Identify the major product of the following reaction:

Three masses $700\,g, 500\,g$ and $400\,g$ are suspended at the end of a spring as shown and are in equilibrium. When the $700\,g$ mass is removed,the system oscillates with a period of $3\,s$. When the $500\,g$ mass is also removed,it will oscillate with a period of .... $s$.

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of the light which does not get transmitted is

If $\int \frac{7x^8+8x^7}{(1+x+x^8)^2} dx = f(x) + c$,then $f(x)$ is equal to

Two particles of masses $m_1$ and $m_2$ are separated by a distance $d$. The shift in the centre of mass when the two particles are interchanged is:

Celestite is a mineral of which of the following?