The value of $\lim _{x \rightarrow 0}\left[\frac{\cos 2 x-\cos 4 x}{x^{2}}\right]$ is ___________.
Two fair six-sided dice are thrown. The probability of getting $12$ as the product of the numbers on the dice (rounded off to two decimal places) is __________.
E. coli is cultivated in a chemostat operated at a dilution rate of $0.2 h^{-1}$. The values of biomass yield due to oxygen consumption and the steady state biomass conce...
E. coli cultivated at $298 \mathrm{~K}$ uptakes an uncharged compound (A) by passive diffusion. The intracellular and extracellular concentrations of $\mathrm{A}$ are $0...
If there are three unrooted trees for four protein sequences, the number of rooted trees for the same number of sequences is _______________.
DNA sample collected from an unidentified bacterial species $(Y)$ contains $13 \%$ of adenine. The $G+C$ content (in percentage) of $Y$ is ____________.
Two straight lines pass through the origin $(x_{0}, y_{0}) = (0, 0)$. One of them passes through the point $(x_{1}, y_{1}) = (1, 3)$ and the other passes through the poin...