$100 \ mL$ of $0.6 \ M$ acetic acid is shaken with $2 \ g$ of activated charcoal. After adsorption,the final concentration of the solution becomes $0.5 \ M$. The amount of acetic acid adsorbed per gram of carbon is .......... $g$.

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream, the value of $x$ is

Identify the correct gland on the basis of the following characteristics:
$(I)$ It is located on the dorsal side of the forebrain.
$(II)$ It plays a very important role in the regulation of the $24$-hour rhythm of our body.
$(III)$ It helps in maintaining the body temperature.
$(IV)$ Its hormone influences metabolism as well as defense capability.

The eccentricity of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of the light which does not get transmitted is