The formula for exponential population growth is

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column,and the temperature remains constant while surface tension is neglected,what is the depth of the lake (in $m$)?

The solution of the differential equation $\frac{dy}{dx} - 2y \tan 2x = e^x \sec 2x$ is

The radius of germanium $(Ge)$ nuclide is measured to be twice the radius of ${}_4^9Be$. The number of nucleons in $Ge$ are

The square of the difference of the slopes of the lines represented by the equation $x^2(\sec^2 \theta - \sin^2 \theta) - 2xy \tan \theta + y^2 \sin^2 \theta = 0$ is:

$A$ sphere of mass $m$ moving with velocity $v$ collides head-on with another sphere of the same mass which is at rest. The ratio of the final velocity of the second sphere to the initial velocity of the first sphere is ($e$ is the coefficient of restitution and the collision is inelastic).