The perimeter of the triangle with vertices at $(1,0,0), (0,1,0)$ and $(0,0,1)$ is

If the volume of a sphere increases at the rate of $2 \pi \text{ cm}^3/\text{s}$, then the rate of increase of its radius (in $\text{cm/s}$), when the volume is $288 \pi \text{ cm}^3$, is

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force, will be in the ratio: (in $:1$)

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then the value of $\lambda$ is

$e^{\log (\cosh^{-1} 2)}$ is equal to :

In a potentiometer experiment,the balancing length with a cell is $240\,cm$. On shunting the cell with a resistance of $2\,\Omega$,the balancing length becomes $120\,cm$. The internal resistance of the cell is ................... $\Omega$.