Let for $$x \in \mathbb{R}$$,

$$ f(x)=\frac{x+|x|}{2} \text { and } g(x)=\left\{\begin{array}{cc} x, & x<0 \\ x^{2}, & x \geq 0 \end{array}\right. \text {. } $$

Then area bounded by the curve $$y=(f \circ g)(x)$$ and the lines $$y=0,2 y-x=15$$ is equal to __________.

If the variance of the frequency distribution

is 3, then $$\alpha$$ is equal to _____________.

The initial speed of a projectile fired from ground is $$\mathrm{u}$$. At the highest point during its motion, the speed of projectile is $$\frac{\sqrt{3}}{2} u$$. The time of flight of the projectile is :

A bar magnet with a magnetic moment $$5.0 \mathrm{Am}^{2}$$ is placed in parallel position relative to a magnetic field of $$0.4 \mathrm{~T}$$. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _____________.