

$\eqalign{ & {\text{Given}}, \cr & \left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 3 \cr & = \frac{{26 \times 4}}{{13}} \cr & = 8 \cr}$

Hello Guest

Simplification - 01

$\frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y}$ $\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$ On simplifying the given equations, which of the following equations will be obtained ?

$\frac{{(0.73)}^{3} + {(0.27)}^{3}}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} = ?$ $\frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} = ?$

03. 67 × 119 + 17 - 27 ÷ 259 = ?

04. If x + y + z = 0, then x³ + y³ + z³ + 3xyz is equal to = ?

05. Solve 14 × 627 ÷ √(1089) = (?)³ + 141

06. Solve 4376 + 3209 - 1784 + 97 = 3125 + ?

07. Solve : 128.43 + 30.21 + ? = 173

Simplify : $\sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} = ?$ $\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?$

If x + y = 2a, then the value of $\frac{a}{x - a} + \frac{a}{y - a} is = ?$ $\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$

${(64 - 38) \times 4} \div 3 = ?$ $\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 3 = ?$

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Hello Guest

Simplification - 01

01. (a−b)2−(a+b)2−4a = xy(a−b)2−(a+b)2−4a = xy\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} On simplifying the given equations, which of the following equations will be obtained ?

02. (0.73)3+(0.27)3(0.73)2+(0.27)2−0.73×0.27=?(0.73)3+(0.27)3(0.73)2+(0.27)2−0.73×0.27=?\frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} = ?

03. 67 × 119 + 17 - 27 ÷ 259 = ?

04. If x + y + z = 0, then x3 + y3 + z3 + 3xyz is equal to = ?

05. Solve 14 × 627 ÷ √(1089) = (?)3 + 141

06. Solve 4376 + 3209 - 1784 + 97 = 3125 + ?

07. Solve : 128.43 + 30.21 + ? = 173

08. Simplify : −2197−−−−−√3×−125−−−−√3÷27512−−−−√3=?−21973×−1253÷275123=?\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?

09. If x + y = 2a, then the value of ax−a+ay−ais = ?ax−a+ay−ais = ?\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}

10. {(64−38)×4}÷3=?{(64−38)×4}÷3=?\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 3 = ?

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$\frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y}$ $\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$ On simplifying the given equations, which of the following equations will be obtained ?

$\frac{{(0.73)}^{3} + {(0.27)}^{3}}{{(0.73)}^{2} + {(0.27)}^{2} - 0.73 \times 0.27} = ?$ $\frac{{{{\left( {0.73} \right)}^3} + {{\left( {0.27} \right)}^3}}}{{{{\left( {0.73} \right)}^2} + {{\left( {0.27} \right)}^2} - 0.73 \times 0.27}} = ?$

04. If x + y + z = 0, then x³ + y³ + z³ + 3xyz is equal to = ?

05. Solve 14 × 627 ÷ √(1089) = (?)³ + 141

Simplify : $\sqrt[3]{- 2197} \times \sqrt[3]{- 125} \div \sqrt[3]{\frac{27}{512}} = ?$ $\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?$

If x + y = 2a, then the value of $\frac{a}{x - a} + \frac{a}{y - a} is = ?$ $\frac{a}{{x - a}} + \frac{a}{{y - a}}\,{\text{is = ?}}$

${(64 - 38) \times 4} \div 3 = ?$ $\left\{ {\left( {64 - 38} \right) \times 4} \right\} \div 3 = ?$

NCERT
6 to 12