If one of the lines $2x^2 - xy + by^2 = 0$ passes through the point $(-4, -2)$,then $b^2 =$

If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is:

In a Young's double slit experiment,$12$ fringes are observed to be formed in a certain segment of the screen,when light of wavelength $600 \, nm$ is used. If the wavelength of light is changed to $400 \, nm$,the number of fringes observed in the same segment of the screen will be

The sensitivity of a galvanometer is $60 \text{ div/A}$. When a shunt is used,its sensitivity becomes $10 \text{ div/A}$. If the resistance of the galvanometer is $20 \ \Omega$,then the value of the shunt used is: (in $Omega$)

If $1^{\circ} = \alpha$ radians,then the approximate value of $\cos(60^{\circ} 1^{\prime})$ is

An integrating factor of the differential equation $(1-x^2) \frac{dy}{dx} + xy = \frac{x^4}{(1+x^5)} (\sqrt{1-x^2})^3$ is