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Question Detail
\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}
1. \begin{align}
\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?}
\end{align}
- 1.5
- 4.5
- 7.5
- 9.5
Answer: Option B
Explanation:
\begin{align}&\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}\\\\
&\Rightarrow \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{a}{b}\right)^{-(x-7)}\\\\
&\Rightarrow x - 2 = -(x - 7)\\\\
&\Rightarrow x - 2 = -x + 7\\\\
&\Rightarrow x-2 = -x + 7\\\\
&\Rightarrow 2x = 9\\\\
&\Rightarrow x = \dfrac{9}{2} = 4.5
\end{align}
2. \begin{aligned}
\text{if }6^m = 46656, \\\text{ What is the value of }6^{m-2}
\end{aligned}
- 7776
- 7782
- 1296
- 1290
Answer: Option C
Explanation:
\begin{aligned}
6^{m-2}\\ = \dfrac{6^m}{6^2}\\ = \dfrac{46656}{6^2}\\ = \dfrac{46656}{36} = 1296
\end{aligned}
3. Find the value of
\begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}
- 10
- 100
- 1000
- 10000
Answer: Option D
Explanation:
\begin{aligned}
= \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000
\end{aligned}
4. \begin{aligned}
x = 3 + 2\sqrt{2}, \text{ then the value of }\\
(\sqrt{x} - \frac{1}{\sqrt{x}})
\end{aligned}
- 1
- 2
- 3
- 4
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 :)
5. \begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2
\end{aligned}
- 25
- 28
- 36
- 44
Answer: Option C
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