The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ is

$\int_\limits{\frac{-\pi}{4}}^{\frac{\pi}{4}}(\sin x)^{-4} \mathrm{~d} x$ has the value

The mean and variance of 7 observations are 8 and 16 respectively. If first five observations are $2,4,10,12,14$, then absolute difference of remaining two observations is

The projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{CD}}$, where $A \equiv(2,-3,0), B \equiv(1,-4,-2), C \equiv(4,6,8)$ and $\mathrm{D} \equiv(7,0,10)$ is