$XOZ$-plane divides the line segment joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio: (in $: 7$)

In the Fraunhofer diffraction experiment,$L$ is the distance between the screen and the obstacle,$b$ is the size of the obstacle,and $\lambda$ is the wavelength of the incident light. The general condition for the applicability of Fraunhofer diffraction is:

The diagram represents Miller's experiment. Choose the correct combination of labelling.

For a reaction,$A + B^{2+} \rightarrow B + A^{2+}$; $E^{\circ} = 0.2955 \ V$. Hence,the equilibrium constant of the reaction at $25^{\circ}C$ is:

If $\overrightarrow{a}=\hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}-3 \hat{j}+\hat{k}$ and the orthogonal projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is $\frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$, then $\lambda$ is equal to

Two steel wires of same length $L$ but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. $A$ force $F$ stretches the combination by $10 \ mm$. How far does the midpoint $A$ move in $mm$?