Simplify : \(\frac{{ - \frac{1}{2} - \frac{2}{3} + \frac{4}{...

Simplify : $\frac{{ - \frac{1}{2} - \frac{2}{3} + \frac{4}{5} - \frac{1}{3} + \frac{1}{5} + \frac{3}{4}}}{{\frac{1}{2} + \frac{2}{3} - \frac{4}{3} + \frac{1}{3} - \frac{1}{5} - \frac{4}{5}}}$

Course Name: Quantitative Aptitude

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-3/10
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-10/3
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1 Discuss	If $x = \sqrt 3 { \text{ + }}\sqrt 2 { \text{,}}$ then the value of ${x^3} - \frac{1}{{{x^3}}}$ is? 1] $10\sqrt 2$ 2] $14\sqrt 2$ 3] $22\sqrt 2$ 4] $8\sqrt 2$ Solution
10 Discuss	The expression $\frac{1}{{x - 1}} - \frac{1}{{x + 1}} - \frac{2}{{{x^2} + 1}} - \frac{4}{{{x^4} + 1}}$ is equal to = ? 1] $\frac{8}{{{x^8} + 1}}$ 2] $\frac{8}{{{x^8} - 1}}$ 3] $\frac{8}{{{x^7} - 1}}$ 4] $\frac{8}{{{x^7} + 1}}$ Solution
2 Discuss	If $\left( {x + \frac{1}{x}} \right) = 3,$ then $\left( {{x^2} + \frac{1}{{{x^2}}}} \right)$ is = ? 1] 10/3 2] 82/9 3] 7 4] 11 Solution
3 Discuss	(755.0% of 523.0) / 777.0 = x 1] 6 2] 4 3] 3 4] 5 Solution
4 Discuss	Assume that $\sqrt {13}$ = 3.605(approximately) and $\sqrt {130}$ = 11.40(approximately) Find the value of: $\sqrt {1.3}$ + $\sqrt {1300}$ + $\sqrt {0.013}$ 1] 36.164 2] 36.304 3] 37.304 4] 37.164 Solution
5 Discuss	The square root of $\frac{{0.342 \times 0.684}}{{0.000342 \times 0.000171}} = ?$ 1] 250 2] 2500 3] 2000 4] 4000 Solution
6 Discuss	$\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{469 \times 174}}$ = ? 1] 2 2] 4 3] 295 4] 643 Solution
7 Discuss	One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ? 1] Rs. 30,000 2] Rs. 50,000 3] Rs. 60,000 4] Rs. 90,000 5] None of these Solution
8 Discuss	Simplification of $\frac{{{{\left( {3.4567} \right)}^2} - {{\left( {3.4533} \right)}^2}}}{{0.0034}} = ?$ 1] 6.91 2] 7 3] 6.81 4] 7.1 Solution
9 Discuss	$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{{14}} + \frac{1}{{28}}$ is equal to = ? 1] 2 2] 2.5 3] 3 4] 3.5 Solution
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