If a body cools from $80^{\circ} C$ to $60^{\circ} C$ in a room temperature of $30^{\circ} C$ in $30 \text{ min}$,then the temperature of the body after one hour is (in $^{\circ} C$)

The normal to a curve at $P(x, y)$ meets the $x$-axis at $G$. If the distance of $G$ from the origin is twice the abscissa of $P$, then the curve is

Let $f$ be a non-negative function defined in $[0, \pi / 2]$, $f^{\prime}$ exists and is continuous for all $x$, and $\int_0^x \sqrt{1-\left(f^{\prime}(t)\right)^2} dt = \int_0^x f(t) dt$ with $f(0) = 0$. Then

The number of solutions of $y' = \frac{y + 1}{x - 1}, y(1) = 2$ is

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

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