$A$ point charge $q$ is placed at a distance $a/2$ directly above the centre of a square of side $a$. The electric flux through the square is

The equation of the radical axis of the pair of circles $7x^2+7y^2-7x+14y+18=0$ and $4x^2+4y^2-7x+8y+20=0$ is

Which of the following is an incorrect statement?

Consider the following statements about Langmuir isotherm.
$I.$ The free gas and adsorbed gas are in dynamic equilibrium.
$II.$ All adsorption sites are equivalent.
$III.$ The initially adsorbed layer can act as a substrate for further adsorption.
$IV.$ The ability of a molecule to get adsorbed at a given site is independent of the occupation of neighboring sites.
The correct statements are

On heating a liquid of coefficient of cubical expansion $\gamma$ in a container having coefficient of linear expansion $\gamma / 3$,the level of liquid in the container will

$A$ curve satisfying the initial condition,$y(1) = 0,$ satisfies the differential equation,$x \frac{dy}{dx} = y - x^2.$ The area bounded by the curve and the $x$-axis is