If $x^y=y^x$, then $x(x-y \log x) \frac{d y}{d x}$ is equal to :

Water is flowing with a velocity of $2\,m/s$ in a horizontal pipe where the cross-sectional area is $2 \times 10^{-2}\, m^2$ at a pressure of $4 \times 10^4\, Pa$. The pressure at a cross-section of area $0.01\, m^2$ in $Pa$ will be:

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

'Himgiri' developed by hybridization and selection for disease resistance against rust pathogens is a variety of

Inbreeding is carried out in animal husbandry because it

The decay rate for a certain mass of a radioactive substance measured at different times varies with time as shown in the figure. The count rate at $t = 8 \, hr$ will be: