The rate of reduction of a person's assets is proportional to the square root of the assets at that moment. If the assets at the beginning are $10000$ and they dwindle down to $5625$ in $2$ years, then in how many years will the person be bankrupt (in $years$)?

The latus rectum of the conic satisfying the differential equation $x dy + y dx = 0$ and passing through the point $(2, 8)$ is:

The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

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

The solution of the differential equation $\frac{dy}{dx} = \frac{a + bx}{c + dy}$ represents a family of circles centered at the origin if...

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is $290 \ K$ and the metal temperature drops from $370 \ K$ to $330 \ K$ in $10 \ \text{minutes}$,then the time required to drop the temperature up to $295 \ K$ is