When a large bubble rises from the bottom of a lake to the surface,its radius doubles. If atmospheric pressure is equal to that of a column of water of height $H$,then the depth of the lake is:

In which of the following is the gametophytic phase reduced,short-lived,and limited to the formation of gametes?

If $g(x) = \int_0^x \cos^4 t \, dt$,then $g(x + \pi)$ equals

Box $A$ contains $2$ black and $3$ red balls, while Box $B$ contains $3$ black and $4$ red balls. Out of these two boxes, one is selected at random; and the probability of choosing Box $A$ is double that of Box $B$. If a red ball is drawn from the selected box, then the probability that it has come from Box $B$ is:

In which reaction will an increase in the volume of the container favour the formation of products?