An oscillator circuit consists of an inductance of $0.5\,mH$ and a capacitor of $20\,\mu F$. The resonant frequency of the circuit is nearly.....$Hz$

If $x > 0$ and $x^y = e^{x-y}$,then $\frac{dy}{dx}$ is equal to

The distance between the two parallel lines represented by $8x^2 - 24xy + 18y^2 - 6x + 9y - 5 = 0$ is

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \, g/cm^3$) standing initially $20 \, cm$ from the bottom in each arm. An immiscible liquid of density $4.0 \, g/cm^3$ is added to one arm until a layer $5 \, cm$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle,then the radius of the circle is

What are the approximate weight and diameter of $Rafflesia$ $arnoldii$?