If the line $y=mx$ is one of the bisectors of $x^2+4xy-y^2=0$,then the value of $2m$ is:

What will be the angular width of the central maxima in Fraunhofer diffraction when light of wavelength $6000 \, \mathring{A}$ is used and the slit width is $12 \times 10^{-5} \, cm$? (in $rad$)

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to

The refractive index of the material of the prism for violet colour is $1.69$ and that for red is $1.65$. If the refractive index for mean colour is $1.66$,what is the dispersive power of the material of the prism?

$A$ beaker full of hot water is kept in a room. If it cools from $80\,^{\circ}C$ to $75\,^{\circ}C$ in $t_1$ minutes,from $75\,^{\circ}C$ to $70\,^{\circ}C$ in $t_2$ minutes,and from $70\,^{\circ}C$ to $65\,^{\circ}C$ in $t_3$ minutes,then:

If $\bar{a}, \bar{b}, \bar{c}$ are mutually perpendicular vectors having magnitudes $1, 2, 3$ respectively,then $[\bar{a}+\bar{b}+\bar{c} \quad \bar{b}-\bar{a} \quad \bar{c}] = $