If a body cools from $80^{\circ} C$ to $50^{\circ} C$ in a room at a temperature of $25^{\circ} C$ in $30$ minutes,then the temperature of the body after $1$ hour is: (in $^{\circ} C$)

The rate at which the population of a city increases varies as the population. In a period of $20$ years,the population increased from $4$ lakhs to $6$ lakhs. In another $20$ years,the population will be (in $lakhs$)

$A$ 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

The differential equation of displacement of all $Simple \ Harmonic \ Motions$ of given period $T = 2\pi / n$ is:

If $y = At^2 + \frac{B}{t}$ ($A, B$ are parameters) is the general solution of the differential equation $f(t) y''(t) + g(t) y'(t) + h(t) y = 0$,then $2 f(t) + t^2 h(t) =$

If the tangent at a point $P(x, y)$ of a curve is perpendicular to the line that joins the origin with the point $P$,then the curve is