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If p - q = 3 and
\begin{aligned} p^2 + q^2 = 29 \end{aligned}, find the value of pq.

  • 7
  • 8
  • 9
  • 10

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}

Similar Questions :

1. 7500 + (1250 / 50)

  • 7500
  • 7525
  • 7550
  • 8000

Answer: Option B

Explanation:

As per BODMAS rule first we will solve the terms in the bracket then other.
= 7500 + (25) = 7525

2. Simplify
(31/10) * (3/10) + (7/5) / 20

  • 0
  • 1
  • 10
  • 100

Answer: Option B

Explanation:

= (31/10) * (3/10) + (7/5) / 20
= (3.1) * (.3) + (1.4) / 20
= 0.93 + 0.07
= 1

3. Simplify
\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{3}{5} \end{aligned}
  • \begin{aligned} \frac{3}{6} \end{aligned}
  • \begin{aligned} \frac{3}{7} \end{aligned}
  • \begin{aligned} \frac{3}{8} \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}

4. Value of
\begin{aligned}
\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}

\end{aligned}

  • \begin{aligned} \frac{6}{19} \end{aligned}
  • \begin{aligned} \frac{7}{19} \end{aligned}
  • \begin{aligned} \frac{8}{19} \end{aligned}
  • \begin{aligned} \frac{9}{19} \end{aligned}

Answer: Option C

Explanation:

\begin{aligned}
= \frac{1}{2+\frac{1}{2+\frac{1}{\frac{3}{2}}}}
\end{aligned}
\begin{aligned}
= \frac{1}{2+\frac{1}{2+\frac{2}{3}}}
\end{aligned}

\begin{aligned}
= \frac{1}{2+\frac{1}{\frac{8}{3}}}
\end{aligned}

\begin{aligned}
= \frac{1}{2+\frac{3}{8}}
\end{aligned}

\begin{aligned}
= \frac{1}{\frac{19}{8}}
\end{aligned}

\begin{aligned}
= \frac{8}{19}
\end{aligned}

5. \begin{aligned}
\frac{4+4 \times 18 -6 - 8}{123 \times 6 - 146 \times 5 }
\end{aligned}

  • 7.50
  • 7.75
  • 8
  • 8.05

Answer: Option B

Explanation:

\begin{aligned}
\frac{4+72-6-8}{738-730}
\end{aligned}
\begin{aligned}
= \frac{76-14}{8}
\end{aligned}
\begin{aligned}
= \frac{62}{8} = 7.75
\end{aligned}

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