Neet 2025 PYQ

Consider a water tank as shown in the figure. It has one wall at $x=L$ and is very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes an angle ${\theta }_0$ (${\theta }_0\ll 1$) with the $x$ -axis at $x=L$. If $y(x)$ is the height of the surface, then the equation for $y(x)$ is:(Take $\theta (x)\approx \sin \theta (x)\approx \tan \theta (x)=\frac{dy}{dx}$ and $g$ as acceleration due to gravity)

A microscope has an objective of focal length $2\text{cm}$, eyepiece of focal length $4\text{cm}$ and the tube length of $40\text{cm}$. If the distance of distinct vision of eye is $25\text{cm}$, the magnification in the microscope is:

An electron (mass $9\times 10^{-31}\text{kg}$ and charge $1.6\times 10^{-19}\text{C}$) moving with speed $c/100$ ($c$ = speed of light) is injected into a magnetic field $\vec{B}$ of magnitude $9\times 10^{-4}\text{T}$ perpendicular to its direction of motion. We wish to apply a uniform electric field $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then (speed of light $c=3\times 10^8{\text{ms}}^{-1}$):

There are two inclined surfaces of equal length ($L$) and same angle of inclination $45^{\circ }$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (${\mu }_k$) between the object and the rough surface is close to:

The kinetic energies of two similar cars A and B are $100\text{J}$ and $225\text{J}$ respectively. On applying breaks, car A stops after $1000\text{m}$ and car B stops after $1500\text{m}$. If $F_A$ and $F_B$ are the forces applied by the breaks on cars A and B, respectively, then the ratio $F_A/F_B$ is: