The coiling of garden pea tendrils around a support is an example of which phenomenon?

$\int_0^2 \frac{2x-2}{2x-x^2} dx$ is equal to

$\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x$ is equal to

In the arrangement shown in the figure,the ends $P$ and $Q$ of an unstretchable string move downwards with a uniform speed $U$. Pulleys $A$ and $B$ are fixed. The mass $M$ moves upwards with a speed:

The $pH$ of $0.05 \ M$ acetic acid is $(K_a = 2 \times 10^{-5})$

Acetone on addition to methyl magnesium bromide forms a complex,which on decomposition with acid gives $X$ and $Mg(OH)Br$. Which one of the following is $X$?