An electric charge $10^{-3} \ \mu C$ is placed at the origin $(0, 0)$ of an $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be......$V$.

Let $P = \{ (x, y) | x^2 + y^2 = 1, x, y \in R \}$. Then $P$ is

Reproducing new plants by cells instead of seeds is known as

$A$ rubber cube of side $5 ~cm$ has one face fixed,while a tangential force $1800 ~N$ is applied on its opposite face. If the modulus of rigidity of rubber is $2.4 \times 10^6 ~N/m^2$,then the lateral displacement of the strained face is . . . . . . (in $mm$)

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane,then the equation of the plane is

$A$ uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (Assume that the cube does not slide):