√(0.04 x 0.4 x a) = 0.004 x 0.4 x √b, then a/b is (a) 16 x 10^-3 (b) 16 x 10^-4 (c) 16 x 10^-5 (d) 16 x 10^-2

Question

If \(\sqrt {0.04 \times 0.4\times a}\) = 0.004 x 0.4 x \(\sqrt b\) ,then \(\frac{a}{b}\) is

(a) 16 × 10^–3

(b) 16 × 10^–4

(c) 16 × 10^–5

(d) 16 × 10^–2

Answer 1

(c) 16 x 10^-5

Given exp.\(\Rightarrow\) \(\sqrt {0.016\times a}\) = 0.0016 x \(\sqrt b\)

\(\Rightarrow\) \(\sqrt {0.016}\times \sqrt a\) = 0.0016 x \(\sqrt b\) \(\Rightarrow\) \(\frac{\sqrt a}{\sqrt{b}}\) = \(\frac{0.0016}{\sqrt{0.016}} \)

\(\Rightarrow\) \(\frac{a}{b}\) = \(\frac{0.0016\times0.0016}{0.016}\) = 0.00016

= \(\frac{16}{100000}\) = 16 x 10^-5.