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 differential equation $y\frac{dy}{dx} + x = a$ ($a$ is any constant) represents:

Radium decomposes at a rate proportional to the amount present at any time. If $P \%$ of the amount disappears in one year,then the amount of radium left after $2$ years is

The slope of the tangent at any point $(x, y)$ on the curve is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point $(\sqrt{2}, e)$ is $ax + by = 1$,then $\frac{b}{a} =$

$A$ body at an unknown temperature is placed in a room which is held at a constant temperature of $30^{\circ} F$. If after $10 \text{ minutes}$ the temperature of the body is $0^{\circ} F$ and after $20 \text{ minutes}$ the temperature of the body is $15^{\circ} F$,then the expression for the temperature of the body at any time $t$ is

Suppose a continuous function $f:(0, \infty) \rightarrow R$ satisfies $f(x)=2 \int_0^x t f(t) d t+1, \forall x \geq 0$. Then,$f(1)$ equals