If $\int \frac{\mathrm{d} x}{\cos ^3 x \sqrt{2 \sin 2 x}}=(\tan x)^A+C(\tan x)^B+\mathrm{k}$ where k is a constant of integration, then $A+B+C$ equals

The maximum value of $\left(\cos \alpha_1\right) \cdot\left(\cos \alpha_2\right) \ldots .\left(\cos \alpha_n\right)$ under the constraints $0 \leq \alpha_1, \alpha_2, \ldots ., \alpha_n \leq \frac{\pi}{2}$ and $\left(\cot \alpha_1\right) \cdot\left(\cot \alpha_2\right) \ldots\left(\cot \alpha_n\right)=1$ is

If $\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3, y+3>0$ and $y(0)=2$, then $y(\log 2)$ is equal to

The assets of a person are 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 ₹$10,00,000$ and due to loss they reduce to ₹$ 10,000$ after 3 years, then the number of years required for the person to go bankrupt will be