$A$ pendulum suspended from the ceiling of a train oscillates with a time period $2\,s$,when the train is accelerating at $10\,m/s^2$. What will be its time period when the train retards at $10\,m/s^2$?

The symbiotic association between algae and fungi is known as -

If $\overrightarrow{a}=-\hat{i}+\hat{j}+2 \hat{k}$,$\overrightarrow{b}=2 \hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{c}=-2 \hat{i}+\hat{j}+3 \hat{k}$,then the angle between $2 \overrightarrow{a}-\overrightarrow{c}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

The value of $\frac{15}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}}$ is

Which of the following statements are correct?
$(i)$ In prokaryotic cells,a special membranous structure formed by the extension of the plasma membrane into the cell is known as polysome.
$(ii)$ The smooth endoplasmic reticulum is the major site for synthesis of glycoproteins.
$(iii)$ $RuBisCO$ is the most abundant protein in the whole biosphere.
$(iv)$ Mitochondria,chloroplasts and peroxisomes are not considered as part of endomembrane system.
Of the above statements:

For a given material, the Young's modulus is $2.4$ times that of the modulus of rigidity. Its Poisson's ratio is