The numerator of a fraction is less than its denominator by 2. If we subtract 2 from the numerator and add 2 to the denominator, then the new fraction is \( \frac{1}{3} \). What is the original fraction?
\( \frac{1}{3} \)
\( \frac{3}{7} \)
\( \frac{5}{9} \)
\( \frac{5}{7} \)
If a ⊕ b = a - b + \(\frac{1}{\sqrt{ab}}\)+ \(\sqrt{\frac{a}{b}}\), then 0.9 ⊕ 0.1 = ?
\( \frac{30}{212} \)
\( \frac{214}{30} \)
\( \frac{212}{30} \)
\( \frac{30}{214} \)
Angles A, B and C of a triangle are in arithmetic progression. M is a point on BC such that AM is perpendicular to BC. What is\( \frac{BM}{AM} \)?
\( \frac{1}{2} \)
\( \frac{3}{3} \)
\( \frac{1}{3} \)
\( \frac{1}{4} \)