A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90 \mathrm{s}, 91 \mathrm{s}, 92 \mathrm{s}$ and $95 \mathrm{s}.$ If the minimum division in the measuring clock is $1\mathrm{s},$ then the reported mean time should be,

A point particle of mass $m$ moves along the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction between the particle and the rough track equals $\mu .$ The particle is released from rest from the point $P$ and it comes to rest at a point $R.$ The energies lost by the ball over the parts $PQ$ and $QR$ of the track are equal to each other and no energy is lost when particle changes direction from $PQ$ to $QR.$ The values of the coefficient of friction $\mu$ and the distance $x\left(=QR\right)$ are respectively close to,

A roller is made by joining together two corners at their vertices $O.$ It is kept on two rails $AB$ and $CD$ which are placed symmetrically (see the figure), with its axis perpendicular to $CD$ and its centre $O$ at the centre of the line joining $AB$ and $CD$ (see the figure). It is given a light path so that it starts rolling with its centre $O$ moving parallel to $CD$ in the direction shown. As it moves, the roller will tend to

$n$ moles of an ideal gas undergoes a process $A$ and $B$ as shown in the figure. The maximum temperature of the gas during the process will be,