Question Detail

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

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}

1. 5004 / 139 - 6

Answer: Option D

2. If a - b = 3 and \begin{aligned} a^2 + b^2 = 29 \end{aligned}, then find the value of ab

Answer: Option C

Explanation:

Remember the formula, if not then cram it :)
\begin{aligned} 2ab = (a^2 + b^2)- (a-b)^2 \end{aligned}
=> 2ab = 29 - 9 = 20
=> ab = 10

3. 3034 - (1002 / 20.04) = ?

2984
2983
2982
2981

Answer: Option A

4. What fraction of \begin{aligned} \frac{4}{7}\end{aligned} should be added to itself to become \begin{aligned} 1\frac{1}{14} \end{aligned}

\begin{aligned} \frac{7}{8} \end{aligned}
\begin{aligned} \frac{7}{9} \end{aligned}
\begin{aligned} \frac{7}{10} \end{aligned}
\begin{aligned} \frac{7}{11} \end{aligned}

Answer: Option A

Explanation:

\begin{aligned}
=> \frac{4}{7}x + \frac{4}{7} = \frac{15}{4}
\end{aligned}
\begin{aligned}
= \frac{4}{7}x = \frac{15}{4} - \frac{4}{7}
\end{aligned}
\begin{aligned}
= \frac{4}{7}x = \frac{7}{14}
\end{aligned}
\begin{aligned}
= x = \frac{1}{2}\times \frac{7}{4} = \frac{7}{8}
\end{aligned}