Neet 2025 PYQ

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of $60\text{km/h}$ in the direction X to Y notices that a bus goes past her every $30\text{minutes}$ in the direction of her motion, and every $10\text{minutes}$ in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

A uniform rod of mass $20\text{kg}$ and length $5\text{m}$ leans against a smooth vertical wall making an angle of $60^{\circ }$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $g=10{\text{m/s}}^2$):

In an oscillating spring-mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega (t)$ and average amplitude $A(t)$ of the system change with time $t$. Which one of the following options schematically depicts these changes correctly?

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius $r$ changes from $R$ to $0$ (zero) in time $T$. If the speed $v(r)$ of gas coming out of the balloon depends on $r$ as $r^{\alpha }$ and $T\propto S^a{A}^{\beta }{\rho }^{\gamma }{R}^{\delta }$ then:

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its $10$ Vernier Scale Divisions (V.S.D.) are equal to its $9$ Main Scale Divisions (M.S.D.). The least division in the M.S. is $0.1\text{cm}$ and the zero of V.S. is at $x=0.1\text{cm}$ when the jaws of Vernier callipers are closed.
If the main scale reading for the diameter is $M=5\text{cm}$ and the number of coinciding vernier division is $8$, the measured diameter after zero error correction, is: