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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. 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}

2. In a group of ducks and buffaloes, the total number of legs are 24 more than twice the number of heads. Find the total number of buffaloes.

  • 8
  • 10
  • 12
  • 14

Answer: Option C

Explanation:

Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24

=> 2x = 24 => x = 12

3. (3080 + 6160) / 28

  • 380
  • 350
  • 330
  • 310

Answer: Option C

Explanation:

As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9240)/28 = 330

4. 100 + 50 * 2 = ?

  • 200
  • 150
  • 100
  • 300

Answer: Option A

Explanation:

After applying BOMAS rule,
First Multiplication will be done then addition
So it will be 100 + 100 = 200

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

  • 7
  • 8.5
  • 10
  • 12

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

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