Simplify
\begin{aligned} 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{7}+\frac{1}{14}+\frac{1}{28} = ? \end{aligned}

Answer: Option D

Explanation:

b-[b-(a+b)-{b-(b-a+b)}+2a]
=b-[b-a-b-{b-(2b-a)}+2a]
=b-[-a-{b-2b+a}+2a]
=b-[-a-{-b+a}+2a]
=b-[-a+b-a+2a]
=b-[-2a+b+2a]
=b-b
=0

Answer: Option D

Explanation:

We know
\begin{aligned} 2ab = (a^2 + b^2) - (a - b)^2 \end{aligned}

\begin{aligned} 2pq = 29 - 9 = 20 \end{aligned}

\begin{aligned} =>pq = 10 \end{aligned}

Answer: Option C

Explanation:

\begin{aligned}
\frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} }\div 5.25
\end{aligned}

\begin{aligned}
= \frac{\frac{7}{2}\times {\frac{2}{5}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{15}{4}}}\div 5.25
\end{aligned}

\begin{aligned}
= \frac{\frac{21}{10}}
{\frac{7}{2} \times { \frac{4}{15}}}\div {\frac{525}{100}}
\end{aligned}

\begin{aligned}
= \frac{21}{10}\times{\frac{15}{14}}\times\frac{100}{525}

= \frac{6}{14}
= \frac{3}{7}
\end{aligned}

Answer: Option A

Answer: Option B

Explanation:

18800 / 470 / 20 = (18800 / 470) / 20 = 40 / 20 = 2