Which of the following elements has the highest reaction rate with water?

$A$ circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

Assertion : In recombinant $DNA$ technology human genes are often transferred into bacteria (prokaryotes) or yeast (eukaryote).
Reason : Both bacteria and yeast multiply very fast to form huge population which expresses the desired gene.

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

If $l_1 = \lim_{x \rightarrow 2^{+}} (x + [x])$,$l_2 = \lim_{x \rightarrow 2^{-}} (2x - [x])$ and $l_3 = \lim_{x \rightarrow \pi / 2} \frac{\cos x}{x - \pi / 2}$,then:

On a rainy day,a small oil film on water shows brilliant colours. This is due to