The equation of a pair of lines is given by a second-degree homogeneous equation. If one of them is perpendicular to the line $x+2y+7=0$ and the other line is parallel to the line $3x+4y+5=0$,then the equation of that pair of lines is:

The intensity of radiation emitted by the Sun has its maximum value at a wavelength of $510 \ nm$ and that emitted by the North Star has the maximum value at $350 \ nm$. If these stars behave like black bodies,then the ratio of the surface temperature of the Sun and the North Star is

Two identical condensers $M$ and $N$ are connected in series with a battery. The space between the plates of $M$ is completely filled with a dielectric medium of dielectric constant $8$,and a copper plate of thickness $d/2$ is introduced between the plates of $N$ ($d$ is the distance between the plates). Then the potential differences across $M$ and $N$ are,respectively,in the ratio:

The impedance of a circuit,when a resistance $R$ and an inductor of inductance $L$ are connected in series in an $AC$ circuit of frequency $f$ is

Product $(A)$ is

Express $372$ as a product of its prime factors.