The number of distinct real roots of the equation $$|x||x+2|-5|x+1|-1=0$$ is __________.

A body of mass $$50 \mathrm{~kg}$$ is lifted to a height of $$20 \mathrm{~m}$$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :

If $$\mathrm{G}$$ be the gravitational constant and $$\mathrm{u}$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{\mathrm{uG}}$$ :

An alternating voltage of amplitude $$40 \mathrm{~V}$$ and frequency $$4 \mathrm{~kHz}$$ is applied directly across the capacitor of $$12 \mu \mathrm{F}$$. The maximum displacement current between the plates of the capacitor is nearly :