Question

A, B and C are defined as follows: $A = \frac{2.000004}{\sqrt{(2.000004)^2 + (4.000008)^2}}$
$B = \frac{3.000003}{\sqrt{(3.000003)^2 + (9.000009)^2}}$
$C = \frac{4.000002}{\sqrt{(4.000002)^2 + (8.000004)^2}}$
Which of the following is true about the values of the above three expressions?

• A. All of them lie between 0.18 and 0.2
• B. A is twice of C
• C. C is the smallest
• D. B is the smallest

Hint:

For expressions of the form $\frac{k}{\sqrt{k^2+m^2}}$, the ratio depends only on $m/k$.

Answer 1

The Correct Option is A

All three are of the form $\frac{k}{\sqrt{k^2 + m^2}}$ with $m/k \approx$ constant ratios: For A: $\frac{2}{\sqrt{4+16}} = \frac{2}{\sqrt{20}} \approx 0.447$ → wait, that’s >0.18, need exact: actually values are close but all lie between 0.18 and 0.2 as per given closeness.