The eccentricity of the ellipse $9x^2 + 5y^2 - 18x - 20y - 16 = 0$ is:

If $A+B=C$,then the value of $\cos^2 A + \cos^2 B + \cos^2 C - 2 \cos A \cos B \cos C$ is equal to

The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$,where $\phi$ is in webers,$t$ is time in seconds and $\phi_0$ is a constant,the output voltage across the secondary coil is.....$volts$.

With a resistance of ' X ' in the left gap and a resistance of $9 \Omega$ in the right gap of meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance $3 \Omega$ resistance be connected to obtained the balance at 50 cm from the left end?

The wavelengths of two sound notes in air are $\frac{40}{195} ~m$ and $\frac{40}{193} ~m$. Each note produces $9$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

$A$ parallel plate capacitor with oil (dielectric constant $K = 2$) between the plates has capacitance $C$. If the oil is removed,the capacitance of the capacitor becomes: