An elevator weighing $6000\, kg$ is pulled upward by a cable with an acceleration of $5\, m/s^2$. Taking $g$ to be $10\, m/s^2$,then the tension in the cable is ........... $N$.

Which of the following is the most important cause for the extinction of animals and plants?

$A$ gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $(C_p/C_v)$ of the mixture is

Two concentric hollow spherical shells have radii $r$ and $R$ $(R \gg r)$. $A$ charge $Q$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

$A$ tension of $20 ~N$ is applied to a copper wire of cross-sectional area $0.01 ~cm^2$. The Young's modulus of copper is $1.1 \times 10^{11} ~N/m^2$ and the Poisson's ratio is $0.32$. The decrease in the cross-sectional area of the wire is:

The maximum value of $\left(\frac{1}{x}\right)^{x}$ is