$A$ wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet,hung in the open air,loses half its moisture during the first hour,then $90 \%$ of the moisture will be lost in ...... hours.

At any point $(x, y)$ on a curve,if the length of the subnormal is $(x - 1)$ and the curve passes through $(1, 2)$,then the curve is a conic. $A$ vertex of the curve is:

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is $1000$ at initial time $t = 0$. The number of bacteria is increased by $20\%$ in $2$ hours. If the population of bacteria is $2000$ after $\frac{k}{\log_{e}\left(\frac{6}{5}\right)}$ hours,then $\left(\frac{k}{\log_{e} 2}\right)^{2}$ is equal to

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is

$A$ curve is such that the area of the region bounded by the coordinate axes,the curve,and the ordinate of any point on it is equal to the cube of that ordinate. The curve represents:

Let $S$ be the set of real numbers $p$ such that there is no non-zero continuous function $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying $\int_0^x f(t) dt = p f(x)$ for all $x \in \mathbb{R}$. Then,$S$ is