Question Detail

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

1. \begin{aligned} 3034 -(1002 \div 20.04) = ? \end{aligned}

1964
1984
2964
2984

Answer: Option D

Explanation:

\begin{aligned}
= 3034 -( \frac{1002}{2004} \times 100)
\end{aligned}
\begin{aligned}
= 3034 - 50 = 2984
\end{aligned}

2. \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}

3. Value of \begin{aligned} 2^5 \times 9^2 \end{aligned} has been written as 2596, what is the difference between actual value.

Answer: Option D

4. \begin{aligned}
(3\frac{1}{4}\div \{1\frac{1}{4} - \frac{1}{2}(2\frac{1}{2} - \overline {\frac{1}{4} - \frac{1}{6}} ) \} )
\end{aligned}

Answer: Option A

Explanation:

Tip:
As you can see, there is bar over
\begin{aligned}
\overline{\frac{1}{4}-\frac{1}{6}}
\end{aligned}
So their sign will be changed from - to + as
\begin{aligned}
\frac{1}{4}+\frac{1}{6}
\end{aligned}

5. In a class free notebooks were distributed among all the children. Each child got notebooks which were one-eighth of the number of children. If number of children been half, then each child would have recieved 16 notebooks in total. Find the total number of books distributed.

Answer: Option B

Explanation:

Let suppose total number of students in class are X.
Then from the question we can conclude it that,
\begin{aligned}
X*\frac{1}{8}X = \frac{X}{2}*16 \\
=> X = 64\\
\text{Total notebooks,} \\
= \frac{1}{8}X^2 \\
= \left( \frac{1}{8} * 64 * 64 \right) \\
= 512
\end{aligned}

Question Detail

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

1. \begin{aligned} 3034 -(1002 \div 20.04) = ? \end{aligned}

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

3. Value of \begin{aligned} 2^5 \times 9^2 \end{aligned} has been written as 2596, what is the difference between actual value.

4. \begin{aligned} (3\frac{1}{4}\div \{1\frac{1}{4} - \frac{1}{2}(2\frac{1}{2} - \overline {\frac{1}{4} - \frac{1}{6}} ) \} ) \end{aligned}

5. In a class free notebooks were distributed among all the children. Each child got notebooks which were one-eighth of the number of children. If number of children been half, then each child would have recieved 16 notebooks in total. Find the total number of books distributed.

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

4. \begin{aligned}
(3\frac{1}{4}\div \{1\frac{1}{4} - \frac{1}{2}(2\frac{1}{2} - \overline {\frac{1}{4} - \frac{1}{6}} ) \} )
\end{aligned}