Question
Which of the following is equivalent to \(\sqrt{16a^{16}}\) ?
- \(4a^4\)
- \(4a^8\)
- \(8a^4\)
- \(8a^8\)
Answer/Explanation
Ans: B
Question
\(\sqrt{14-2x}\)= \(x\)-7
What value of \(x\) satisfies the given equation?
Answer/Explanation
Ans: 7
Question
Which expression is equivalent to \(g\)4/5 \(h\)2/5 , where \(g\) and \(h\) are positive?
- \(\sqrt[4]{g^{5}h^{10}}\)
- \(\sqrt[5]{g^{4}h^{2}}\)
- \(\frac{1}{\sqrt[4]{g^{5}h^{10}}}\)
- \(\frac{1}{\sqrt[5]{g^{4}h^{2}}}\)
Answer/Explanation
Ans: B
Question
\(\left ( \sqrt{x^3} \right )^a\), where \(x \geq 0\)
In the given expression, \(a\) is a constant. the expression is equivalent to x6 , where \(x \geq 0\). What is the value of \(a\)?
Answer/Explanation
Ans: 4
Question
\(L=S\sqrt{1-\frac{v^{2}}{c^{2}}}\)
When the speed of an object approaches the speed of light, its length as seen by an observer changes. When the object is stationary relative to an observer, its length is \(S\), and when the same object is moving at speed \(v\) relative to the observer, its length is \(L\). The formula above expresses \(L\) in terms of \(S\), \(v\), and \(c\), the speed of light. Which of the following gives the speed of the object in terms of the other quantities?
- \(v=c\sqrt{1-\frac{L^{2}}{S^{2}}}\)
- \(v=c\sqrt{1+\frac{L^{2}}{S^{2}}}\)
- \(v=c^{2}\left ( {1-\frac{L^{2}}{S^{2}}} \right )\)
- \(v=c^{2}\left ( {1+\frac{L^{2}}{S^{2}}} \right )\)
Answer/Explanation
Ans: A