There exists a close association between the alga and the fungus within a lichen. The fungus

If $3 \hat{i}+3 \hat{j}+\sqrt{3} \hat{k}$, $\hat{i}+\hat{k}$, and $\sqrt{3} \hat{i}+\sqrt{3} \hat{j}+\lambda \hat{k}$ are coplanar, then $\lambda$ is equal to

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centered cubic,and face-centered cubic,then the ratio of radii of the spheres in these systems will be respectively:

Let $O$ be the origin and $A$ be a point on the curve $y^2=4x$. Then the locus of the midpoint of $OA$ is:

$A$ centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $140^{\circ}F$. What is the fall in temperature as registered by the Centigrade thermometer in $^{\circ}C$?

$A$ parallel plate capacitor with plate area $A$ and separation between the plates $d$ is charged by a constant current $I$. Consider a plane surface of area $A/2$ parallel to the plates and drawn between the plates. The displacement current through the area is