On addition of $1 \, mL$ of $10 \% \, NaCl$ solution to $10 \, mL$ gold sol in the presence of $0.25 \, g$ of starch,the coagulation is just prevented. The gold number of starch is:

$A$ mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision,the first mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to its initial direction of motion. The speed of the second mass after collision is:

Four point positive charges of same magnitude $Q$ are placed at four corners of a rigid square frame of side length $L$ as shown in the figure. The plane of the frame is perpendicular to the $Z$-axis. If a negative point charge $-q$ is placed at a distance $z$ away from the centre along the axis $(z << L)$, then:

$A$ thin plano-convex lens of focal length $73.5 \text{ cm}$ has a circular aperture of diameter $8.4 \text{ cm}$. If the refractive index of the material of the lens is $\frac{5}{3}$, then the thickness of the lens is nearly

The $[Fe(CN)_6]^{3-}$ complex ion

If $\sqrt{9 x^2+6 x+1} < (2-x)$,then: