A body at an unknown temperature is placed in a room which is held at a constant temperature of $$30^{\circ} \mathrm{F}$$. If after 10 minutes the temperature of the body is $$0^{\circ} \mathrm{F}$$ and after 20 minutes the temperature of the body is $$15^{\circ} \mathrm{F}$$, then the expression for the temperature of the body at any time $$\mathrm{t}$$ is

The equation of a line passing through $$(\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)$$ ) and making an angle $$(90+\propto)$$ with positive direction of $$\mathrm{X}$$-axis is

If $$|\bar{a}|=3,|\bar{b}|=4,|\bar{a}-\bar{b}|=5$$, then $$|\bar{a}+\bar{b}|=$$

$$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$$, then the values of $$x$$ are