The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is given by

In what ratio does the $y-$axis divide the line segment joining the points $(-3, -4)$ and $(1, 2)$?

If $A$ is a square matrix such that $A(\operatorname{adj} A) = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,then $\operatorname{det}(\operatorname{adj} A)$ is equal to

The energy band diagrams for three semiconductor samples of silicon are as shown. We can then assert that

Give the number of electrons in the species $H_{2}^{+}$,$H_{2}$,and $O_{2}^{+}$.

Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):
| List-$I$ (Fundamental forces in nature) | List-$II$ (Relative strength) |
| :--- | :--- |
| $(A)$ Strong nuclear force | $(e)$ $10^{-2}$ |
| $(B)$ Weak nuclear force | $(f)$ $1$ |
| $(C)$ Electromagnetic force | $(g)$ $10^{10}$ |
| $(D)$ Gravitational force | $(h)$ $10^{-13}$ |
| | $(i)$ $10^{-39}$ |
The correct match is: