What is the figure given below showing in particular?

The area (in square units) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

We have two spheres,one of which is hollow and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by

$ \cos^4 \frac{\pi}{8} + \cos^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \cos^4 \frac{7\pi}{8} = $

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is

$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16$ days. Its half-life is ........ $days$.