If the population grows at the rate of $$8 \%$$ per year, then the time taken for the population to be doubled is

(Given $$\log 2=0.6912$$)

If the lines respresented by $$a x^2-b x y-y^2=0$$ make angle $$\alpha$$ and $$\beta$$ with the positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$

If the probability distribution function of a random variable X is given as

Then F(0) is equal to

The particular solution of the differential equation $$ \frac{d y}{d x}=\frac{x+y+1}{x+y-1} $$ when $$ \mathrm{x}=\frac{2}{3} $$ and $$ y=\frac{1}{3} $$ is