The diameter of a cylinder is measured using Vernier calipers with no zero error. It is found that the zero of the Vernier scale lies between $5.10 \mathrm{cm}$ and $5.15 \mathrm{cm}$ of the main scale. The Vernier scale has $50$ divisions equivalent to $2.45 \mathrm{cm}$. The $24\mathrm{th}$ division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

There are two Vernier calipers both of which have $1 \mathrm{cm}$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $\left({\mathrm{C}}_1\right)$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $\left({\mathrm{C}}_2\right)$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $\mathrm{cm}$) by calipers ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$, respectively, are

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and image distance $v$, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45°$ with the $\mathrm{X}$-axis meets the experimental curve at $\mathrm{P}$. The coordinates of $\mathrm{P}$ will be