In the following structure,the double bonds are marked as $I, II, III$ and $IV$. Geometrical isomerism is not possible at site$(s)$:

When a wave travels in a medium,the particle displacements are given by $y = a \sin 2\pi (bt - cx)$ where $a, b,$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

Which of the following elements shows polymorphism?

For the stationary wave $y = 4 \sin \left( \frac{\pi x}{15} \right) \cos (96 \pi t)$,the distance between a node and the next antinode is

If $0 < y < 2^{1/3}$ and $x(y^3 - 1) = 1$,then $\frac{2}{x} + \frac{2}{3x^3} + \frac{2}{5x^5} + \dots$ is equal to:

Two vibrating tuning forks produce progressive waves given by $Y_1 = 4 \sin(500\pi t)$ and $Y_2 = 2 \sin(506\pi t)$. The number of beats produced per minute is: