The lines $\overline{\mathrm{r}}=\overline{\mathrm{a}}+\lambda(\overline{\mathrm{b}} \times \overline{\mathrm{c}})$ and $\overline{\mathrm{r}}=\overline{\mathrm{c}}+\lambda(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ will intersect if

$$ 3 \tan ^6 10^{\circ}-27 \tan ^4 10^{\circ}+33 \tan ^2 10^{\circ}= $$

The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ 10 lakhs and due to loss they reduce to ₹ 10000 after 3 years, then the number of years required for the person to be bankrupt will be

Two simple harmonic motions of angular frequency $300 \mathrm{rad} / \mathrm{s}$ and $3000 \mathrm{rad} / \mathrm{s}$ have same amplitude. The ratio of their maximum accelerations is