Question Detail

\begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}

Answer: Option B

Explanation:

Clue:

\begin{aligned}
(\sqrt{x} - \frac{1}{\sqrt{x}})^2 = x + \frac{1}{x} - 2 \
\end{aligned}
Now put the value of x to calculate the answer :)

1. \begin{aligned}
\frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ?
\end{aligned}

Answer: Option A

Explanation:

\begin{aligned}
= \frac{1}{\left( 1 + \frac{a^n}{a^m} \right)} +
\frac{1}{\left( 1 + \frac{a^m}{a^n} \right)} \\
= \frac{a^m}{(a^m+a^n)} + \frac{a^n}{(a^m+a^n)} \\
= \frac{(a^m+a^n)}{(a^m+a^n)} = 1
\end{aligned}

2. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}

Answer: Option B

Explanation:

Clue:

\begin{aligned}
(\sqrt{x} - \frac{1}{\sqrt{x}})^2 = x + \frac{1}{x} - 2 \
\end{aligned}
Now put the value of x to calculate the answer :)

3. Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}

1012
1024
1048
525

Answer: Option B

Explanation:

\begin{aligned}
= (256)^{\frac{5}{4}} = (4^4)^{\frac{5}{4}} = 4^5 = 1024
\end{aligned}

4. \begin{aligned}
\text{If }2x = \sqrt[3]{32}, \text{ then x is equal to}
\end{aligned}

\begin{aligned} \frac{5}{2} \end{aligned}
\begin{aligned} \frac{2}{5} \end{aligned}
\begin{aligned} \frac{3}{5} \end{aligned}
\begin{aligned} \frac{5}{3} \end{aligned}

Answer: Option D

Explanation:

\begin{aligned}
= (32)^{\frac{1}{3}}\\
= (2^5)^{\frac{1}{3}}\\
= 2^{\frac{5}{3}}\\
=> x= \frac{5}{3}
\end{aligned}

5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2

\end{aligned}

Answer: Option C

Question Detail

\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}

1. \begin{aligned} \frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ? \end{aligned}

2. \begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}

3. Value of \begin{aligned} (256)^{\frac{5}{4}} \end{aligned}

4. \begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}

5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}

\begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}

1. \begin{aligned}
\frac{1}{1+a^{(n-m)}} + \frac{1}{1+a^{(m-n)}} = ?
\end{aligned}

2. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}

4. \begin{aligned}
\text{If }2x = \sqrt[3]{32}, \text{ then x is equal to}
\end{aligned}

5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2

\end{aligned}