MCQ
The fractional value of 2.357 is:
- A$\frac{2355}{1001}$
- B$\frac{2379}{997}$
- C$\frac{2355}{999}$
- DNone of these.
Solution:
$2.\overline{357}=2.0+0.357+0.000357+0.000000357+\dots\infty$
$\Rightarrow2.\overline{357}=2+\Big[\frac{357}{10^3}+\frac{357}{10^6}+\frac{357}{10^9}+\dots\infty\Big]$
$\Rightarrow2.\overline{357}=2+\frac{\frac{357}{10^3}}{1-\frac{1}{10^3}}$
$\Rightarrow2.\overline{357}=2+\frac{357}{999}$
$\Rightarrow2.\overline{357}=\frac{2355}{999}$
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If $\text{f(x)}=\cos^2\text{x}+\sec^2\text{x},$ then:
$\text{f(x)}<1$
$\text{f(x)}=1$
$2<\text{f(x)}<1$
$\text{f(x)}\geq2$
[Hint: $\text{A.M}\geq\text{G.M.}$]