If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to

The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is

If $A$ and $B$ are square matrices of the same order and $|B| \neq 0$,then $(B^{-1}AB)^5 =$

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is . . . . . . .

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

$A$ charge $+Q$ is moving upwards vertically. It enters a magnetic field directed to the north. The force on the charge will be towards