When a system is taken from state $i$ to state $f$ along the path $iaf$,$Q = 50 \, cal$ and $W = 20 \, cal$. Along the path $ibf$,if $Q = 36 \, cal$,find the work $W$ for the path $ibf$ in $cal$.

Let $A$ and $B$ be subsets of a set $X$. Then

The tyre of a motor car contains air at $15^{\circ} C$. If the temperature increases to $35^{\circ} C$,the approximate percentage increase in pressure is (ignore the expansion of the tyre).

In the figure shown,the potential energy $(U)$ of a particle is plotted against its position $x$ from the origin. The particle at:

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^\circ$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is height,$x$ is horizontal distance,and $A$ and $B$ are constants. The ratio $A : B$ is $(g = 10 \ m/s^2)$.

Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$,while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)