If $\frac{x^2}{(x^2 + a^2)(x^2 + b^2)} = K \left( \frac{a^2}{x^2 + a^2} - \frac{b^2}{x^2 + b^2} \right)$,then $K =$

Liquid $X$ is used in a bubble chamber to detect neutral mesons and gamma photons. Then,$X$ is

The path difference between the two waves $y_1 = a_1 \sin \left( \omega t - \frac{2\pi x}{\lambda} \right)$ and $y_2 = a_2 \cos \left( \omega t - \frac{2\pi x}{\lambda} + \phi \right)$ is

The limiting points of the co-axial system containing the two circles $x^2+y^2+2x-2y+2=0$ and $25(x^2+y^2)-10x-80y+65=0$ are

$A$ black body at a temperature of $1640\,K$ has the wavelength corresponding to maximum emission equal to $1.75\,\mu m$. Assuming the moon to be a perfectly black body,the temperature of the moon,if the wavelength corresponding to maximum emission is $14.35\,\mu m$,is.......$K$.

$A$ wheel of mass $m$ has charges $+q$ and $-q$ at diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a uniform vertical electric field $E$. Find the value of $E$.