The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:

The $V-Q$ graph is shown below. What does the area of $\Delta OAB$ represent in this graph?

The imperfect fungi which are decomposers of litter and help in mineral cycling belong to:

Find the value$(s)$ of $k$ such that the distance between the two parallel lines represented by $(x-2y)^2 + k(x-2y) = 0$ is $3$ units.

When one end of a capillary tube is dipped in water,the height of the water column is $h$. The upward force of $105 \text{ dyne}$ due to surface tension is balanced by the force due to the weight of the water column. What is the inner circumference of the capillary (in $\text{ cm}$)? (Surface tension of water $= 7 \times 10^{-2} \text{ N m}^{-1}$)

If $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$ and $x \neq y \neq z$,then $1+x y z$ is equal to