The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

How many $ATP$ molecules are released when one molecule of glucose is oxidized in our liver cells?

$A$ lens of power $+2 \text{ diopters}$ is placed in contact with a lens of power $-1 \text{ diopter}$. The combination will behave like:

$A$ solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. $A$ massless piston of area $a$ floats on the surface of the liquid,covering the entire cross-section of the cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid,the fractional decrement in the radius of the sphere $\left( \frac{dr}{r} \right)$ is

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$,the surface tension of water is $T$ and the atmospheric pressure is $P_0$. Consider a vertical section $ABCD$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

The minimum value of $(x-\alpha)(x-\beta)$ is