CAT 2006 | Question: 51

Question

If $x=-0.5$ then which of the following has the smallest value?

• A. $2^{\frac{1}{x}}$
• B. $\frac{1}{x}$
• C. $\frac{1}{x^2}$
• D. $2^x$
• E. $\frac{1}{\sqrt{-x}}$

Answer 1

1. $2^{\frac{1}{x}} = 2^{\frac{1}{-0.5}} = 0.25$

2. $\frac{1}{x} = \frac{1}{-0.5} = -2$

3. $\frac{1}{x^{2}} = \frac{1}{(-0.5)^{2}} = 4$

4. $2^{x} = 2^{-0.5}=.70$

5. $\frac{1}{(-x)^\frac{1}{2}} = \frac{1}{(0.5)^\frac{1}{2}}$ = 1.41

Hence (2) $\frac{1}{x}$ is the Answer.